Caroline Word Graph or CWG


Updated On:  Monday, April 18, 2011.

Introduction | | The CWG Structure | | How To Build A CWG | | C & Java Implementation | | Traditional DAWG Documentation | | Dense Boggle Board Solution - Full Disclosure | | Contact Information |


Introduction

577 KB (Perfect & Complete)-Incremental-Hash-Function For The English Language

TWL06 CWG-Demo      Nothing but the very best ever.

    Now that I have your attention, this lexicon-data-structure is named after my dear aunt, Caroline Furgiuele, for being one of my strongest supporters.  Make no mistake, CWG is The World's Most Advanced Lexicon Data Structure.

    On Java:  It has a praiseworthy graphical-user-interface framework.  I'm not a Java guy, but it provides a convenient way to distribute knowledge.

    Caroline Word Graph is the culmination of several years of work in lexicon-data-structure optimization.  It fills the void between compressed-postfix-Boolean-graphs, and incremental-Trie-hash-functions.  In layman's terms, CWG is an aggressively-pruned-graph, with the ability to keep a running-index value for the words it contains.  The CWG's encoding presented here, along with its built-in hash-functionality combine to produce unprecedented performance in a lexicon-data-structure.

    A common Trie can operate as an incremental-lexicon-hash-function, but it requires lots of memory-space to do so.  A traditional DAWG encoding will reduce the space requirement, but in doing so, it exists as a Boolean-graph, scrolling through node lists, and cannot return index-values for the words contained within.  CWG starts its life as a Trie, progresses to a traditional DAWG, then reduces its node-count further using an optimized pop-count, and finally takes on the additional power of a (Perfect & Complete)-Incremental-Hash-Function by including an extra Byte per node.  A small number of nodes need two extra Bytes, and the 26 root nodes use four Bytes for TWL06.

    I invite you to investigate the World's Most Powerful encoding for the 178,691 words in the TWL06 Tournament Scrabble Word List.  The 1800 lines of creator-code, presented below, are justified by the dazzling performance and small-size of CWG.  This performance will be the most impressive when CWG is used to solve NP-Complete search problems.  As long as, on-CPU 6-MOSFET-per-bit static-RAM is in short-supply, smaller lexicon-data-structures are also going to be faster lexicon-data-structures.  CWG is the Ferrari of lexicon-data-structures.  And just like a hand-crafted, high-performance, and dazzling super-car, CWG beckons you to take it for a ride.


The CWG Structure

    The CWG encoding consists of several basic integer arrays.  All told, there are 3 CWG components, stored in 5 arrays.  The first two arrays are sufficient for CWG to function as a Boolean-graph.  Keep in mind that as a Boolean-graph, CWG is both smaller and faster than a Traditional-DAWG encoding.  The remaining three arrays hold the values which transform the Boolean-graph into a (Perfect & Complete)-Incremental-Hash-Function.  Three arrays hold the Words-To-End-Of-Branch-List (WTEOBL) values to reduce the space required for this final CWG component.

CWG is stored in “CWG_Data_For_Word-List.dat” using the format below:

| Six Four-Byte Integers | Five Basic-Type Arrays |

Six Four-Byte Integers:

1 - | NumberOfWords |
2 - | NumberOfNodes |
3 - | NumberOfListFormats |
4 - | NumberOfRootNodes |
5 - | NumberOfShortWTEOBLs |
6 - | NumberOfUnsignedCharWTEOBLs |

Five Basic-Type Arrays:

1 - | int Array Of Nodes |
2 - | int Array Of List Formats |
3 - | int Array Of Root WTEOBLs |
4 - | short int Array Of WTEOBLs |
5 - | unsigned char Array Of WTEOBLs |

#1) Node-Array:  CWG nodes do not hold letter information inside of them.  The letter associated with a node is assigned by the parent node used to reach it.  Thus each node must contain full-information about its Child-List.  Explicit-list-format information for the 26 English letters requires 26 bits, but there are a limited number of Child-list configurations in TWL06, so that only 13 bits are needed to index the available List-Formats.  An index value representing the position of the First-Child node is also required, and TWL06 with its 112,125 CWG-Nodes, requires 17 bits to store this value.  A Single bit is needed to store an End-Of-Word flag, and 1 bit remains unused.  A 32-bit signed-integer is used in the Node-Array, and its format is presented below:

    [__32-Bit-Integer CWG-Node Format___]
    ----------------------------------------------------
    [_|0|0000000000000|11111111111111111] - CHILD_MASK
    [_|0|1111111111111|00000000000000000] - LIST_FORMAT_INDEX_MASK
    [_|1|0000000000000|00000000000000000] - END_OF_WORD_MASK

#2) List-Format-Array:  This array holds explicit Child-List information in the form of 26 toggle-bits held inside of 32-bit integers.  The patterns present in the English language make this array quite small.  TWL06 contains only 6180 unique Child-List-Formats.  Testing for the existence of a particular Child-Letter amounts to a bitwise-AND with 2^n for the n'th letter, where 'A' = '0'th letter.  Obtaining the offset from the First-Child is calculated by performing a bitwise-AND with 2^n - 1, and then running a jump-table optimized pop-count.  Below is an example of how a Child-List is encoded as a 32-Bit integer:

    Letters in Child-List: |CEGLNPRSTWZ|

    26-Bit Decimal Encoding: |38709332|

    26-Bit Binary Encoding: [______|10010011101010100001010100]

#3) Words-To-End-Of-Branch-List-Arrays:  In a word-graph with compressed-postfix-structures, END_OF_WORD nodes are able to terminate a large number of unique words, and so unique index numbers are non-trivial to obtain.  The core-insights required to understand how to generate the unique index values are presented below:

    - A constant number for each node must exist, which binds each node to the number of words, before or after it, within its list structure.

    - Nodes within a list need not share a common beginning, thanks to the pruning algorithm, but they must necessarily share a common end node.

    - Number-Of-Words-To-End-Of-Branch-List fits the bill for this constant, and a majority of nodes require only "1" Byte to hold this number.

    - A simple equation using WTEOBL values will produce an Incremental-Index-Marker during graph traversal.

    - When arriving at a particular node, an Index-Marker can be inherited from the path used to reach it.

    - The inherited Index-Marker minus "1" will define a unique Index-Value for each word when an END_OF_WORD node is reached.

    - The Index-Markers for the 26 root-nodes are just their WTEOBL values.  Only these nodes require 4-Bytes for their WTEOBL values.

    - Using this scheme, "AA" will hash to "178,690", and "ZZZ" hashes to "0".  Correct by subtracting from TotalNumberOfWords.

    - These insights lead us to the Governing CWG Hash Equation:
Next_Index_Marker = Current_Index_Marker - FC_WTEOBL + NC_WTEOBL - EOW_FLAG
    FC_WTEOBL = First-Child Words-To-End-Of-Branch-List

    NC_WTEOBL = Next-Child Words-To-End-Of-Branch-List

    EOW_Flag = END_OF_WORD_FLAG

    - Next_Index_Marker represents the number of words remaining in the graph, assuming a Depth-First-Preorder traversal.

    - For TWL06, the WTEOBL-Values are contained in 27 ints, 4821 shorts, and 107,304 unsigned chars.  The shorts hold 27 empty values up front, to eliminate a needless subtraction.


How to Create CWG

    If you really want to understand the 29-step process I've developed for creating a CWG, then you must read through the 1800 lines of code published in the C Implementation section.  In the current section, I will isolate the critical steps, and proceed to hand-wave the CWG-Creation process at you.


C Implementation

    The algorithms needed to create CWG in a reasonable amount of time are complex.

C code:
----------------------------------------------------------------------------
1) Word-List.txt - The TWL06 Tournament-Scrabble-Word-List in a correct format.
2) CWG-Creator.c - The CWG-Creation C code.
3) Justin-CWG-Search.c - The Boolean-search and hash-function demonstration C code.


Java Web-Start code:
----------------------------------------------------------------------------
1) Cwg.java - DAWG functionality code, slanted for use in Java.
2) Interface.java - GUI container, a product of NetBeans.
3) CWG_Data_For_Word-List.dat - TWL06 pre-compiled CWG data file.
4) CWG-Demo.jar - A runnable Jar file via the Eclipse IDE.
5) CWG-Demo.jnlp - Java-Web-Start launching protocol file.


CWG-Creator.c
// This program will first compile a traditional DAWG encoding from the "Word-List.txt" file.
// Next, data files are written to assist in the "CWG" creation process.
// A "Caroline Word Graph" will then be created using the intermediate data files, and stored in "CWG_Data_For_Word-List.dat".
// There is a very good reason for why this program is 1800 lines long.  The CWG is a perfect and complete hash function for English-Language in TWL06.

// 1) "Word-List.txt" is a text file with the number of words written on the very first line, and 1 word per line after that.  The words are case-insensitive.
// 2) The "CWG" encoding is very sensitive to the size and content of "Word-List.txt", so only minor alterations are guaranteed to work without code analysis.

// Include the big-three header files.
#include <stdlib.h>
#include <stdio.h>
#include <string.h>

// General high-level program constants.
#define MAX 15
#define NUMBER_OF_ENGLISH_LETTERS 26
#define INPUT_LIMIT 30
#define LOWER_IT 32
#define TEN 10
#define BIT_COUNT_FOR_CHILD_INDEX 17
#define EOW_FLAG 0X40000000
#define INT_BITS 32
#define CHILD_MASK 0X0001FFFF
#define LIST_FORMAT_INDEX_MASK 0X3FFE0000
#define LIST_FORMAT_BIT_SHIFT 17
#define TRADITIONAL_CHILD_SHIFT 5
#define TRADITIONAL_EOW_FLAG 0X00800000
#define TRADITIONAL_EOL_FLAG 0X00400000

// C requires a boolean variable type so use C's typedef concept to create one.
typedef enum { FALSE = 0, TRUE = 1 } Bool;
typedef Bool* BoolPtr;

// The lexicon text file.
#define RAW_LEXICON "Word-List.txt"

// This program will create "5" binary-data files for use, and "1" text-data file for inspection.
#define TRADITIONAL_DAWG_DATA "Traditional_Dawg_For_Word-List.dat"
#define TRADITIONAL_DAWG_TEXT_DATA "Traditional_Dawg_Text_For_Word-List.txt"

#define DIRECT_GRAPH_DATA_PART_ONE "Part_One_Direct_Graph_For_Word-List.dat"
#define DIRECT_GRAPH_DATA_PART_TWO "Part_Two_Direct_Graph_For_Word-List.dat"
#define FINAL_NODES_DATA "Final_Nodes_For_Word-List.dat"

// The complete "CWG" graph is stored here.
#define CWG_DATA "CWG_Data_For_Word-List.dat"

// Lookup tables used for node encoding and number-string decoding.
const unsigned int PowersOfTwo[INT_BITS - 1] = { 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384,
 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728,
 268435456, 536870912, 1073741824 };
const unsigned int PowersOfTen[TEN] = { 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 };

// Lookup tables used to extract child-offset values.
const unsigned char PopCountTable[256] = { 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4,
 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3,
 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4,
 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4,
 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6,
 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8 };
const int ChildListMasks[NUMBER_OF_ENGLISH_LETTERS] = { 0X1, 0X3, 0X7, 0XF, 0X1F, 0X3F, 0X7F, 0XFF, 0X1FF, 0X3FF, 0X7FF, 0XFFF,
 0X1FFF, 0X3FFF, 0X7FFF, 0XFFFF, 0X1FFFF, 0X3FFFF, 0X7FFFF, 0XFFFFF, 0X1FFFFF, 0X3FFFFF, 0X7FFFFF, 0XFFFFFF, 0X1FFFFFF, 0X3FFFFFF };

// This simple function clips off the extra chars for each "fgets()" line.  Works for Linux and Windows text format.
void CutOffExtraChars(char *ThisLine){
    if ( ThisLine[strlen(ThisLine) - 2] == '\r' ) ThisLine[strlen(ThisLine) - 2] = '\0';
    else if ( ThisLine[strlen(ThisLine) - 1] == '\n' ) ThisLine[strlen(ThisLine) - 1] = '\0';
}

// This is an important function involved in any movement through the CWG.
// The "CompleteChildList" is masked according to "LetterPosition", and then a byte-wise pop-count is carried out. ('A' => 0).
// The function retruns the corresponding offset for the "LetterPosition"th letter.
int ListFormatPopCount(int CompleteChildList, int LetterPosition){
    // This jump-table eliminates needless instructions and cumbersome conditional tests.
    const static void *PositionJumpTable[NUMBER_OF_ENGLISH_LETTERS] = { &&On, &&On, &&On, &&On, &&On, &&On, &&On, &&On, &&Tw, &&Tw, &&Tw, 
    &&Tw, &&Tw, &&Tw, &&Tw, &&Tw, &&Th, &&Th, &&Th, &&Th, &&Th, &&Th, &&Th, &&Th, &&Fo, &&Fo };
    int Result = 0;
    // By casting the agrument variable "CompleteChildList" as an "unsigned char *" we can access each byte within it using simple arithmetic.
    // Computer-programs in C use "little-endian" byte-order.  The least significant bit comes first.
    unsigned char *ByteZero = (unsigned char *)&CompleteChildList;
    
    // Mask "CompleteChildList" according to "LetterPosition".
    CompleteChildList &= ChildListMasks[LetterPosition];
    // Query the "PopCountTable" a minimum number of times.
    goto *PositionJumpTable[LetterPosition];
    Fo:
        Result += PopCountTable[*(ByteZero + 3)];
    Th:
        Result += PopCountTable[*(ByteZero + 2)];
    Tw:
        Result += PopCountTable[*(ByteZero + 1)];
    On:
        Result += PopCountTable[*ByteZero];
    return Result;
}

// Returns the positive "int" rerpresented by "TheNumberNotYet" string.  An invalid "TheNumberNotYet" returns "0".
int StringToPositiveInt(char* TheNumberNotYet){
    int Result = 0;
    int X;
    int Length = strlen(TheNumberNotYet);
    if ( Length > TEN ) return 0;
    for ( X = 0; X < Length; X++ ) {
        if ( TheNumberNotYet[X] < '0' || TheNumberNotYet[X] > '9' ) return 0;
        Result += ((TheNumberNotYet[X] - '0')*PowersOfTen[Length - X - 1 ]);
    }
    return Result;
}


// The "BinaryNode" string must be at least 32 + 5 + 1 bytes in length.  Space for the bits, the seperation pipes, and the end of string char.
// This function is used to fill the text file used to inspect the graph created in the first segment of the program.
void ConvertIntNodeToBinaryString(int TheNode, char *BinaryNode){
    int X;
    int Bit;
    BinaryNode[0] = '[';
    // Bit 31 is not being used.  It will always be '0'.
    BinaryNode[1] = '_';
    BinaryNode[2] = '|';
    // Bit 30 holds the End-Of-Word, EOW_FLAG.
    BinaryNode[3] = (TheNode & PowersOfTwo[30])?'1':'0';
    BinaryNode[4] = '|';
    // 13 Bits, (29-->17) represent the child-format index.
    Bit = 29;
    for ( X = 5; X <= 17; X++, Bit-- ) BinaryNode[X] = (TheNode & PowersOfTwo[Bit])?'1':'0';
    BinaryNode[18] = '|';
    // The "Child" index requires 17 bits, and it will complete the 32 bit int.
    Bit = 16;
    for ( X = 19; X <= 35; X++, Bit-- ) BinaryNode[X] = (TheNode & PowersOfTwo[Bit])?'1':'0';
    BinaryNode[36] = ']';
    BinaryNode[37] = '\0';
}


// The "BinaryChildList" string must be at least 32 + 3 + 1 bytes in length.  Space for the bits, the seperation pipes, and the end of string char.
void ConvertChildListIntToBinaryString(int TheChildList, char *BinaryChildList){
    int X;
    int Bit;
    BinaryChildList[0] = '[';
    // Bit 31 to bit 26 remain unused in a "ChildList".
    for ( X = 1; X <= 6; X++ ) BinaryChildList[X] = '_';
    BinaryChildList[7] = '|';
    Bit = 25;
    for ( X = 8; X <= 33; X++, Bit-- ) BinaryChildList[X] = (TheChildList & PowersOfTwo[Bit])?'1':'0';
    BinaryChildList[34] = ']';
    BinaryChildList[35] = '\0';
}

//This Function converts any lower case letters inside "RawWord" to capitals, so that the whole string is made of capital letters.
void MakeMeAllCapital(char *RawWord){
    unsigned int Count = 0;
    unsigned int Length = strlen(RawWord);
    for ( Count = 0; Count < Length; Count++ ) {
        if ( RawWord[Count] >= 'a' && RawWord[Count] <= 'z' ) RawWord[Count] -= LOWER_IT;
    }
}

/*Trie to Dawg TypeDefs*/
struct tnode {
    struct tnode* Next;
    struct tnode* Child;
    struct tnode* ParentalUnit;
    struct tnode* ReplaceMeWith;
    // When populating the DAWG array, you must know the index assigned to each "Child".
    // To get this information, "ArrayIndex" is stored in every node, so that we can mine the information from the reduced pointer-style-trie.
    int ArrayIndex;
    char DirectChild;
    char Letter;
    char MaxChildDepth;
    char Level;
    char NumberOfChildren;
    char Dangling;
    char Protected;
    char EndOfWordFlag;
};

typedef struct tnode Tnode;
typedef Tnode* TnodePtr;

// Functions to access internal "Tnode" members.
int TnodeArrayIndex(TnodePtr ThisTnode){
    return ThisTnode->ArrayIndex;
}

char TnodeDirectChild(TnodePtr ThisTnode){
    return ThisTnode->DirectChild;
}

TnodePtr TnodeNext(TnodePtr ThisTnode){
    return ThisTnode->Next;
}

TnodePtr TnodeChild (TnodePtr ThisTnode){
    return ThisTnode->Child;
}

TnodePtr TnodeParentalUnit(TnodePtr ThisTnode){
    return ThisTnode->ParentalUnit;
}

TnodePtr TnodeReplaceMeWith(TnodePtr ThisTnode){
    return ThisTnode->ReplaceMeWith;
}

char TnodeLetter(TnodePtr ThisTnode){
    return ThisTnode->Letter;
}

char TnodeMaxChildDepth(TnodePtr ThisTnode){
    return ThisTnode->MaxChildDepth;
}

char TnodeNumberOfChildren(TnodePtr ThisTnode){
    return ThisTnode->NumberOfChildren;
}

char TnodeEndOfWordFlag(TnodePtr ThisTnode){
    return ThisTnode->EndOfWordFlag;
}

char TnodeLevel(TnodePtr ThisTnode){
    return ThisTnode->Level;
}

char TnodeDangling(TnodePtr ThisTnode){
    return ThisTnode->Dangling;
}

char TnodeProtected(TnodePtr ThisTnode){
    return ThisTnode->Protected;
}

// Allocate a "Tnode" and fill it with initial values.
TnodePtr TnodeInit(char Chap, TnodePtr OverOne, char WordEnding, char Leveler, int StarterDepth, TnodePtr Parent, char IsaChild){
    TnodePtr Result = (Tnode *)malloc(sizeof(Tnode));
    Result->Letter = Chap;
    Result->ArrayIndex = 0;
    Result->NumberOfChildren = 0;
    Result->MaxChildDepth = StarterDepth;
    Result->Next = OverOne;
    Result->Child = NULL;
    Result->ParentalUnit = Parent;
    Result->Dangling = FALSE;
    Result->Protected = FALSE;
    Result->ReplaceMeWith = NULL;
    Result->EndOfWordFlag = WordEnding;
    Result->Level = Leveler;
    Result->DirectChild = IsaChild;
    return Result;
}

// Modify internal "Tnode" member values.
void TnodeSetArrayIndex(TnodePtr ThisTnode, int TheWhat){
    ThisTnode->ArrayIndex = TheWhat;
}

void TnodeSetChild(TnodePtr ThisTnode, TnodePtr Chump){
    ThisTnode->Child = Chump;
}
    
void TnodeSetNext(TnodePtr ThisTnode, TnodePtr Nexis){
    ThisTnode->Next = Nexis;
}

void TnodeSetParentalUnit(TnodePtr ThisTnode, TnodePtr Parent){
    ThisTnode->ParentalUnit = Parent;
}

void TnodeSetReplaceMeWith(TnodePtr ThisTnode, TnodePtr Living){
    ThisTnode->ReplaceMeWith = Living;
}

void TnodeSetMaxChildDepth(TnodePtr ThisTnode, int NewDepth){
    ThisTnode->MaxChildDepth = NewDepth;
}

void TnodeSetDirectChild(TnodePtr ThisTnode, char Status){
    ThisTnode->DirectChild = Status;
}

void TnodeFlyEndOfWordFlag(TnodePtr ThisTnode){
    ThisTnode->EndOfWordFlag = TRUE;
}

// This function Dangles a node, but also recursively dangles every node under it as well.
// Dangling a "Tnode" means that it will be exculded from the "DAWG".
// By recursion, nodes that are not direct children will get dangled.
// The function returns the total number of nodes dangled as a result.
int TnodeDangle(TnodePtr ThisTnode){
    if ( ThisTnode->Dangling == TRUE ) return 0;
    int Result = 0;
    if ( (ThisTnode->Next) != NULL ) Result += TnodeDangle(ThisTnode->Next);
    if ( (ThisTnode->Child) != NULL ) Result += TnodeDangle(ThisTnode->Child);
    ThisTnode->Dangling = TRUE;
    Result += 1;
    return Result;
}


// This function "Protects" a node being directly referenced in the elimination process.
// "Protected" nodes can be "Dangled", but special precautions need to be taken to ensure graph-integrity.
void TnodeProtect(TnodePtr ThisTnode){
    ThisTnode->Protected = TRUE;
}

// This function removes "Protection" status from "ThisNode".
void TnodeUnProtect(TnodePtr ThisTnode){
    ThisTnode->Protected = FALSE;
}

// This function returns a Boolean value indicating if a node coming after "ThisTnode" is "Protected".
// The Boolean argument "CheckThisNode" determines if "ThisTnode" is included in the search.
// A "Tnode" being eliminated with "Protected" nodes beneath it requires special precautions.
Bool TnodeProtectionCheck(TnodePtr ThisTnode, Bool CheckThisTnode){
    if ( ThisTnode == NULL ) return FALSE;
    if ( CheckThisTnode == TRUE ) if ( ThisTnode->Protected == TRUE ) return TRUE;
    if ( TnodeProtectionCheck(ThisTnode->Next, TRUE) == TRUE ) return TRUE;
    if ( TnodeProtectionCheck(ThisTnode->Child, TRUE) == TRUE ) return TRUE;
    return FALSE;
}

// This function returns the pointer to the Tnode in a parallel list of nodes with the letter "ThisLetter", and returns NULL if the Tnode does not exist.
// If the function returns NULL, then an insertion is required.
TnodePtr TnodeFindParaNode(TnodePtr ThisTnode, char ThisLetter){
    if ( ThisTnode == NULL ) return NULL;
    TnodePtr Result = ThisTnode;
    if ( Result->Letter == ThisLetter ) return Result;
    while ( Result->Letter < ThisLetter ) {
        Result = Result->Next;
        if ( Result == NULL ) return NULL;
    }
    if ( Result->Letter == ThisLetter ) return Result;
    else return NULL;
}

// This function inserts a new Tnode before a larger letter node or at the end of a para list If the list does not esist then it is put at the beginnung.  
// The new node has ThisLetter in it.  AboveTnode is the node 1 level above where the new node will be placed.
// This function should never be passed a "NULL" pointer.  "ThisLetter" should never exist in the "Child" para-list.
void TnodeInsertParaNode(TnodePtr AboveTnode, char ThisLetter, char WordEnder, int StartDepth){
    AboveTnode->NumberOfChildren += 1;
    TnodePtr Holder = NULL;
    TnodePtr Currently = NULL;
    // Case 1: ParaList does not exist yet so start it.
    if ( AboveTnode->Child == NULL ) AboveTnode->Child = TnodeInit(ThisLetter, NULL, WordEnder, AboveTnode->Level + 1, StartDepth, AboveTnode, TRUE);
    // Case 2: ThisLetter should be the first in the ParaList.
    else if ( ((AboveTnode->Child)->Letter) > ThisLetter ) {
        Holder = AboveTnode->Child;
        // The holder node is no longer a direct child so set it as such.
        TnodeSetDirectChild(Holder, FALSE);
        AboveTnode->Child = TnodeInit(ThisLetter, Holder, WordEnder, AboveTnode->Level + 1, StartDepth, AboveTnode, TRUE);
        // The parent node needs to be changed on what used to be the child. it is the Tnode in "Holder".
        Holder->ParentalUnit = AboveTnode->Child;
    }
    // Case 3: The ParaList exists and ThisLetter is not first in the list.
    else if ( (AboveTnode->Child)->Letter < ThisLetter ) {
        Currently = AboveTnode->Child;
        while ( Currently->Next !=NULL ) {
            if ( TnodeLetter(Currently->Next) > ThisLetter ) break;
            Currently = Currently->Next;
        }
        Holder = Currently->Next;
        Currently->Next = TnodeInit(ThisLetter, Holder, WordEnder, AboveTnode->Level + 1, StartDepth, Currently, FALSE);
        if ( Holder != NULL ) Holder->ParentalUnit = Currently->Next;
    }
}

// The "MaxChildDepth" of the two nodes cannot be assumed equal due to the recursive nature of this function, so we must check for equivalence.
char TnodeAreWeTheSame(TnodePtr FirstNode, TnodePtr SecondNode){
    if ( FirstNode == SecondNode ) return TRUE;
    if ( FirstNode == NULL || SecondNode == NULL ) return FALSE;
    if ( FirstNode->Letter != SecondNode->Letter ) return FALSE;
    if ( FirstNode->MaxChildDepth != SecondNode->MaxChildDepth ) return FALSE;
    if ( FirstNode->NumberOfChildren != SecondNode->NumberOfChildren ) return FALSE;
    if ( FirstNode->EndOfWordFlag != SecondNode->EndOfWordFlag ) return FALSE;
    if ( TnodeAreWeTheSame(FirstNode->Child, SecondNode->Child) == FALSE ) return FALSE;
    if ( TnodeAreWeTheSame(FirstNode->Next, SecondNode->Next) == FALSE ) return FALSE;
    else return TRUE;
}

struct dawg {
    int NumberOfTotalWords;
    int NumberOfTotalNodes;
    TnodePtr First;
};

typedef struct dawg Dawg;
typedef Dawg* DawgPtr;

// Set up the parent nodes in the Dawg.
DawgPtr DawgInit(void){
    DawgPtr Result = (Dawg *)malloc(sizeof(Dawg));
    Result->NumberOfTotalWords = 0;
    Result->NumberOfTotalNodes = 0;
    Result->First = TnodeInit('0', NULL, FALSE, 0, 0, NULL, FALSE);
    return Result;
}

// This function is responsible for adding "Word" to the "Dawg" under its root node.  It returns the number of new nodes inserted.
int TnodeDawgAddWord(TnodePtr ParentNode, const char *Word){
    int Result = 0;
    int X, Y = 0;
    int WordLength = strlen(Word);
    TnodePtr HangPoint = NULL;
    TnodePtr Current = ParentNode;
    for ( X = 0; X < WordLength; X++){
        HangPoint = TnodeFindParaNode(TnodeChild(Current), Word[X]);
        if ( HangPoint == NULL ) {
            TnodeInsertParaNode(Current, Word[X], (X == WordLength - 1 ? TRUE : FALSE), WordLength - X - 1);
            Result++;
            Current = TnodeFindParaNode(TnodeChild(Current), Word[X]);
            for ( Y = X + 1; Y < WordLength; Y++ ) {
                TnodeInsertParaNode(Current, Word[Y], (Y == WordLength - 1 ? TRUE : FALSE), WordLength - Y - 1);
                Result += 1;
                Current = TnodeChild(Current);
            }
            break;
        }
        else {
            if ( TnodeMaxChildDepth(HangPoint) < WordLength - X - 1 ) TnodeSetMaxChildDepth(HangPoint, WordLength - X - 1);
        }
        Current = HangPoint;
        // The path for the word that we are trying to insert already exists, so just make sure that the end flag is flying on the last node.
        // This should never happen if we are to add words in increasing word length.
        if ( X == WordLength - 1 ) TnodeFlyEndOfWordFlag(Current);
    }
    return Result;
}

// Add "NewWord" to "ThisDawg", which at this point is a "Trie" with a lot of information in each node.
// "NewWord" must not exist in "ThisDawg" already.
void DawgAddWord(DawgPtr ThisDawg, char * NewWord){
    ThisDawg->NumberOfTotalWords += 1;
    int NodesAdded = TnodeDawgAddWord(ThisDawg->First, NewWord);
    ThisDawg->NumberOfTotalNodes += NodesAdded;
}

// This is a standard depth first preorder tree traversal.
// The objective is to count "Living" "Tnodes" of various "MaxChildDepths", and store these values into "Tabulator".
void TnodeGraphTabulateRecurse(TnodePtr ThisTnode, int Level, int* Tabulator){
    if ( Level == 0 ) TnodeGraphTabulateRecurse(TnodeChild(ThisTnode), 1, Tabulator);
    else {
        // We will only ever be concerned with "Living" nodes.  "Dangling" Nodes will be eliminated, so don't count them.
        if ( ThisTnode->Dangling == FALSE ) {
            Tabulator[ThisTnode->MaxChildDepth] += 1;
            // Go Down if possible.
            if ( ThisTnode->Child != NULL ) TnodeGraphTabulateRecurse(TnodeChild(ThisTnode), Level + 1, Tabulator);
            // Go Right if possible.
            if ( ThisTnode->Next != NULL ) TnodeGraphTabulateRecurse(TnodeNext(ThisTnode), Level, Tabulator);
        }
    }
}

// Count the "Living" "Tnode"s of each "MaxChildDepth" in "ThisDawg", and store the values in "Count".
void DawgGraphTabulate(DawgPtr ThisDawg, int* Count){
    int Numbers[MAX];
    int X = 0;
    for ( X = 0; X < MAX; X++ ) Numbers[X] = 0;
    if ( ThisDawg->NumberOfTotalWords > 0 ) {
        TnodeGraphTabulateRecurse(ThisDawg->First, 0, Numbers);
        for ( X = 0; X < MAX; X++ ) {
            Count[X] = Numbers[X];
        }
    }
}

// This function can never be called after a trie has been "Mowed" because this will result in pointers being freed twice.
// A core dump is bad.
void FreeTnodeRecurse(TnodePtr ThisTnode){
    if ( ThisTnode->Child != NULL ) FreeTnodeRecurse(ThisTnode->Child);
    if ( ThisTnode->Next != NULL ) FreeTnodeRecurse(ThisTnode->Next);
    free(ThisTnode);
}

// This function can never be called after a trie has been "Mowed" because this will result in pointers being freed twice.
// A core dump is bad.
void FreeDawg(DawgPtr ThisDawg){
    if ( ThisDawg->NumberOfTotalWords > 0 ) {
        FreeTnodeRecurse(ThisDawg->First);
    }
    free(ThisDawg);
}

// Recursively replaces all redundant nodes under "ThisTnode".
// "DirectChild" "Tnode" in a "Dangling" state have "ReplaceMeWith" set within them.
// Crosslinking of "Tnode"s being eliminated must be taken-care-of before this function gets called.
// When "Tnode" branches are crosslinked, the living branch has members being replaced with "Tnode"s in the branch being killed.
void TnodeLawnMowerRecurse(TnodePtr ThisTnode){
    if ( ThisTnode->Level == 0 ) TnodeLawnMowerRecurse(ThisTnode->Child);
    else {
        if ( ThisTnode->Next == NULL && ThisTnode->Child == NULL ) return;
        // The first "Tnode" being eliminated will always be a "DirectChild".
        if ( ThisTnode->Child != NULL ) {
            // The node is tagged to be "Mowed", so replace it with "ReplaceMeWith", keep following "ReplaceMeWith" until an un"Dangling" "Tnode" is found.
            if ( (ThisTnode->Child)->Dangling == TRUE ) {
                ThisTnode->Child = TnodeReplaceMeWith(ThisTnode->Child);
                while ( (ThisTnode->Child)->Dangling == TRUE ) ThisTnode->Child = TnodeReplaceMeWith(ThisTnode->Child);
            }
            else {
                TnodeLawnMowerRecurse(ThisTnode->Child);
            }
        }
        if ( ThisTnode->Next != NULL ){
            TnodeLawnMowerRecurse(ThisTnode->Next);
        }
    }
}

// Replaces all pointers to "Dangling" "Tnodes" in the "ThisDawg" Trie with living ones.
void DawgLawnMower(DawgPtr ThisDawg){
    TnodeLawnMowerRecurse(ThisDawg->First);
}

// This function accepts two identical node branch structures, "EliminateThis" and "ReplaceWith".  It is recursive.
// The Boolean "ValidReplacement" determines if the function will check for "Crosslink"s or alter "Protected" and "ReplaceMeWith" states.
// When "ValidReplacement" is ON, it must set "ReplaceMeWith" values for "Protected" nodes under "EliminateThis".
// It will also assign "Protected" status to the corresponding nodes under "ReplaceWith".
// This function returns "FALSE" if a "Crosslink" is found.  It returns "TRUE" if replacement is a GO.
Bool TnodeProtectAndReplaceBranchStructure(TnodePtr EliminateThis, TnodePtr ReplaceWith, Bool ValidReplacement){
    if ( EliminateThis == NULL || ReplaceWith == NULL) return TRUE;
    if ( TnodeProtected(EliminateThis) == TRUE ) {
        if ( TnodeDangling(ReplaceWith) == TRUE ) {
            // Though we verify the "Crosslink" condition for confirmation, the two conditions above guarantee the condition below.
            if ( EliminateThis == TnodeReplaceMeWith(ReplaceWith) ) {
                // In the case of a confirmed "Crosslink", "EliminateThis" will be a "DirectChild".
                // The logic is that "EliminateThis" and "ReplaceWith" have the same structure.
                // Since "ReplaceWith" is "Dangling" with a valid "ReplaceMeWith", it is a "DirectChild".
                // Thus "EliminateThis" must also be a "DirectChild".  Verify this.
                printf("\n   -***- Crosslink found, so exchange branches first, then Dangle the unProtected Tnodes.\n");
                // Resort to drastic measures:  Simply flip the actual nodes in the Trie.
                (ReplaceWith->ParentalUnit)->Child = EliminateThis;
                (EliminateThis->ParentalUnit)->Child = ReplaceWith;
                return FALSE;
            }
        }
        // When "ValidReplacement" is set, if "EliminateThis" is a protected "Tnode", "ReplaceWith" isn't "Dangling".
        // We can "Dangle" "Protected" "Tnodes", as long as we set a proper "ReplaceMeWith" value for them.
        // Since we are now pointing "Tnode"s at "ReplaceWith", protect it.
        if ( ValidReplacement ) {
            TnodeSetReplaceMeWith(EliminateThis, ReplaceWith);
            TnodeProtect(ReplaceWith);
        }
    }
    if ( TnodeProtectAndReplaceBranchStructure(EliminateThis->Next, ReplaceWith->Next, ValidReplacement) == FALSE ) return FALSE;
    if ( TnodeProtectAndReplaceBranchStructure(EliminateThis->Child, ReplaceWith->Child, ValidReplacement) == TRUE ) return TRUE;
    else return FALSE;
}

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

// A queue is required for breadth first traversal, and the rest is self-evident.

struct breadthqueuenode {
    TnodePtr Element;
    struct breadthqueuenode *Next;
};

typedef struct breadthqueuenode BreadthQueueNode;
typedef BreadthQueueNode* BreadthQueueNodePtr;

void BreadthQueueNodeSetNext(BreadthQueueNodePtr ThisBreadthQueueNode, BreadthQueueNodePtr Nexit){
        ThisBreadthQueueNode->Next = Nexit;
}

BreadthQueueNodePtr BreadthQueueNodeNext(BreadthQueueNodePtr ThisBreadthQueueNode){
        return ThisBreadthQueueNode->Next;
}

TnodePtr BreadthQueueNodeElement(BreadthQueueNodePtr ThisBreadthQueueNode){
        return ThisBreadthQueueNode->Element;
}

BreadthQueueNodePtr BreadthQueueNodeInit(TnodePtr NewElement){
    BreadthQueueNodePtr Result = (BreadthQueueNode *)malloc(sizeof(BreadthQueueNode));
    Result->Element = NewElement;
    Result->Next = NULL;
    return Result;
}

struct breadthqueue {
    BreadthQueueNodePtr Front;
    BreadthQueueNodePtr Back;
    int Size;
};

typedef struct breadthqueue BreadthQueue;
typedef BreadthQueue* BreadthQueuePtr;

BreadthQueuePtr BreadthQueueInit(void){
    BreadthQueuePtr Result = (BreadthQueue *)malloc(sizeof(BreadthQueue));
    Result->Front = NULL;
    Result->Back = NULL;
    Result->Size = 0;
}

void BreadthQueuePush(BreadthQueuePtr ThisBreadthQueue, TnodePtr NewElemental){
    BreadthQueueNodePtr Noob = BreadthQueueNodeInit(NewElemental);
    if ( (ThisBreadthQueue->Back) != NULL ) BreadthQueueNodeSetNext(ThisBreadthQueue->Back, Noob);
    else ThisBreadthQueue->Front = Noob;
    ThisBreadthQueue->Back = Noob;
    (ThisBreadthQueue->Size) += 1;
}

TnodePtr BreadthQueuePop(BreadthQueuePtr ThisBreadthQueue){
    if ( ThisBreadthQueue->Size == 0 ) return NULL;
    if ( ThisBreadthQueue->Size == 1 ) {
        ThisBreadthQueue->Back = NULL;
        ThisBreadthQueue->Size = 0;
        TnodePtr Result = (ThisBreadthQueue->Front)->Element;
        free(ThisBreadthQueue->Front);
        ThisBreadthQueue->Front = NULL;
        return Result;
    }
    TnodePtr Result = (ThisBreadthQueue->Front)->Element;
    BreadthQueueNodePtr Holder = ThisBreadthQueue->Front;
    ThisBreadthQueue->Front = (ThisBreadthQueue->Front)->Next;
    free(Holder);
    ThisBreadthQueue->Size -= 1;
    return Result;
}


// For the "Tnode" "Dangling" process, arrange the "Tnodes" in the "Holder" array, with breadth-first traversal order.
void BreadthQueuePopulateReductionArray(BreadthQueuePtr ThisBreadthQueue, TnodePtr Root, TnodePtr **Holder){
    int Taker[MAX];
    int X = 0;
    memset(Taker, 0, MAX*sizeof(int));
    int CurrentMaxChildDepth = 0;
    TnodePtr Current = Root;
    // Push the first row onto the queue.
    while ( Current != NULL ) {
        BreadthQueuePush(ThisBreadthQueue, Current);
        Current = Current->Next;
    }
    // Initiate the pop followed by push all children loop.
    while ( (ThisBreadthQueue->Size) != 0 ) {
        Current = BreadthQueuePop(ThisBreadthQueue);
        CurrentMaxChildDepth = Current->MaxChildDepth;
        Holder[CurrentMaxChildDepth][Taker[CurrentMaxChildDepth]] = Current;
        Taker[CurrentMaxChildDepth] += 1;
        Current = TnodeChild(Current);
        while ( Current != NULL ) {
            BreadthQueuePush(ThisBreadthQueue, Current);
            Current = TnodeNext(Current);
        }
    }
}


// It is of absolutely critical importance that only "DirectChild" nodes are pushed onto the queue as child nodes.  This will not always be the case.
// In a DAWG a child pointer may point to an internal node in a longer list.  Check for this.
int BreadthQueueUseToIndex(BreadthQueuePtr ThisBreadthQueue, TnodePtr Root){
    int IndexNow = 0;
    TnodePtr Current = Root;
    // Push the first row onto the queue.
    while ( Current != NULL ) {
        BreadthQueuePush(ThisBreadthQueue, Current);
        Current = Current->Next;
    }
    // Pop each element off of the queue and only push its children if has not been "Dangled" yet.  Assign index if one has not been given to it yet.
    while ( (ThisBreadthQueue->Size) != 0 ) {
        Current = BreadthQueuePop(ThisBreadthQueue);
        // A traversal of the Trie will never land on "Dangling" "Tnodes", but it will try to visit certain "Tnodes" many times.
        if ( TnodeArrayIndex(Current) == 0 ) {
            IndexNow += 1;
            TnodeSetArrayIndex(Current, IndexNow);
            Current = TnodeChild(Current);
            if ( Current != NULL ) {
                // The graph will lead to intermediate positions, but we cannot start numbering "Tnodes" from the middle of a list.
                if ( TnodeDirectChild(Current) == TRUE && TnodeArrayIndex(Current) == 0 ) {
                    while ( Current != NULL ) {
                        BreadthQueuePush(ThisBreadthQueue, Current);
                        Current = Current->Next;
                    }
                }
            }
        }
    }
    return IndexNow;
}

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

// Next and Child become indices.
struct arraydnode{
    int Next;
    int Child;
    char Letter;
    char EndOfWordFlag;
    char Level;
};

typedef struct arraydnode ArrayDnode;
typedef ArrayDnode* ArrayDnodePtr;

void ArrayDnodeInit(ArrayDnodePtr ThisArrayDnode, char Chap, int Nextt, int Childd, char EndingFlag, char Breadth){
    ThisArrayDnode->Letter = Chap;
    ThisArrayDnode->EndOfWordFlag = EndingFlag;
    ThisArrayDnode->Next = Nextt;
    ThisArrayDnode->Child = Childd;
    ThisArrayDnode->Level = Breadth;
}

void ArrayDnodeTnodeTranspose(ArrayDnodePtr ThisArrayDnode, TnodePtr ThisTnode){
    ThisArrayDnode->Letter = ThisTnode->Letter;
    ThisArrayDnode->EndOfWordFlag = ThisTnode->EndOfWordFlag;
    ThisArrayDnode->Level = ThisTnode->Level;
    if ( ThisTnode->Next == NULL ) ThisArrayDnode->Next = 0;
    else ThisArrayDnode->Next = (ThisTnode->Next)->ArrayIndex;
    if ( ThisTnode->Child == NULL ) ThisArrayDnode->Child = 0;
    else ThisArrayDnode->Child = (ThisTnode->Child)->ArrayIndex;
}

int ArrayDnodeNext(ArrayDnodePtr ThisArrayDnode){
    return ThisArrayDnode->Next;
}

int ArrayDnodeChild (ArrayDnodePtr ThisArrayDnode){
    return ThisArrayDnode->Child;
}

char ArrayDnodeLetter(ArrayDnodePtr ThisArrayDnode){
    return ThisArrayDnode->Letter;
}

char ArrayDnodeEndOfWordFlag(ArrayDnodePtr ThisArrayDnode){
    return ThisArrayDnode->EndOfWordFlag;
}

int ArrayDnodeNumberOfChildrenPlusString(ArrayDnodePtr DoggieDog, int Index, char* FillThisString){
    int X;
    int CurrentArrayPosition;
    
    if ( (DoggieDog[Index]).Child == 0 ) {
        FillThisString[0] = '\0';
        return 0;
    }
    CurrentArrayPosition = (DoggieDog[Index]).Child;
    for ( X = 0; X < NUMBER_OF_ENGLISH_LETTERS; X++ ) {
        FillThisString[X] = (DoggieDog[CurrentArrayPosition]).Letter;
        if ( (DoggieDog[CurrentArrayPosition]).Next == 0 ) {
            FillThisString[X + 1] = '\0';
            return (X + 1);
        }
        CurrentArrayPosition += 1;
    }
}

struct arraydawg {
    int NumberOfStrings;
    ArrayDnodePtr DawgArray;
    int First;
    char MinStringLength;
    char MaxStringLength;
};

typedef struct arraydawg ArrayDawg;
typedef ArrayDawg* ArrayDawgPtr;

//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

int CrossLinkCount = 0;

// This function is the core of the dawg creation procedure.  Pay close attention to the order of the steps involved.

ArrayDawgPtr ArrayDawgInit(char **Dictionary, int *SegmentLenghts, int MaxStringLength){
    int X = 0;
    int Y = 0;
    int *ChildCount;
    char *ChildStrings;
    
    printf("Step 0 - Allocate the framework for the intermediate Array-Data-Structure.\n");
    // Dynamically allocate the upper Data-Structure.
    ArrayDawgPtr Result = (ArrayDawgPtr)malloc(sizeof(ArrayDawg));
    // set MinStringLength, MaxStringLength, and NumberOfStrings.
    
    while ( SegmentLenghts[X] == 0 ) X++;
    Result->MinStringLength = X;
    Result->MaxStringLength = MaxStringLength;
    Result->NumberOfStrings = 0;
    for ( X = Result->MinStringLength; X <= Result->MaxStringLength ; X++ ) Result->NumberOfStrings += SegmentLenghts[X];

    printf("\nStep 1 - Create a Temporary-Working-Trie and begin filling it with the |%d| words.\n", Result->NumberOfStrings);
    /// Create a Temp Trie structure and then feed in the given dictionary.
    DawgPtr TemporaryTrie = DawgInit();
    for ( Y = Result->MinStringLength; Y <= Result->MaxStringLength; Y++ ) {
        for ( X = 0; X < SegmentLenghts[Y]; X++ ) {
            DawgAddWord(TemporaryTrie, &(Dictionary[Y][(Y + 1)*X]));
        }
    }

    printf("\nStep 2 - Finished adding words to the Temporary-Working-Trie.\n");
    // Allocate two "Tnode" counter arrays.
    int *NodeNumberCounter = (int*)calloc((Result->MaxStringLength), sizeof(int));
    int *NodeNumberCounterInit = (int*)calloc((Result->MaxStringLength), sizeof(int));
    
    // Count up the number of "Tnode"s in the Raw-Trie according to MaxChildDepth.
    printf("\nStep 3 - Count the total number of Tnodes in the Raw-Trie according to MaxChildDepth.\n");
    DawgGraphTabulate(TemporaryTrie, NodeNumberCounter);
    
    printf("\nStep 4 - Initial Tnode counting is complete, so display results:\n\n");
    int TotalNodeSum = 0;
    for ( X = 0; X < Result->MaxStringLength; X++ ){
    NodeNumberCounterInit[X] = NodeNumberCounter[X];
        TotalNodeSum += NodeNumberCounter[X];
    }
    for ( X = 0; X < Result->MaxStringLength; X++ ){
        printf("  Initial Tnode Count For MaxChildDepth =|%2d| is |%6d|\n", X, NodeNumberCounterInit[X]);
    }
    printf("\n  Total Tnode Count For The Raw-Trie = |%d| \n", TotalNodeSum);
    // We will have exactly enough space for all of the Tnode pointers.

    printf("\nStep 5 - Allocate a 2 dimensional array of Tnode pointers to search for redundant Tnodes.\n");
    TnodePtr ** HolderOfAllTnodePointers = (TnodePtr **)malloc((Result->MaxStringLength)*sizeof(TnodePtr *));
    for ( X = 0; X < MAX; X++ ) HolderOfAllTnodePointers[X] = (TnodePtr *)malloc(NodeNumberCounterInit[X]*sizeof(TnodePtr));
    // A breadth-first traversal is used when populating the final array.
    // It is then much more likely for living "Tnode"s to appear first, if we fill "HolderOfAllTnodePointers" breadth first.

    printf("\nStep 6 - Populate the 2 dimensional Tnode pointer array.\n");
    // Use a breadth first traversal to populate the "HolderOfAllTnodePointers" array.
    BreadthQueuePtr Populator = BreadthQueueInit();
    BreadthQueuePopulateReductionArray(Populator, (TemporaryTrie->First)->Child, HolderOfAllTnodePointers);

    printf("\nStep 7 - Population complete.\n");
    // Flag all of the reduntant "Tnode"s, and store a "ReplaceMeWith" "Tnode" reference inside the "Dangling" "Tnode"s.
    // Flagging requires the "TnodeAreWeTheSame()" function, and beginning with the highest "MaxChildDepth" "Tnode"s will reduce the processing time.
    int NumberDangled = 0;
    int DangledNow;
    int NumberAtHeight;
    int TotalDangled = 0;
    int W = 0;
    
    // keep track of the number of nodes of each MaxChildDepth dangled recursively so we can check how many remaining nodes we need for the optimal array.
    int DangleCount[Result->MaxStringLength];
    for ( X = 0; X < Result->MaxStringLength; X++) DangleCount[X] = 0;

    printf("\nStep 8 - Tag redundant Tnodes as Dangling - Use recursion, because only DirectChild Tnodes are considered for elimination:\n");
    printf("\n  This procedure is at the very heart of the CWG creation alogirthm, and it would be much slower, without heavy optimization.\n");
    printf("\n  ---------------------------------------------------------------------------------------------------------------------------\n");
    // *** Test the other way.  Start at the largest "MaxChildDepth" and work down from there for recursive reduction to take place.
    for ( Y = Result->MaxStringLength - 1; Y >= 0; Y-- ) {
        NumberDangled = 0;
        NumberAtHeight = 0;
        // "X" is the index of the node we are trying to kill.
        for ( X = NodeNumberCounterInit[Y] - 1; X >= 0; X-- ) {
            // If the node is "Dangling" already, or it is not a "DirectChild", then "continue".
            if ( TnodeDangling(HolderOfAllTnodePointers[Y][X]) == TRUE ) continue;
            if ( TnodeDirectChild(HolderOfAllTnodePointers[Y][X]) == FALSE ) continue;
            // Make sure that we don't emiminate "Tnodes" being pointed to by other "Tnodes" in the graph.
            // This is a tricky procedure because node beneath "X" can be "Protected".
            // "W" will be the index of the first undangled "Tnode" with the same structure, if one exists.
            for ( W = 0; W < NodeNumberCounterInit[Y]; W++ ) {
                if ( W == X ) continue;
                if ( TnodeDangling(HolderOfAllTnodePointers[Y][W]) == FALSE ) {
                    if ( TnodeAreWeTheSame(HolderOfAllTnodePointers[Y][X], HolderOfAllTnodePointers[Y][W]) == TRUE ) {
                        // In the special case where the node being "Dangled" has "Protected" nodes beneath it, more needs to be done.
                        // When we "Dangle" a "Protected" "Tnode", we must set it's "ReplaceMeWith", and a recursive function is needed for this special case.
                        // This construct deals with regular and "Crosslink"ed branch structures.
                        // It happens when "Protected" "Tnodes come beneath the one we want to "Dangle".
                        if ( TnodeProtectionCheck(HolderOfAllTnodePointers[Y][X], FALSE) == TRUE ) {
                            while ( !TnodeProtectAndReplaceBranchStructure(HolderOfAllTnodePointers[Y][X], HolderOfAllTnodePointers[Y][W], FALSE) ) ;
                            TnodeProtectAndReplaceBranchStructure(HolderOfAllTnodePointers[Y][X], HolderOfAllTnodePointers[Y][W], TRUE);
                        }
                        // Set the "Protected" and "ReplaceMeWith" status of the corresponding top-level "Tnode"s.
                        TnodeProtect(HolderOfAllTnodePointers[Y][W]);
                        TnodeSetReplaceMeWith(HolderOfAllTnodePointers[Y][X], HolderOfAllTnodePointers[Y][W]);
                        // "Dangle" all nodes under "HolderOfAllTnodePointers[Y][X]", and update the "Dangle" counters.
                        NumberAtHeight += 1;
                        DangledNow = TnodeDangle(HolderOfAllTnodePointers[Y][X]);
                        NumberDangled += DangledNow;
                        break;
                    }
                }
            }
        }
        printf("  Dangled |%5d| Tnodes, and |%5d| Tnodes In all, through recursion, for MaxChildDepth of |%2d|\n", NumberAtHeight, NumberDangled, Y);
        DangleCount[Y] = NumberDangled;
        TotalDangled += NumberDangled;
    }
    printf("  ---------------------------------------------------------------------------------------------------------------------------\n");
    
    int NumberOfLivingNodes;
    printf("\n  |%6d| = Original # of Tnodes.\n", TotalNodeSum);    
    printf("  |%6d| = Dangled # of Tnodes.\n", TotalDangled);
    printf("  |%6d| = Remaining # of Tnodes.\n", NumberOfLivingNodes = TotalNodeSum - TotalDangled);

    printf("\nStep 9 - Count the number of living Tnodes by traversing the Raw-Trie to check the Dangling numbers.\n\n");
    DawgGraphTabulate(TemporaryTrie, NodeNumberCounter);
    for ( X = 0; X < Result->MaxStringLength; X++ ) {
        printf("  New count for MaxChildDepth |%2d| Tnodes is |%5d|.  Tnode count was |%6d| in Raw-Trie pre-Dangling.  Killed |%6d| Tnodes.\n"
        , X, NodeNumberCounter[X], NodeNumberCounterInit[X], NodeNumberCounterInit[X] - NodeNumberCounter[X]);
    }
    int TotalDangledCheck = 0;
    for ( X = 0; X < MAX; X++ ) {
        TotalDangledCheck += (NodeNumberCounterInit[X] - NodeNumberCounter[X]);
    }
    if ( TotalDangled == TotalDangledCheck ) printf("\n  Tnode Dangling count is consistent.\n");
    else printf("\n  MISMATCH for Tnode Dangling count.\n");
    
    printf("\nStep 9.5 - Run a final check to verify that all redundant nodes have been Dangled.\n\n");
    
    for ( Y = Result->MaxStringLength - 1; Y >= 0; Y-- ) {
        NumberAtHeight = 0;
        // "X" is the index of the node we are trying to kill.
        for ( X = NodeNumberCounterInit[Y] - 1; X >= 0; X-- ) {
            // If the node is "Dangling" already, or it is not a "DirectChild", then "continue".
            if ( TnodeDangling(HolderOfAllTnodePointers[Y][X]) == TRUE ) continue;
            if ( TnodeDirectChild(HolderOfAllTnodePointers[Y][X]) == FALSE ) continue;
            // "W" will be the index of the first undangled "Tnode" with the same structure, if one slipped through the cracks.
            for ( W = 0; W < NodeNumberCounterInit[Y]; W++ ) {
                if ( W == X ) continue;
                if ( TnodeDangling(HolderOfAllTnodePointers[Y][W]) == FALSE ) {
                    if ( TnodeAreWeTheSame(HolderOfAllTnodePointers[Y][X], HolderOfAllTnodePointers[Y][W]) == TRUE ) {
                        NumberAtHeight += 1;
                        break;
                    }
                }
            }
        }
        printf("  MaxChildDepth |%2d| - Identical living nodes found = |%2d|.\n", Y, NumberAtHeight);
    }

    printf("\nstep 10 - Kill the Dangling Tnodes using the internal \"ReplaceMeWith\" values.\n");
    // Node replacement has to take place before indices are set up so nothing points to redundant nodes.
    // - This step is absolutely critical.  Mow The Lawn so to speak!  Then Index.
    DawgLawnMower(TemporaryTrie);
    printf("\n  Killing complete.\n");

    printf("\nStep 11 - Dawg-Lawn-Mowing is now complete, so assign array indexes to all living Tnodes using a Breadth-First-Queue.\n");
    BreadthQueuePtr OrderMatters = BreadthQueueInit();
    // The Breadth-First-Queue must assign an index value to each living "Tnode" only once.
    // "HolderOfAllTnodePointers[MAX - 1][0]" becomes the first node in the new DAWG array.
    int IndexCount = BreadthQueueUseToIndex(OrderMatters, HolderOfAllTnodePointers[MAX - 1][0]);
    printf("\n  Index assignment is now complete.\n");
    printf("\n  |%d| = NumberOfLivingNodes from after the Dangling process.\n", NumberOfLivingNodes);
    printf("  |%d| = IndexCount from the breadth-first assignment function.\n", IndexCount);

    // Allocate the space needed to store the "DawgArray".
    Result->DawgArray = (ArrayDnodePtr)calloc((NumberOfLivingNodes + 1), sizeof(ArrayDnode));
    int IndexFollow = 0;
    int IndexFollower = 0;
    int TransposeCount = 0;
    // Roll through the pointer arrays and use the "ArrayDnodeTnodeTranspose" function to populate it.
    // Set the dummy entry at the beginning of the array.
    ArrayDnodeInit(&(Result->DawgArray[0]), 0, 0, 0, 0, 0);
    Result->First = 1;

    printf("\nStep 12 - Populate the new Working-Array-Dawg structure, which is used to verify validity and create the final integer-graph-encodings.\n");
    // Scroll through "HolderOfAllTnodePointers" and look for un"Dangling" "Tnodes", if so then transpose them into "Result->DawgArray".
    for ( X = Result->MaxStringLength - 1; X >= 0; X-- ) {
        for (W = 0; W < NodeNumberCounterInit[X]; W++ ) {
            if ( TnodeDangling(HolderOfAllTnodePointers[X][W]) == FALSE ) {
                IndexFollow = TnodeArrayIndex(HolderOfAllTnodePointers[X][W]);
                ArrayDnodeTnodeTranspose(&(Result->DawgArray[IndexFollow]), HolderOfAllTnodePointers[X][W]);
                TransposeCount += 1;
                if ( IndexFollow > IndexFollower ) IndexFollower = IndexFollow;
            }
        }
    }
    printf("\n  |%d| = IndexFollower, which is the largest index assigned in the Working-Array-Dawg.\n", IndexFollower);
    printf("  |%d| = TransposeCount, holds the number of Tnodes transposed into the Working-Array-Dawg.\n", TransposeCount);
    printf("  |%d| = NumberOfLivingNodes.  Make sure that these three values are equal, because they must be.\n", NumberOfLivingNodes);
    if ( (IndexFollower == TransposeCount) && (IndexFollower == NumberOfLivingNodes) ) printf("\n  Equality assertion passed.\n");
    else printf("\n  Equality assertion failed.\n");
    
    // Conduct dynamic-memory-cleanup and free the whole Raw-Trie, which is no longer needed.
    for ( X = 0; X < Result->MaxStringLength; X++ ) for ( W = 0; W < NodeNumberCounterInit[X]; W++ ) free(HolderOfAllTnodePointers[X][W]);
    free(TemporaryTrie);
    free(NodeNumberCounter);
    free(NodeNumberCounterInit);
    for ( X = 0; X < Result->MaxStringLength; X++ ) free(HolderOfAllTnodePointers[X]);
    free(HolderOfAllTnodePointers);
    
    printf("\nStep 13 - Creation of the traditional-DAWG is complete, so store it in a binary file for use.\n");
    
    FILE *Data;
    Data = fopen( TRADITIONAL_DAWG_DATA,"wb" );
    // The "NULL" node in position "0" must be counted now.
    int CurrentNodeInteger = NumberOfLivingNodes + 1;
    // It is critical, especially in a binary file, that the first integer written to the file be the number of nodes stored in the file.
    fwrite( &CurrentNodeInteger, sizeof(int), 1, Data );
    // Write the "NULL" node to the file first.
    CurrentNodeInteger = 0;
    fwrite( &CurrentNodeInteger, sizeof(int), 1, Data );
    for ( X = 1; X <= NumberOfLivingNodes ; X++ ){
        CurrentNodeInteger = (Result->DawgArray)[X].Child;
        CurrentNodeInteger <<= TRADITIONAL_CHILD_SHIFT;
        CurrentNodeInteger += ((Result->DawgArray)[X].Letter) - 'A';
        if ( (Result->DawgArray)[X].EndOfWordFlag == TRUE ) CurrentNodeInteger += TRADITIONAL_EOW_FLAG;
        if ( (Result->DawgArray)[X].Next == 0 ) CurrentNodeInteger += TRADITIONAL_EOL_FLAG;
        fwrite( &CurrentNodeInteger, sizeof(int), 1, Data );
    }
    fclose(Data);
    printf( "\n  The Traditional-DAWG-Encoding data file is now written.\n" );
    
    printf("\nStep 14 - Create a preliminary encoding of the more advanced CWG, and store these intermediate arrays into data files.\n");
    
    FILE *Text;
    Text = fopen(TRADITIONAL_DAWG_TEXT_DATA,"w");
    
    FILE *Main;
    FILE *Secondary;
    Main = fopen(DIRECT_GRAPH_DATA_PART_ONE,"wb" );
    Secondary = fopen(DIRECT_GRAPH_DATA_PART_TWO,"wb" );
    
    // The following variables will be used when setting up the child-List-Format integer values.
    int CurrentNumberOfChildren = 0;
    
    char CurrentChildLetterString[NUMBER_OF_ENGLISH_LETTERS + 1];
    CurrentChildLetterString[0] = '\0';
    char TheNodeInBinary[32+5+1];
    char TheChildListInBinary[32+3+1];
    TheNodeInBinary[0] = '\0';
    
    int CompleteChildList;
    int CurrentOffsetNumberIndex;
    int CompleteThirtyTwoBitNode;
    fwrite(&NumberOfLivingNodes, 4, 1, Main);
    
    FILE *ListE;
    int EndOfListCount = 0;
    int EOLTracker = 0;
    int *EndOfListIndicies;
    ListE = fopen(FINAL_NODES_DATA, "wb");
    
    // Set up an array to hold all of the unique child strings for the reduced lexicon DAWG.  The empty placeholder will be all zeds.
    int NumberOfUniqueChildStrings = 0;
    int InsertionPoint = 0;
    Bool IsSheUnique = TRUE;
    char *TempHolder;
    char **HolderOfUniqueChildStrings = (char**)malloc(NumberOfLivingNodes * sizeof(char*));
    for ( X = 0; X < NumberOfLivingNodes; X++ ) {
        HolderOfUniqueChildStrings[X] = (char*)malloc((NUMBER_OF_ENGLISH_LETTERS + 1) * sizeof(char));
        strcpy(HolderOfUniqueChildStrings[X], "ZZZZZZZZZZZZZZZZZZZZZZZZZZ");
    }
    
    // Right here we will tabulate the child information so that it can be turned into an "int" array and stored in a data file.
    // Also, we need to count the number of unique list structures, and calculate the number of bits required to store index values for them.
    // The idea is that there are a small number of actual values that these 26 bits will hold due to patterns in the English Language.
    for ( X = 1; X <= NumberOfLivingNodes ; X++ ) {
        CurrentNumberOfChildren = ArrayDnodeNumberOfChildrenPlusString(Result->DawgArray, X, CurrentChildLetterString);
        // Insert the "CurrentChildLetterString" into the "HolderOfUniqueChildStrings" if, and only if, it is unique.
        for ( Y = 0; Y <= NumberOfUniqueChildStrings; Y++ ) {
            if ( strcmp(CurrentChildLetterString, HolderOfUniqueChildStrings[Y]) == 0 ) {
                IsSheUnique = FALSE;
                InsertionPoint = 0;
                break;
            }
            if ( strcmp(CurrentChildLetterString, HolderOfUniqueChildStrings[Y]) < 0 ) {
                IsSheUnique = TRUE;
                InsertionPoint = Y;
                break;
            }
        }
        if ( IsSheUnique == TRUE ) {
            TempHolder = HolderOfUniqueChildStrings[NumberOfUniqueChildStrings];
            strcpy(TempHolder, CurrentChildLetterString);
            memmove(HolderOfUniqueChildStrings + InsertionPoint + 1, HolderOfUniqueChildStrings + InsertionPoint
            , (NumberOfUniqueChildStrings - InsertionPoint)*sizeof(char*));
            HolderOfUniqueChildStrings[InsertionPoint] = TempHolder;
            NumberOfUniqueChildStrings += 1;
        }
    }
    
    printf("\nStep 15 - NumberOfUniqueChildStrings = |%d|.\n", NumberOfUniqueChildStrings);
    
    int *ChildListValues = (int*)malloc(NumberOfUniqueChildStrings*sizeof(int));
    
    // Encode the unique child strings as "int"s, so that each corresponding bit is popped.
    for ( X = 0; X < NumberOfUniqueChildStrings ; X++ ) {
        strcpy(CurrentChildLetterString, HolderOfUniqueChildStrings[X]);
        CurrentNumberOfChildren = strlen(CurrentChildLetterString);
        CompleteChildList = 0;
        for ( Y = 0; Y < CurrentNumberOfChildren; Y++ ) {
            CompleteChildList += PowersOfTwo[CurrentChildLetterString[Y] - 'A'];
        }
        ChildListValues[X] = CompleteChildList;
    }
    
    fprintf(Text, "Behold, the |%d| graph nodes are decoded below.\r\n\r\n", NumberOfLivingNodes);
    
    // We are now ready to output to the text file, and the "Main" intermediate binary data file.
    for ( X = 1; X <= NumberOfLivingNodes ; X++ ){
        CurrentNumberOfChildren = ArrayDnodeNumberOfChildrenPlusString(Result->DawgArray, X, CurrentChildLetterString);
        
        // Get the correct offset index to store into the current node
        for ( Y = 0; Y < NumberOfUniqueChildStrings; Y++ ) {
            if ( strcmp(CurrentChildLetterString, HolderOfUniqueChildStrings[Y]) == 0 ) {
                CurrentOffsetNumberIndex = Y;
                break;
            }
        }
        
        CompleteThirtyTwoBitNode = CurrentOffsetNumberIndex;
        CompleteThirtyTwoBitNode <<= BIT_COUNT_FOR_CHILD_INDEX;
        CompleteThirtyTwoBitNode += (Result->DawgArray)[X].Child;
        // The first "BIT_COUNT_FOR_GRAPH_INDEX" are for the first child index.  The EOW_FLAG is stored in the 2^30 bit.
        // The remaining bits will hold a reference to the child list configuration.  No space is used for a letter.
        // The 2's complement sign bit is not needed, so a signed integer is acceptable.
        if ( (Result->DawgArray)[X].EndOfWordFlag == 1 ) CompleteThirtyTwoBitNode += EOW_FLAG;
        fwrite(&CompleteThirtyTwoBitNode, sizeof(int), 1, Main);
        ConvertIntNodeToBinaryString(CompleteThirtyTwoBitNode, TheNodeInBinary);
        ConvertChildListIntToBinaryString(ChildListValues[CurrentOffsetNumberIndex], TheChildListInBinary);
        fprintf(Text, "N%6d-%s,Raw|%10d|,Lev|%2d|", X, TheNodeInBinary, CompleteThirtyTwoBitNode, (Result->DawgArray)[X].Level);
        fprintf(Text, ",{'%c',%d,%6d", (Result->DawgArray)[X].Letter, (Result->DawgArray)[X].EndOfWordFlag, (Result->DawgArray)[X].Next);
        fprintf(Text, ",%6d},Childs|%2d|-|%26s|", (Result->DawgArray)[X].Child , CurrentNumberOfChildren, CurrentChildLetterString);
        fprintf(Text, ",ChildList%s-|%8d|.\r\n", TheChildListInBinary, ChildListValues[CurrentOffsetNumberIndex] );
        if ( CompleteThirtyTwoBitNode == 0 ) printf("\n  Error in node encoding process.\n");
    }
    fclose(Main);
    
    fwrite(&NumberOfUniqueChildStrings, sizeof(int), 1, Secondary);
    fwrite(ChildListValues, sizeof(int), NumberOfUniqueChildStrings, Secondary);
    fclose(Secondary);
    
    fprintf(Text, "\r\nNumber Of Living Nodes |%d| Plus The NULL Node.  Also, there are %d child list ints.\r\n\r\n"
    , NumberOfLivingNodes, NumberOfUniqueChildStrings);
    
    for ( X = 0; X < NumberOfUniqueChildStrings; X++ ) {
        fprintf(Text, "#%4d - |%26s| - |%8d|\r\n", X, HolderOfUniqueChildStrings[X], ChildListValues[X] );
    }
    
    // free all of the memory used to compile the Child-List-Format array.
    for ( X = 0; X < NumberOfLivingNodes; X++ ) {
        free(HolderOfUniqueChildStrings[X]);
    }
    free(HolderOfUniqueChildStrings);
    free(ChildListValues);
    
    printf("\nStep 16 - Create an array with all End-Of-List index values.\n");
    
    for ( X = 1; X <= NumberOfLivingNodes; X++ ) {
        if ( (Result->DawgArray)[X].Next == 0 ){
            EndOfListCount += 1;
        }
    }
    EndOfListIndicies = (int*)malloc(EndOfListCount*sizeof(int));
    fwrite(&EndOfListCount, sizeof(int), 1, ListE);
    
    for ( X = 1; X <= NumberOfLivingNodes; X++ ) {
        if ( (Result->DawgArray)[X].Next == 0 ) {
            EndOfListIndicies[EOLTracker] = X;
            EOLTracker += 1;
        }
    }    
    
    printf("\n  EndOfListCount = |%d|\n", EndOfListCount);
    
    fwrite(EndOfListIndicies, sizeof(int), EndOfListCount, ListE);
    
    fclose(ListE);
    
    fprintf(Text, "\nEndOfListCount |%d|\r\n\r\n", EndOfListCount);
    
    for ( X = 0; X < EndOfListCount; X++ ) {
        fprintf(Text, "#%5d - |%d|\r\n", X, EndOfListIndicies[X]);
    }
    
    fclose(Text);
    
    printf("\nStep 17 - Creation of Traditional-DAWG-Encoding file, Intermediate-Array files, and text-inspection-file complete.\n");

    return Result;
}

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

int TraverseTheDawgArrayRecurse(int *TheDawg, int *ListFormats, int *OnIt, int CurrentIndex, char *TheWordSoFar
    , int FillThisPosition, char CurrentLetter, int *WordCounter, Bool PrintMe){
    int X;
    int ChildListFormat;
    int CurrentChild;
    int WhatsBelowMe = 0;
    int CorrectOffset;
    TheWordSoFar[FillThisPosition] = CurrentLetter;
    if ( TheDawg[CurrentIndex] & EOW_FLAG ) {
        *WordCounter += 1;
        TheWordSoFar[FillThisPosition+ 1] = '\0';
        if ( PrintMe ) printf("#|%d| - |%s|\n", *WordCounter, TheWordSoFar);
        WhatsBelowMe += 1;
    }
    if ( CurrentChild = (TheDawg[CurrentIndex] & CHILD_MASK) ) {
        ChildListFormat = ListFormats[(TheDawg[CurrentIndex] & LIST_FORMAT_INDEX_MASK) >> LIST_FORMAT_BIT_SHIFT];
        for ( X = 0; X < NUMBER_OF_ENGLISH_LETTERS ; X++ ) {
            // Verify if the X'th letter exists in the Child-List.
            if ( ChildListFormat & PowersOfTwo[X] ) {
                // Because the X'th letter exists, run "ListFormatPopCount", to extract the "CorrectOffset".
                CorrectOffset = ListFormatPopCount(ChildListFormat, X);
                CorrectOffset -= 1;
                WhatsBelowMe += TraverseTheDawgArrayRecurse(TheDawg, ListFormats, OnIt, CurrentChild + CorrectOffset, TheWordSoFar
                , FillThisPosition + 1, X + 'A', WordCounter, PrintMe);
            }
        }
    }
    // Because CWG is a compressed graph, many values of the "OnIt" array will be updated multiple times with the same values.
    OnIt[CurrentIndex] = WhatsBelowMe;
    return WhatsBelowMe;
}

void TraverseTheDawgArray(int *TheDawg, int *TheListFormats, int *BelowingMe, Bool PrintToScreen){
    int X;
    int TheCounter = 0;
    char RunningWord[MAX + 1];
    for ( X = 0; X < NUMBER_OF_ENGLISH_LETTERS ; X++ ) {
        TraverseTheDawgArrayRecurse(TheDawg, TheListFormats, BelowingMe, X + 1, RunningWord, 0, 'A' + X, &TheCounter, PrintToScreen);
    }
}

int main(){
    printf("\n  The 29-Step CWG-Creation-Process has commenced: (Hang in there, it will be over soon.)\n");
    int X;
    int Y;
    // All of the words of similar length will be stored sequentially in the same array so that there will be (MAX + 1)  arrays in total.
    // The Smallest length of a string is assumed to be 2.
    char *AllWordsInEnglish[MAX + 1];
    for ( X = 0; X < (MAX + 1); X++ ) AllWordsInEnglish[X] = NULL;
    
    FILE *Input;
    Input = fopen(RAW_LEXICON,"r");
    char ThisLine[100] = "\0";
    int FirstLineIsSize;
    int LineLength;
    
    fgets(ThisLine, 100, Input);
    CutOffExtraChars(ThisLine);
    FirstLineIsSize = StringToPositiveInt(ThisLine);
    
    printf("\n  FirstLineIsSize = Number-Of-Words = |%d|\n", FirstLineIsSize);
    int DictionarySizeIndex[MAX + 1];
    for ( X = 0; X <= MAX; X++ ) DictionarySizeIndex[X] = 0;
    char **LexiconInRam = (char**)malloc(FirstLineIsSize*sizeof(char *)); 
    
    // The first line is the Number-Of-Words, so read them all into RAM, temporarily.
    for ( X = 0; X < FirstLineIsSize; X++ ) {
        fgets(ThisLine, 100, Input);
        CutOffExtraChars(ThisLine);
        LineLength = strlen(ThisLine);
        if ( LineLength <= MAX ) DictionarySizeIndex[LineLength] += 1;
        LexiconInRam[X] = (char *)malloc((LineLength + 1)*sizeof(char));
        strcpy(LexiconInRam[X], ThisLine);
    }
    printf("\n  Word-List.txt is now in RAM.\n");
    // Allocate enough space to hold all of the words in strings so that we can add them to the trie by length.
    for ( X = 2; X < (MAX + 1); X++ ) AllWordsInEnglish[X] = (char *)malloc((X + 1)*DictionarySizeIndex[X]*sizeof(char));
    
    int CurrentTracker[MAX + 1];
    for ( X = 0; X < (MAX + 1); X++ ) CurrentTracker[X] = 0;
    int CurrentLength;
    // Copy all of the strings into the halfway house 1.
    for ( X = 0; X < FirstLineIsSize; X++ ) {
        CurrentLength = strlen(LexiconInRam[X]);
        // Simply copy a string from its temporary ram location to the array of length equivelant strings for processing in making the DAWG.
        if ( CurrentLength <= MAX ) strcpy( &((AllWordsInEnglish[CurrentLength])[(CurrentTracker[CurrentLength]*(CurrentLength + 1))]), LexiconInRam[X] );
        CurrentTracker[CurrentLength] += 1;
    }
    printf("\n  The words are now stored in an array according to length.\n\n");
    // Make sure that the counting has resulted in all of the strings being placed correctly.
    for ( X = 0; X < (MAX + 1); X++ ) {
        if ( DictionarySizeIndex[X] == CurrentTracker[X] ) printf("  |%2d| Letter word count = |%5d| is verified.\n", X, CurrentTracker[X]);
        else printf("  Something went wrong with |%2d| letter words.\n", X);
    }
    
    // Free the the initial dynamically allocated memory.
    for ( X = 0; X < FirstLineIsSize; X++ ) free(LexiconInRam[X]);
    free(LexiconInRam);
    
    printf("\n  Begin Creator init function.\n\n");
    
    ArrayDawgPtr Adoggy = ArrayDawgInit(AllWordsInEnglish, DictionarySizeIndex, MAX);
    
    //-----------------------------------------------------------------------------------
    // Begin tabulation of "NumberOfWordsToEndOfBranchList" array.
    FILE *PartOne = fopen(DIRECT_GRAPH_DATA_PART_ONE, "rb");
    FILE *PartTwo = fopen(DIRECT_GRAPH_DATA_PART_TWO, "rb");
    FILE *ListE = fopen(FINAL_NODES_DATA, "rb");
    int NumberOfPartOneNodes;
    int NumberOfPartTwoNodes;
    int NumberOfFinalNodes;
    int CurrentFinalNodeIndex;
    int CurrentCount;
    
    fread(&NumberOfPartOneNodes, sizeof(int), 1, PartOne);
    fread(&NumberOfPartTwoNodes, sizeof(int), 1, PartTwo);
    fread(&NumberOfFinalNodes, sizeof(int), 1, ListE);
    int *PartOneArray = (int *)malloc((NumberOfPartOneNodes + 1)*sizeof(int));
    int *PartTwoArray = (int *)malloc(NumberOfPartTwoNodes*sizeof(int));
    int *FinalNodeLocations = (int *)malloc(NumberOfFinalNodes*sizeof(int));
    
    fread(PartOneArray + 1, sizeof(int), NumberOfPartOneNodes, PartOne);
    fread(PartTwoArray, sizeof(int), NumberOfPartTwoNodes, PartTwo);
    fread(FinalNodeLocations, sizeof(int), NumberOfFinalNodes, ListE);
    
    int *NumberOfWordsBelowMe = (int *)malloc((NumberOfPartOneNodes + 1)*sizeof(int));
    int *NumberOfWordsToEndOfBranchList =(int *)malloc((NumberOfPartOneNodes + 1)*sizeof(int));
    int *RearrangedNumberOfWordsToEndOfBranchList =(int *)malloc((NumberOfPartOneNodes + 1)*sizeof(int));
    
    NumberOfWordsBelowMe[0] = 0;
    NumberOfWordsToEndOfBranchList[0] = 0;
    RearrangedNumberOfWordsToEndOfBranchList[0] = 0;
    PartOneArray[0] = 0;
    
    fclose(PartOne);
    fclose(PartTwo);
    fclose(ListE);
    
    printf("\nStep 18 - Display the Mask-Format for CWG Main-Nodes:\n\n");
    
    char Something[38];
    ConvertIntNodeToBinaryString(CHILD_MASK, Something);
    printf("  %s - CHILD_MASK\n", Something);
    
    ConvertIntNodeToBinaryString(LIST_FORMAT_INDEX_MASK, Something);
    printf("  %s - LIST_FORMAT_INDEX_MASK\n", Something);
    
    printf("\nStep 19 - Traverse the DawgArray to fill the NumberOfWordsBelowMe array.\n");
    
    // This function is run to fill the "NumberOfWordsBelowMe" array.
    TraverseTheDawgArray(PartOneArray, PartTwoArray, NumberOfWordsBelowMe, FALSE);
    
    printf("\nStep 20 - Use FinalNodeLocations and NumberOfWordsBelowMe to fill the NumberOfWordsToEndOfBranchList array.\n");
    
    // This little piece of code compiles the "NumberOfWordsToEndOfBranchList" array.
    // The requirements are the "NumberOfWordsBelowMe" array and the "FinalNodeLocations" array.
    CurrentFinalNodeIndex = 0;
    for ( X = 1; X <= NumberOfPartOneNodes; X++ ) {
        CurrentCount = 0;
        for ( Y = X; Y <= FinalNodeLocations[CurrentFinalNodeIndex]; Y++ ) {
            CurrentCount += NumberOfWordsBelowMe[Y];
        }
        NumberOfWordsToEndOfBranchList[X] = CurrentCount;
        if ( X ==  FinalNodeLocations[CurrentFinalNodeIndex] ) CurrentFinalNodeIndex +=1;
    }
    
    //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    // Now with preliminary analysis complete, it is time to rearrange the PartOne nodes and then set up PartThree.
    
    int ListSizeCounter[NUMBER_OF_ENGLISH_LETTERS + 1];
    int TotalNumberOfLists = 0;
    Bool AreWeInBigList = FALSE;
    int TheCurrentChild;
    int StartOfCurrentList = 1;
    int SizeOfCurrentList = FinalNodeLocations[0];
    int EndOfCurrentList = FinalNodeLocations[0];
    int InsertionPoint = 1;
    int CurrentlyCopyingThisList = 0;
    int *PartOneRearrangedArray = (int *)malloc((NumberOfPartOneNodes + 1)*sizeof(int));
    int *CurrentAdjustments = (int *)malloc((NumberOfPartOneNodes + 1)*sizeof(int));
    
    PartOneRearrangedArray[0] = 0;
    for ( X = 0; X <= NumberOfPartOneNodes; X++ ) CurrentAdjustments[X] = 0;
    
    for ( X = 0; X <= NUMBER_OF_ENGLISH_LETTERS; X++ ) ListSizeCounter[X] = 0;
    
    printf("\nStep 21 - Relocate all node-lists with WTEOBL values greater than 255, to the front of the Main CWG array.\n");
    
    printf("\n  All corresponding node data and End-Of-List data must also be shifted around.\n");
    
    // This code is responsible for rearranging the node lists inside of the CWG int array so the word-heavy lists filter to the front.
    CurrentFinalNodeIndex = 0;
    for ( X = 1; X <= NumberOfPartOneNodes; X++ ) {
        if ( NumberOfWordsToEndOfBranchList[X] > 255 ) AreWeInBigList = TRUE;
        if ( X ==  EndOfCurrentList ) {
            ListSizeCounter[SizeOfCurrentList] += 1;
            // We are now at the end of a big list that must to be moved up to the InsertionPoint.
            // This also implies moving everything between its current location and its new one.
            if ( AreWeInBigList == TRUE ) {
                // First step is to copy the CurrentList into the new array at its correct position.
                for ( Y = 0; Y < SizeOfCurrentList; Y++ ) {
                    PartOneRearrangedArray[InsertionPoint + Y] = PartOneArray[StartOfCurrentList + Y];
                    RearrangedNumberOfWordsToEndOfBranchList[InsertionPoint + Y] = NumberOfWordsToEndOfBranchList[StartOfCurrentList + Y];
                }
                // The following steps are required when we are actually moving the position of a list.  The first set of lists will bypass these steps.
                if ( InsertionPoint !=  StartOfCurrentList ) {
                    // Step 2 is to move all of the nodes between the original and final location, "SizeOfCurrentList" number of places back, starting from the end.
                    for ( Y = EndOfCurrentList; Y >= (InsertionPoint + SizeOfCurrentList); Y-- ) {
                        PartOneArray[Y] = PartOneArray[Y - SizeOfCurrentList];
                        NumberOfWordsToEndOfBranchList[Y] = NumberOfWordsToEndOfBranchList[Y - SizeOfCurrentList];
                    }
                    // Step 3 is to copy the list we are moving up from the rearranged array back into the original.
                    for ( Y = InsertionPoint; Y < (InsertionPoint + SizeOfCurrentList); Y++ ) {
                        PartOneArray[Y] = PartOneRearrangedArray[Y];
                        NumberOfWordsToEndOfBranchList[Y] = RearrangedNumberOfWordsToEndOfBranchList[Y];
                    }
                    // Step 4 is to fill the "CurrentAdjustments" array with the amount that each child references must be moved.
                    // The two arrays are identical now up to the new insertion point.
                    // At this stage, the "CurrentAdjustments" array is all zeros.
                    for ( Y = 1; Y <= NumberOfPartOneNodes; Y++ ) {
                        TheCurrentChild = (PartOneArray[Y] & CHILD_MASK);
                        if ( (TheCurrentChild >= InsertionPoint) && (TheCurrentChild < StartOfCurrentList) ) CurrentAdjustments[Y] = SizeOfCurrentList;
                        if ( (TheCurrentChild >= StartOfCurrentList) && (TheCurrentChild <= EndOfCurrentList) ) CurrentAdjustments[Y] = InsertionPoint - StartOfCurrentList;
                    }
                    // Step 5 is to fix all of the child reference values in both of the arrays.
                    // Start with the rearranged array.
                    for ( Y = 1; Y < (InsertionPoint + SizeOfCurrentList); Y++ ) {
                        if ( CurrentAdjustments[Y] != 0 ) PartOneRearrangedArray[Y] += CurrentAdjustments[Y];
                    }
                    // Finish with the original array.  Make sure to zero all the values after the adjustments have been made to get ready for the next round.
                    for ( Y = 1; Y <= NumberOfPartOneNodes; Y++ ) {
                        if ( CurrentAdjustments[Y] != 0 ) {
                            PartOneArray[Y] += CurrentAdjustments[Y];
                            CurrentAdjustments[Y] = 0;
                        }
                    }
                }
                // Step 7 is to set the new InsertionPoint and change the "FinalNodeLocations", so that they reflect the shift.
                InsertionPoint += SizeOfCurrentList;
                // Shift all of the end of lists between the "CurrentlyCopyingThisList" and "CurrentFinalNodeIndex".
                for ( Y = CurrentFinalNodeIndex; Y > CurrentlyCopyingThisList; Y-- ) {
                    FinalNodeLocations[Y] = FinalNodeLocations[Y - 1] + SizeOfCurrentList;
                }
                FinalNodeLocations[CurrentlyCopyingThisList] = InsertionPoint - 1;
                CurrentlyCopyingThisList += 1;
                
            }
            // Even when we are not in a big list, we still need to update the current list parameters.
            CurrentFinalNodeIndex += 1;
            SizeOfCurrentList = FinalNodeLocations[CurrentFinalNodeIndex] - EndOfCurrentList;
            EndOfCurrentList = FinalNodeLocations[CurrentFinalNodeIndex];
            StartOfCurrentList = X + 1;
            AreWeInBigList = FALSE;
        }
    }
    
    printf("\n  Word-Heavy list-shifting is now complete.\n");
    
    // Step 8 is to copy all of the small lists from the original array to the rearranged array.  All of the references should be properly adjusted at this point.
    for ( X = InsertionPoint; X <= NumberOfPartOneNodes; X++  ) {
        PartOneRearrangedArray[X] = PartOneArray[X];
        RearrangedNumberOfWordsToEndOfBranchList[X] = NumberOfWordsToEndOfBranchList[X];
    }
    
    // Rearrangement of the DAWG lists to reduce size of the PartThree data file is complete, so check if the new and old lists are identical, because they should be.
    for ( X = 1; X <= NumberOfPartOneNodes; X++  ) {
        if ( PartOneArray[X] != PartOneRearrangedArray[X] ) printf("  What A Mistake!\n");
        if ( RearrangedNumberOfWordsToEndOfBranchList[X] != NumberOfWordsToEndOfBranchList[X] ) printf("  Mistaken.\n");
    }
    
    // The two arrays are now identical, so as a final precaution, traverse the rearranged array.
    TraverseTheDawgArray(PartOneRearrangedArray, PartTwoArray, NumberOfWordsBelowMe, FALSE);
    
    // Check for duplicate lists.  It is now highly likely that there are some duplicates.
    // Lists of size X, can be replaced with partial lists of size X+n.  Make sure to check for this case.
    
    printf("\nStep 22 - Create an array to organize End-Of-List values by size.\n\n");
    
    // Add up the total number of lists.
    for ( X = 1; X <= NUMBER_OF_ENGLISH_LETTERS; X++ ) {
        TotalNumberOfLists += ListSizeCounter[X];
        printf("  Size|%2d| Lists = |%5d|\n", X, ListSizeCounter[X]);
    }
    printf("\n  TotalNumberOfLists = |%d|\n", TotalNumberOfLists);
    
    int **NodeListsBySize = (int **)malloc((NUMBER_OF_ENGLISH_LETTERS + 1)*sizeof(int *));
    int WhereWeAt[NUMBER_OF_ENGLISH_LETTERS + 1];
    for ( X = 0; X <= NUMBER_OF_ENGLISH_LETTERS; X++ ) WhereWeAt[X] = 0;
    
    for ( X = 1; X <= NUMBER_OF_ENGLISH_LETTERS; X++ ) {
        NodeListsBySize[X] = (int *)malloc(ListSizeCounter[X]*sizeof(int));
    }
    
    // We are now required to fill the "NodeListsBySize" array.  Simply copy over the correct "FinalNode" information.  
    // Note that the "FinalNode" information reflects the readjustment that just took place.
    
    CurrentFinalNodeIndex = 0;
    EndOfCurrentList = FinalNodeLocations[0];
    SizeOfCurrentList = FinalNodeLocations[0];
    for ( X = 0; X < NumberOfFinalNodes; X++ ) {
        (NodeListsBySize[SizeOfCurrentList])[WhereWeAt[SizeOfCurrentList]] = EndOfCurrentList;
        WhereWeAt[SizeOfCurrentList] += 1;
        CurrentFinalNodeIndex += 1;
        SizeOfCurrentList = FinalNodeLocations[CurrentFinalNodeIndex] - EndOfCurrentList;
        EndOfCurrentList = FinalNodeLocations[CurrentFinalNodeIndex];
    }
    
    printf("\n  End-Of-List values are now organized.\n");
    
    int Z;
    int V;
    int W;
    int U;
    int TheNewChild;
    int TotalNumberOfKilledLists = 0;
    int TotalNumberOfKilledNodes = 0;
    int NewNumberOfKilledLists = -1;
    int InspectThisEndOfList;
    int MaybeReplaceWithThisEndOfList;
    int NumberOfListsKilledThisRound = -1;
    int CurrentNumberOfPartOneNodes = NumberOfPartOneNodes;
    Bool EliminateCurrentList = TRUE;
    
    printf("\nStep 23 - Kill more lists by using the ends of longer lists or lists of equal size.\n\n");
    
    // Try to eliminate lists with partial lists.
    // "X" is the list-length of lists we are trying to kill.
    //for ( X = 1; X < NUMBER_OF_ENGLISH_LETTERS; X++ ) {
    for ( X = NUMBER_OF_ENGLISH_LETTERS; X >= 1; X-- ) {
        printf("  Try To Eliminate Lists of Size |%2d| - ", X);
        NewNumberOfKilledLists = 0;
        // Look for partial lists at the end of "Y" sized lists, to replace the "X" sized lists with.
        for ( Y = NUMBER_OF_ENGLISH_LETTERS; Y >= X; Y-- ) {
            // Try to kill list # "Z".
            for ( Z = 0; Z < ListSizeCounter[X]; Z++ ) {
                InspectThisEndOfList = (NodeListsBySize[X])[Z];
                // Try to replace with list # "Z".
                for ( W = 0; W < ListSizeCounter[Y]; W++ ) {
                    // Never try to replace a list with itself.
                    if ( (X == Y) && (Z == W) ) continue;
                    MaybeReplaceWithThisEndOfList = (NodeListsBySize[Y])[W];
                    for( V = 0; V < X; V++ ) {
                        if ( PartOneArray[InspectThisEndOfList - V] != PartOneArray[MaybeReplaceWithThisEndOfList - V] ) {
                            EliminateCurrentList = FALSE;
                            break;
                        }
                    }
                    // When eliminating a list, make sure to adjust the WTEOBL data.
                    if ( EliminateCurrentList == TRUE ) {
                        // Step 1 - Replace all references to the duplicate list with the earlier equivalent.
                        for( V = 1; V <= CurrentNumberOfPartOneNodes; V++ ) {
                            TheCurrentChild = (PartOneArray[V] & CHILD_MASK);
                            if ( (TheCurrentChild > (InspectThisEndOfList - X)) && (TheCurrentChild <= InspectThisEndOfList) ) {
                                TheNewChild = MaybeReplaceWithThisEndOfList - (InspectThisEndOfList - TheCurrentChild);
                                PartOneArray[V] -= TheCurrentChild;
                                PartOneArray[V] += TheNewChild;
                            }
                        }
                        // Step 2 - Eliminate the dupe list by moving the higher lists forward.
                        for ( V = (InspectThisEndOfList - X + 1); V <= (CurrentNumberOfPartOneNodes - X); V++ ) {
                            PartOneArray[V] = PartOneArray[V + X];
                            NumberOfWordsToEndOfBranchList[V] = NumberOfWordsToEndOfBranchList[V + X];
                        }
                        // Step 3 - Change CurrentNumberOfPartOneNodes.
                        CurrentNumberOfPartOneNodes -= X;
                        // Step 4 - Lower all references to the nodes coming after the dupe list.
                        for ( V = 1; V <= CurrentNumberOfPartOneNodes; V++ ) {
                            TheCurrentChild = (PartOneArray[V] & CHILD_MASK);
                            if ( TheCurrentChild > InspectThisEndOfList ){
                                PartOneArray[V] -= X;
                            }
                        }
                        // Step 5 - Readjust all of the lists after "Z" forward 1 and down X to the value, and lower ListSizeCounter[X] by 1.
                        for( V = Z; V < (ListSizeCounter[X] - 1); V++ ) {
                            (NodeListsBySize[X])[V] = (NodeListsBySize[X])[V + 1] - X;
                        }
                        ListSizeCounter[X] -= 1;
                        // Step 6 - Lower any list, of any size, greater than (NodeListsBySize[X])[Z], down by X.
                        for ( V = 1; V <= (X - 1); V++ ) {
                            for ( U = 0; U < ListSizeCounter[V]; U++ ) {
                                if ( (NodeListsBySize[V])[U] > InspectThisEndOfList ) (NodeListsBySize[V])[U] -= X;
                            }
                        }
                        for ( V = (X + 1); V <= NUMBER_OF_ENGLISH_LETTERS; V++ ) {
                            for ( U = 0; U < ListSizeCounter[V]; U++ ) {
                                if ( (NodeListsBySize[V])[U] > InspectThisEndOfList ) (NodeListsBySize[V])[U] -= X;
                            }
                        }
                        // Step 7 - Lower "Z" by 1 and increase "TotalNumberOfKilledLists".
                        Z -= 1;
                        TotalNumberOfKilledLists += 1;
                        NewNumberOfKilledLists += 1;
                        TotalNumberOfKilledNodes += X;
                        break;
                    }
                    EliminateCurrentList = TRUE;
                }
            }
        }
        if ( NewNumberOfKilledLists > 0 ) printf("Killed |%d| lists.\n", NewNumberOfKilledLists);
        else printf("Empty handed.\n");
        NewNumberOfKilledLists = 0;
    }
    
    printf("\n  Removal of the new-redundant-lists is now complete:\n");
    printf("\n  |%5d| = Original # of lists.\n", TotalNumberOfLists);
    printf("  |%5d| = Killed # of lists.\n", TotalNumberOfKilledLists);
    printf("  |%5d| = Remaining # of lists.\n", TotalNumberOfLists = TotalNumberOfLists - TotalNumberOfKilledLists);

    printf("\n  |%6d| = Original # of nodes.\n", NumberOfPartOneNodes);    
    printf("  |%6d| = Killed # of nodes.\n", TotalNumberOfKilledNodes);
    printf("  |%6d| = Remaining # of nodes.\n", CurrentNumberOfPartOneNodes);
    
    // Try to eliminate lists with partial lists again to check that we've got em all.
    printf("\nStep 24 - Run the redundant-list-analysis one more time to test that no-more exist.\n\n");
    NumberOfPartOneNodes = CurrentNumberOfPartOneNodes;
    TotalNumberOfKilledLists = 0;
    TotalNumberOfKilledNodes = 0;
    EliminateCurrentList = TRUE;
    // "X" is the list-length of lists we are trying to kill.
    for ( X = NUMBER_OF_ENGLISH_LETTERS; X >= 1; X-- ) {
        printf("  Try To Eliminate Lists of Size |%2d| - ", X);
        NewNumberOfKilledLists = 0;
        // Look for partial lists at the end of "Y" sized lists, to replace the "X" sized lists with.
        for ( Y = NUMBER_OF_ENGLISH_LETTERS; Y >= X; Y-- ) {
            // Try to kill list # "Z".
            for ( Z = 0; Z < ListSizeCounter[X]; Z++ ) {
                InspectThisEndOfList = (NodeListsBySize[X])[Z];
                // Try to replace with list # "Z".
                for ( W = 0; W < ListSizeCounter[Y]; W++ ) {
                    // Never try to replace a list with itself.
                    if ( (X == Y) && (Z == W) ) continue;
                    MaybeReplaceWithThisEndOfList = (NodeListsBySize[Y])[W];
                    for( V = 0; V < X; V++ ) {
                        if ( PartOneArray[InspectThisEndOfList - V] != PartOneArray[MaybeReplaceWithThisEndOfList - V] ) {
                            EliminateCurrentList = FALSE;
                            break;
                        }
                    }
                    // When eliminating a list, make sure to adjust the WTEOBL data.
                    if ( EliminateCurrentList == TRUE ) {
                        // Step 1 - Replace all references to the duplicate list with the earlier equivalent.
                        for( V = 1; V <= CurrentNumberOfPartOneNodes; V++ ) {
                            TheCurrentChild = (PartOneArray[V] & CHILD_MASK);
                            if ( (TheCurrentChild > (InspectThisEndOfList - X)) && (TheCurrentChild <= InspectThisEndOfList) ) {
                                TheNewChild = MaybeReplaceWithThisEndOfList - (InspectThisEndOfList - TheCurrentChild);
                                PartOneArray[V] -= TheCurrentChild;
                                PartOneArray[V] += TheNewChild;
                            }
                        }
                        // Step 2 - Eliminate the dupe list by moving the higher lists forward.
                        for ( V = (InspectThisEndOfList - X + 1); V <= (CurrentNumberOfPartOneNodes - X); V++ ) {
                            PartOneArray[V] = PartOneArray[V + X];
                            NumberOfWordsToEndOfBranchList[V] = NumberOfWordsToEndOfBranchList[V + X];
                        }
                        // Step 3 - Change CurrentNumberOfPartOneNodes.
                        CurrentNumberOfPartOneNodes -= X;
                        // Step 4 - Lower all references to the nodes coming after the dupe list.
                        for ( V = 1; V <= CurrentNumberOfPartOneNodes; V++ ) {
                            TheCurrentChild = (PartOneArray[V] & CHILD_MASK);
                            if ( TheCurrentChild > InspectThisEndOfList ){
                                PartOneArray[V] -= X;
                            }
                        }
                        // Step 5 - Readjust all of the lists after "Z" forward 1 and down X to the value, and lower ListSizeCounter[X] by 1.
                        for( V = Z; V < (ListSizeCounter[X] - 1); V++ ) {
                            (NodeListsBySize[X])[V] = (NodeListsBySize[X])[V + 1] - X;
                        }
                        ListSizeCounter[X] -= 1;
                        // Step 6 - Lower any list, of any size, greater than (NodeListsBySize[X])[Z], down by X.
                        for ( V = 1; V <= (X - 1); V++ ) {
                            for ( U = 0; U < ListSizeCounter[V]; U++ ) {
                                if ( (NodeListsBySize[V])[U] > InspectThisEndOfList ) (NodeListsBySize[V])[U] -= X;
                            }
                        }
                        for ( V = (X + 1); V <= NUMBER_OF_ENGLISH_LETTERS; V++ ) {
                            for ( U = 0; U < ListSizeCounter[V]; U++ ) {
                                if ( (NodeListsBySize[V])[U] > InspectThisEndOfList ) (NodeListsBySize[V])[U] -= X;
                            }
                        }
                        // Step 7 - Lower "Z" by 1 and increase "TotalNumberOfKilledLists".
                        Z -= 1;
                        TotalNumberOfKilledLists += 1;
                        NewNumberOfKilledLists += 1;
                        TotalNumberOfKilledNodes += X;
                        break;
                    }
                    EliminateCurrentList = TRUE;
                }
            }
        }
        if ( NewNumberOfKilledLists > 0 ) printf("Killed |%d| lists.\n", NewNumberOfKilledLists);
        else printf("Empty handed.\n");
        NewNumberOfKilledLists = 0;
    }
    
    printf("\n  The no-more redundant-list-test is now complete:\n");
    printf("\n  |%5d| = Original # of lists.\n", TotalNumberOfLists);
    printf("  |%5d| = Killed # of lists.\n", TotalNumberOfKilledLists);
    printf("  |%5d| = Remaining # of lists.\n", TotalNumberOfLists - TotalNumberOfKilledLists);

    printf("\n  |%6d| = Original # of nodes.\n", NumberOfPartOneNodes);    
    printf("  |%6d| = Killed # of nodes.\n", TotalNumberOfKilledNodes);
    printf("  |%6d| = Remaining # of nodes.\n", CurrentNumberOfPartOneNodes);
    
    // verify that the reduction procedures have resulted in a valid word graph. 
    
    // "FinalNodeLocations" needs to be recompiled from what is left in the "NodeListsBySize" arrays.
    
    printf("\nStep 25 - Recompile the FinalNodeLocations array and display the distribution.\n\n");
    
    TotalNumberOfLists = 0;
    for ( X = 1; X <= NUMBER_OF_ENGLISH_LETTERS; X++ ) {
        TotalNumberOfLists += ListSizeCounter[X];
        printf("  List Size|%2d| - Number Of Lists|%5d|\n", X, ListSizeCounter[X]);
    }
    printf("\n  TotalNumberOfLists|%d|\n", TotalNumberOfLists);
    
    // Set all initial values in "FinalNodeLocations" array to BOGUS numbers.
    for ( X = 0; X < TotalNumberOfLists; X++ ) {
        FinalNodeLocations[X] = 1000000;
    }
    
    // Filter all of the living "FinalNode" values into the "FinalNodeLocations" array.
    
    int TempValue;
    
    for ( X = NUMBER_OF_ENGLISH_LETTERS; X >= 1; X-- ) {
        for ( Y = 0; Y < ListSizeCounter[X]; Y++ ) {
            FinalNodeLocations[TotalNumberOfLists - 1] = (NodeListsBySize[X])[Y];
            // The new list has been placed at the end of the "FinalNodeLocations" array, now filter it up to where it should be.
            for ( Z = (TotalNumberOfLists - 1); Z > 0; Z-- ) {
                if ( FinalNodeLocations[Z - 1] > FinalNodeLocations[Z] ) {
                    TempValue = FinalNodeLocations[Z - 1];
                    FinalNodeLocations[Z - 1] = FinalNodeLocations[Z];
                    FinalNodeLocations[Z] = TempValue;
                }
                else break;
            }
        }
    }
    
    
    // Test for logical errors in the list elimination procedure.
    for ( X = 0; X < (TotalNumberOfLists - 1); X++ ) {
        if ( FinalNodeLocations[X] == FinalNodeLocations[X + 1] ) printf("\nNo Two Lists Can End On The Same Node. |%d|%d|\n", X, FinalNodeLocations[X]);
    }
    
    printf("\n  The FinalNodeLocations array is now compiled and tested for obvious errors.\n");
    
    printf("\nStep 26 - Recompile WTEOBL array by graph traversal, and test equivalence with the one modified during list-killing.\n");
    
    // Compile "RearrangedNumberOfWordsToEndOfBranchList", and verify that it is the same as "NumberOfWordsToEndOfBranchList".
    TraverseTheDawgArray(PartOneArray, PartTwoArray, NumberOfWordsBelowMe, FALSE);
    
    // This little piece of code compiles the "RearrangedNumberOfWordsToEndOfBranchList" array.
    // The requirements are the "NumberOfWordsBelowMe" array and the "FinalNodeLocations" array.
    CurrentFinalNodeIndex = 0;
    for ( X = 1; X <= CurrentNumberOfPartOneNodes; X++ ) {
        CurrentCount = 0;
        for ( Y = X; Y <= FinalNodeLocations[CurrentFinalNodeIndex]; Y++ ) {
            CurrentCount += NumberOfWordsBelowMe[Y];
        }
        RearrangedNumberOfWordsToEndOfBranchList[X] = CurrentCount;
        if ( X ==  FinalNodeLocations[CurrentFinalNodeIndex] ) CurrentFinalNodeIndex +=1;
    }
    
    printf("\n  New WTEOBL array is compiled, so test for equality.\n");
    
    for ( X = 1; X <= CurrentNumberOfPartOneNodes; X++ ) {
        if ( RearrangedNumberOfWordsToEndOfBranchList[X] != NumberOfWordsToEndOfBranchList[X] ) printf("\nMismatch found.\n");
    }
    
    printf("\n  Equality test complete.\n");
    
    printf("\nStep 27 - Determine the final node index that requires a short integer for its WTEOBL value.\n");
    
    // Find out the final index number that requires an integer greater in size than a byte to hold it. Part 3 of the data structure will be held in three arrays.
    int FurthestBigNode = 0;
    int FirstSmallNode;
    for ( X = 1; X <= CurrentNumberOfPartOneNodes; X++ ) {
        if ( RearrangedNumberOfWordsToEndOfBranchList[X] > 0XFF ) FurthestBigNode = X;
    }
    
    for ( X = 0; X < TotalNumberOfLists; X++ ) {
        if ( FinalNodeLocations[X] >= FurthestBigNode ) {
            printf("\n  End of final short-integer WTEOBL list = |%d|.\n", FinalNodeLocations[X]);
            FurthestBigNode = FinalNodeLocations[X];
            break;
        }
    }
    
    FirstSmallNode = FurthestBigNode + 1;
    
    printf("\n  Index of first node requiring only an unsigned-char for its WTEOBL = |%d|.\n", FirstSmallNode);
    
    // The first 26 nodes are the only ones in need of 4-Byte int variables to hold their WTEOBL values.
    // Being the entry points for the graph, it makes sense to hold these values in a "const int" array, defined in the program code.
    
    // The "short int" array holding the medium size WTEOBL values will hold '0's for elements [0, 26], inclusive.
    // The "unsigned char" array must be unsigned because many of the values require 8-bit representation.
    
    // The entire CWG will be stored inside of the one "CWG_Data_For_Word-List.dat" data file.
    // The first integer will be the total number of words in the graph.
    // The next five integers will be the array sizes.
    // After these header values, each array will then be written to the file in order, using the correct integer type.
    
    printf("\nStep 28 - Separate the final 3 WTEOBL arrays, and write all 5 arrays to the FinalProduct CWG data file.\n");
    
    int ArrayOneSize = CurrentNumberOfPartOneNodes + 1;
    int ArrayTwoSize = NumberOfPartTwoNodes;
    int ArrayThreeSize = NUMBER_OF_ENGLISH_LETTERS + 1;
    int ArrayFourSize = FurthestBigNode + 1;
    int ArrayFiveSize = CurrentNumberOfPartOneNodes - FurthestBigNode;
    
    // Allocate the final three arrays.
    int *PartThreeArray = (int *)malloc(ArrayThreeSize*sizeof(int));
    short int *PartFourArray = (short int *)malloc(ArrayFourSize*sizeof(short int));
    unsigned char *PartFiveArray = (unsigned char *)malloc(ArrayFiveSize*sizeof(unsigned char));
    
    // Fill the final three CWG arrays.
    for ( X = 0; X < ArrayThreeSize; X++ ) {
        PartThreeArray[X] = RearrangedNumberOfWordsToEndOfBranchList[X];
        PartFourArray[X] = 0;
    }
    for ( X = ArrayThreeSize; X < ArrayFourSize; X++ ) PartFourArray[X] = RearrangedNumberOfWordsToEndOfBranchList[X];
    for ( X = 0; X < ArrayFiveSize; X++ ) PartFiveArray[X] = RearrangedNumberOfWordsToEndOfBranchList[ArrayFourSize + X];
    
    FILE* FinalProduct = fopen(CWG_DATA, "wb");
    
    fwrite(&FirstLineIsSize, sizeof(int), 1, FinalProduct);
    fwrite(&ArrayOneSize, sizeof(int), 1, FinalProduct);
    fwrite(&ArrayTwoSize, sizeof(int), 1, FinalProduct);
    fwrite(&ArrayThreeSize, sizeof(int), 1, FinalProduct);
    fwrite(&ArrayFourSize, sizeof(int), 1, FinalProduct);
    fwrite(&ArrayFiveSize, sizeof(int), 1, FinalProduct);
    
    fwrite(PartOneArray, sizeof(int), ArrayOneSize, FinalProduct);
    fwrite(PartTwoArray, sizeof(int), ArrayTwoSize, FinalProduct);
    fwrite(PartThreeArray, sizeof(int), ArrayThreeSize, FinalProduct);
    fwrite(PartFourArray, sizeof(short int), ArrayFourSize, FinalProduct);
    fwrite(PartFiveArray, sizeof(unsigned char), ArrayFiveSize, FinalProduct);
    
    fclose(FinalProduct);
    
    printf("\n  The new CWG is ready to use.  Now, understand it, then go out and use it.\n\n");
    
    return 0;
}


Justin-CWG-Search.c
// This is a very simple word-search and word-hash-function program.
// In addition to its primary functions, the program writes a "Numbered-Word-List.txt" file, for inspection.
// This incremental-hash-function for 178,691 words fits in less than 600K, which is very small.

#include <stdlib.h>
#include <stdio.h>
#include <string.h>

#define GRAPH_DATA "CWG_Data_For_Word-List.dat"
#define OUT_LIST "Numbered-Word-List.txt"

#define NUMBER_OF_ENGLISH_LETTERS 26
#define LOWER_IT 32
#define INPUT_BUFFER_SIZE 100
#define MAX 15
#define THREE 3
#define ESCAPE_SEQUENCE "999"
#define TWO_UP_EIGHT 256

#define EOW_FLAG 1073741824
#define LIST_FORMAT_INDEX_MASK 0X3FFE0000
#define LIST_FORMAT_BIT_SHIFT 17
#define CHILD_MASK 0X0001FFFF

// Define a Boolean, enumerated data type.
typedef enum { FALSE = 0, TRUE = 1 } Bool;

const int PowersOfTwo[NUMBER_OF_ENGLISH_LETTERS] = { 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384,
 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432 };
// When using the "ChildListMasks", the letter being investigated is known to exist, so its bit will not be included in the claculated offset.
const int ChildListMasks[NUMBER_OF_ENGLISH_LETTERS] = { 0X0, 0X1, 0X3, 0X7, 0XF, 0X1F, 0X3F, 0X7F, 0XFF, 0X1FF, 0X3FF, 0X7FF, 0XFFF,
 0X1FFF, 0X3FFF, 0X7FFF, 0XFFFF, 0X1FFFF, 0X3FFFF, 0X7FFFF, 0XFFFFF, 0X1FFFFF, 0X3FFFFF, 0X7FFFFF, 0XFFFFFF, 0X1FFFFFF };
const char PopCountTable[TWO_UP_EIGHT] = { 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4,
 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3,
 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5,
 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3,
 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5,
 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6,
 6, 7, 6, 7, 7, 8 };

// Using an explicit jump table, this is an optimized 4-byte integer pop-count.
// The function returns the offset of the "LetterPosition"th letter from the "FirstChild" node in a list.
// If "LetterPosition" holds the first letter, then "0" is returned.
int ListFormatPopCount(int CompleteChildList, int LetterPosition){
    const static void *PositionJumpTable[NUMBER_OF_ENGLISH_LETTERS] = { &&Ze, &&On, &&On, &&On, &&On, &&On, &&On, &&On, &&Tw, &&Tw,
    &&Tw, &&Tw, &&Tw, &&Tw, &&Tw, &&Tw, &&Th, &&Th, &&Th, &&Th, &&Th, &&Th, &&Th, &&Th, &&Fo, &&Fo };
    int Result = 0;
    // By casting the internal integer variable "CompleteChildList" as an "unsigned char *" we can access each byte within it.
    // Remember that computer-programs in C use "little-endian" byte-order.
    unsigned char *ByteZero = (unsigned char *)&CompleteChildList;
    
    // Mask "CompleteChildList" so that
    CompleteChildList &= ChildListMasks[LetterPosition];
    goto *PositionJumpTable[LetterPosition];
    Fo:
        Result += PopCountTable[*(ByteZero + 3)];
    Th:
        Result += PopCountTable[*(ByteZero + 2)];
    Tw:
        Result += PopCountTable[*(ByteZero + 1)];
    On:
        Result += PopCountTable[*ByteZero];
    Ze:
    return Result;
}


// This simple function clips off the extra chars for each "fgets()" line.  Works for Linux and Windows text format.
void CutOffExtraChars(char *ThisLine){
    if ( ThisLine[strlen(ThisLine) - 2] == '\r' ) ThisLine[strlen(ThisLine) - 2] = '\0';
    else if ( ThisLine[strlen(ThisLine) - 1] == '\n' ) ThisLine[strlen(ThisLine) - 1] = '\0';
}

// This Function converts any lower case letters inside "RawWord" to capitals, so that the whole string is made of capital letters.
void MakeMeAllCapital(char *RawWord){
    int X;
    int Length = strlen(RawWord);
    for ( X = 0; X < Length; X++ ) {
        if ( RawWord[X] >= 'a' && RawWord[X] <= 'z' ) RawWord[X] = RawWord[X] - LOWER_IT;
    }
}

// Tests the capitalized user input string for valid length and valid characters.
// Returns "TRUE" for valid, and "FALSE" for invalid.
Bool ValidateInput(char *CappedInput){
    int X;
    int Length = strlen(CappedInput);
    if ( Length > MAX ) return FALSE;
    for ( X = 0; X < Length; X++ ) {
        if ( CappedInput[X] < 'A' || CappedInput[X] > 'Z' ) return FALSE;
    }
    return TRUE;
}

// The CWG basic-type arrays will have global scope to reduce function-argument overhead.
int *TheNodeArray;
int *TheListFormatArray;
int *TheRoot_WTEOBL_Array;
short *TheShort_WTEOBL_Array;
unsigned char *TheUnsignedChar_WTEOBL_Array;

// These two values are needed for the CWG Hash-Function.
int WTEOBL_Transition;
int IndexCorrection;

// Use the first two CWG arrays to return a Boolean value indicating if "TheCandidate" word is in the lexicon.
Bool SingleWordSearchBoolean(char *TheCandidate, int CandidateLength){
    int X;
    int CurrentLetterPosition = TheCandidate[0] - 'A';
    int CurrentNodeIndex = CurrentLetterPosition + 1;
    int CurrentChildListFormat;
    for ( X = 1; X < CandidateLength; X++ ) {
        if ( !(TheNodeArray[CurrentNodeIndex] & CHILD_MASK) ) return FALSE;
        CurrentChildListFormat = TheListFormatArray[(TheNodeArray[CurrentNodeIndex] & LIST_FORMAT_INDEX_MASK) >> LIST_FORMAT_BIT_SHIFT];
        CurrentLetterPosition = TheCandidate[X] - 'A';
        if ( !(CurrentChildListFormat & PowersOfTwo[CurrentLetterPosition]) ) return FALSE;
        else CurrentNodeIndex = (TheNodeArray[CurrentNodeIndex] & CHILD_MASK) + ListFormatPopCount(CurrentChildListFormat, CurrentLetterPosition);
    }
    if ( TheNodeArray[CurrentNodeIndex] & EOW_FLAG ) return TRUE;
    return FALSE;
}

// Using a novel graph mark-up scheme, this function returns the hash index of "TheCandidate", and "0" if it does not exist.
// This function uses the additional 3 WTEOBL arrays.
int SingleWordHashFunction(char *TheCandidate, int CandidateLength){
    int X;
    int CurrentLetterPosition = TheCandidate[0] - 'A';
    int CurrentNodeIndex = CurrentLetterPosition + 1;
    int CurrentChildListFormat;
    int CurrentHashMarker = TheRoot_WTEOBL_Array[CurrentNodeIndex];
    for ( X = 1; X < CandidateLength; X++ ) {
        if ( !(TheNodeArray[CurrentNodeIndex] & CHILD_MASK) ) return 0;
        CurrentChildListFormat = TheListFormatArray[(TheNodeArray[CurrentNodeIndex] & LIST_FORMAT_INDEX_MASK) >> LIST_FORMAT_BIT_SHIFT];
        CurrentLetterPosition = TheCandidate[X] - 'A';
        if ( !(CurrentChildListFormat & PowersOfTwo[CurrentLetterPosition]) ) return 0;
        else {
            CurrentNodeIndex = TheNodeArray[CurrentNodeIndex] & CHILD_MASK;
            // Use "TheShort_WTEOBL_Array".
            if ( CurrentNodeIndex < WTEOBL_Transition ) {
                CurrentHashMarker -= TheShort_WTEOBL_Array[CurrentNodeIndex];
                CurrentNodeIndex += ListFormatPopCount(CurrentChildListFormat, CurrentLetterPosition);
                CurrentHashMarker += TheShort_WTEOBL_Array[CurrentNodeIndex];
            }
            // Use "TheUnsignedChar_WTEOBL_Array".
            else {
                CurrentHashMarker -= TheUnsignedChar_WTEOBL_Array[CurrentNodeIndex - WTEOBL_Transition];
                CurrentNodeIndex += ListFormatPopCount(CurrentChildListFormat, CurrentLetterPosition);
                CurrentHashMarker += TheUnsignedChar_WTEOBL_Array[CurrentNodeIndex - WTEOBL_Transition];
            }
            if ( TheNodeArray[CurrentNodeIndex] & EOW_FLAG ) CurrentHashMarker -= 1;
        }
    }
    if ( TheNodeArray[CurrentNodeIndex] & EOW_FLAG ) return IndexCorrection - CurrentHashMarker;
    return 0;
}

// List output variables.
FILE *WordDump;
int LastPosition = 0;

// A recursive function to print the lexicon contained in the CWG to a text file.
// The function also tests the hash-tracking logic.  If the words are output using successive numbers, the graph works perfectly.
void Print_CWG_Word_ListRecurse(int ThisIndex, int FillThisPlace, char ThisLetter, char *WorkingWord, int CurrentHashMarker){
    int X;
    int TheChildIndex = TheNodeArray[ThisIndex] & CHILD_MASK;
    int TheChildListFormat;
    int ConstHashChange;
    int HashCheck;
    
    WorkingWord[FillThisPlace] = ThisLetter;
    if ( TheNodeArray[ThisIndex] & EOW_FLAG ) {
        WorkingWord[FillThisPlace + 1] = '\0';
        CurrentHashMarker -= 1;
        fprintf(WordDump, "[%d]-|%s|\r\n", HashCheck = (IndexCorrection - CurrentHashMarker), WorkingWord);
        if ( HashCheck != (LastPosition + 1) ) printf("Major Mistake|%d|!\n", HashCheck);
        LastPosition = HashCheck;
    }
    if ( TheChildIndex ) {
        TheChildListFormat = TheListFormatArray[(TheNodeArray[ThisIndex] & LIST_FORMAT_INDEX_MASK) >> LIST_FORMAT_BIT_SHIFT];
        if ( TheChildIndex < WTEOBL_Transition ) {
            ConstHashChange = TheShort_WTEOBL_Array[TheChildIndex];
            for ( X = 0; X < NUMBER_OF_ENGLISH_LETTERS; X++ ) {
                if ( TheChildListFormat & PowersOfTwo[X] ) {
                    Print_CWG_Word_ListRecurse(TheChildIndex, FillThisPlace + 1, X + 'A', WorkingWord,
                    CurrentHashMarker - ConstHashChange + TheShort_WTEOBL_Array[TheChildIndex]);
                    TheChildIndex += 1;
                }
            }
        }
        else {
            ConstHashChange = TheUnsignedChar_WTEOBL_Array[TheChildIndex - WTEOBL_Transition];
            for ( X = 0; X < NUMBER_OF_ENGLISH_LETTERS; X++ ) {
                if ( TheChildListFormat & PowersOfTwo[X] ) {
                    Print_CWG_Word_ListRecurse(TheChildIndex, FillThisPlace + 1, X + 'A', WorkingWord,
                    CurrentHashMarker - ConstHashChange + TheUnsignedChar_WTEOBL_Array[TheChildIndex - WTEOBL_Transition]);
                    TheChildIndex += 1;
                }
            }
        }
    }
}

// This function will print the word list to a numbered text file.
void Print_CWG_Word_List(void){
    int X;
    char MessWithMe[MAX + 1];
    WordDump = fopen(OUT_LIST, "w");
    for ( X = 1; X <= NUMBER_OF_ENGLISH_LETTERS; X ++ ) {
        Print_CWG_Word_ListRecurse(X, 0, X + '@', MessWithMe, TheRoot_WTEOBL_Array[X]);
    }
    fclose(WordDump);
}

int main(){
    int X;
    int HashReturnValue;
    
    // Array size variables.
    int TotalNumberOfWords;
    int NodeArraySize;
    int ListFormatArraySize;
    int Root_WTEOBL_ArraySize;
    int Short_WTEOBL_ArraySize;
    int UnsignedChar_WTEOBL_ArraySize;
    
    char RawUserInput[INPUT_BUFFER_SIZE];
    
    // Read the CWG graph, from the "GRAPH_DATA" file, into the global arrays.
    FILE *Data = fopen(GRAPH_DATA, "rb");
    
    // Read the array sizes.
    fread(&TotalNumberOfWords, sizeof(int), 1, Data);
    fread(&NodeArraySize, sizeof(int), 1, Data);
    fread(&ListFormatArraySize, sizeof(int), 1, Data);
    fread(&Root_WTEOBL_ArraySize, sizeof(int), 1, Data);
    fread(&Short_WTEOBL_ArraySize, sizeof(int), 1, Data);
    fread(&UnsignedChar_WTEOBL_ArraySize, sizeof(int), 1, Data);
    
    // Allocate memory to hold the arrays.
    TheNodeArray = (int *)malloc(NodeArraySize*sizeof(int));
    TheListFormatArray = (int *)malloc(ListFormatArraySize*sizeof(int));
    TheRoot_WTEOBL_Array = (int *)malloc(Root_WTEOBL_ArraySize*sizeof(int));
    TheShort_WTEOBL_Array = (short int *)malloc(Short_WTEOBL_ArraySize*sizeof(short int));
    TheUnsignedChar_WTEOBL_Array = (unsigned char *)malloc(UnsignedChar_WTEOBL_ArraySize*sizeof(unsigned char));
    
    // Read the 5 arrays into memory.
    fread(TheNodeArray, sizeof(int), NodeArraySize, Data);
    fread(TheListFormatArray, sizeof(int), ListFormatArraySize, Data);
    fread(TheRoot_WTEOBL_Array, sizeof(int), Root_WTEOBL_ArraySize, Data);
    fread(TheShort_WTEOBL_Array, sizeof(short int), Short_WTEOBL_ArraySize, Data);
    fread(TheUnsignedChar_WTEOBL_Array, sizeof(unsigned char), UnsignedChar_WTEOBL_ArraySize, Data);
    
    fclose(Data);
    
    // Make the proper assignments and adjustments to use the CWG.
    IndexCorrection = TotalNumberOfWords;
    WTEOBL_Transition = Short_WTEOBL_ArraySize;
    
    printf("The CWG data-structure is in memory and ready to use.\n\n");
    printf("CWG Header Values = |%7d |%7d |%5d |%3d |%5d |%7d |\n", TotalNumberOfWords, NodeArraySize, ListFormatArraySize,
    Root_WTEOBL_ArraySize, Short_WTEOBL_ArraySize, UnsignedChar_WTEOBL_ArraySize);
    
    Print_CWG_Word_List();
    
    // Run the demonstration program loop.
    while ( TRUE ) {
        printf("\nEnter a valid word to search for in the CWG...  Enter \"999\" to exit.\nInput: ");
        fgets(RawUserInput, INPUT_BUFFER_SIZE, stdin);
        CutOffExtraChars(RawUserInput);
        if ( !strncmp(RawUserInput, ESCAPE_SEQUENCE, THREE) ) break;
        MakeMeAllCapital(RawUserInput);
        if ( !ValidateInput(RawUserInput) ) {
            printf("\nInvalid user input...  Try again.\n\n");
            continue;
        }
        if ( SingleWordSearchBoolean(RawUserInput, strlen(RawUserInput)) ) printf("\n|%s|=[FOUND]", RawUserInput);
        else printf("\n|%s|=[BOGUS]", RawUserInput);
        HashReturnValue = SingleWordHashFunction(RawUserInput, strlen(RawUserInput));
        printf(", Hash Value|%d|\n\n", HashReturnValue);
    }
    
    // Free the dynamically allocated memory.
    free(TheNodeArray);
    free(TheListFormatArray);
    free(TheRoot_WTEOBL_Array);
    free(TheShort_WTEOBL_Array);
    free(TheUnsignedChar_WTEOBL_Array);
    
    return 0;
}



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