/*
* Board.h
* Permutation
*
* Created by James Pate Williams, Jr. on 7/21/08.
* Modified on Monday 11/24/2025
* Copyright 2008 James Pate Williams, Jr. All rights reserved.
*
*/
#ifndef _Board_
#define _Board_
#include <fstream>
#include <vector>
class Board {
private:
char state[9];
std::vector<std::vector<char>> board;
public:
Board(void);
Board(const Board &board);
Board(const char b[3][3]);
Board(const std::vector<char> &v);
char GetState(int n) const;
void PrintBoard(int n) const;
void WriteBoard(std::ofstream &out) const;
friend bool operator == (const Board &b1, const Board &b2);
friend bool operator != (const Board &b1, const Board &b2);
friend bool Found(const Board &initial, const Board &board);
friend bool Win(const Board b, char winner[8]);
friend bool LegalBoard(
bool& legal, bool& won, char& whoWon, const Board b);
friend void PrintBoard(char board[3][3], int number);
static const char CharX, CharO, CharS;
};
#endif
/*
* Board.cpp
* Permutation
*
* Created by James Pate Williams, Jr. on 7/21/08.
* Copyright 2008 James Pate Williams, Jr. All rights reserved.
*
*/
#include <algorithm>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <vector>
#include "Board.h"
const char Board::CharO = 'o';
const char Board::CharX = 'x';
const char Board::CharS = '_';
Board::Board(void) {
board.resize(3, std::vector<char>(3));
for (int i = 0; i < 9; i++)
state[i] = '\0';
}
Board::Board(const Board &b) {
board.resize(3, std::vector<char>(3));
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
state[3 * i + j] = board[i][j] = b.state[3 * i + j];
}
Board::Board(const char b[3][3]) {
board.resize(3, std::vector<char>(3));
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
state[3 * i + j] = board[i][j] = b[i][j];
}
Board::Board(const std::vector<char> &v) {
board.resize(3, std::vector<char>(3));
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
state[3 * i + j] = board[i][j] = v[3LL * i + j];
}
char Board::GetState(int n) const {
return state[n];
}
void Board::PrintBoard(int n) const {
std::cout << n << std::endl;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++)
std::cout << state[3 * i + j];
std::cout << std::endl;
}
std::cout << std::endl;
std::cout << std::endl;
}
void Board::WriteBoard(std::ofstream &out) const {
for (int i = 0; i < 9; i++)
out << state[i];
out << std::endl;
}
bool operator == (const Board &b1, const Board &b2) {
int i, equal = 0;
for (i = 0; i < 9; i++)
if (b1.state[i] == b2.state[i])
equal++;
return equal == 9;
}
bool operator != (const Board &b1, const Board &b2) {
for (int i = 0; i < 9; i++)
if (b1.state[i] == b2.state[i])
return false;
return true;
}
bool Found(const Board &initial, const Board &board) {
// reflections
if (initial.state[0] == board.state[6] && initial.state[1] == board.state[7] &&
initial.state[2] == board.state[8] && initial.state[3] == board.state[3] &&
initial.state[4] == board.state[4] && initial.state[5] == board.state[5] &&
initial.state[6] == board.state[0] && initial.state[7] == board.state[1] &&
initial.state[8] == board.state[2])
return true;
if (initial.state[0] == board.state[2] && initial.state[1] == board.state[1] &&
initial.state[2] == board.state[0] && initial.state[3] == board.state[5] &&
initial.state[4] == board.state[4] && initial.state[5] == board.state[3] &&
initial.state[6] == board.state[8] && initial.state[7] == board.state[7] &&
initial.state[8] == board.state[6])
return true;
if (initial.state[0] == board.state[0] && initial.state[1] == board.state[3] &&
initial.state[2] == board.state[6] && initial.state[3] == board.state[1] &&
initial.state[4] == board.state[4] && initial.state[5] == board.state[7] &&
initial.state[6] == board.state[2] && initial.state[7] == board.state[5] &&
initial.state[8] == board.state[8])
return true;
if (initial.state[0] == board.state[8] && initial.state[1] == board.state[5] &&
initial.state[2] == board.state[2] && initial.state[3] == board.state[7] &&
initial.state[4] == board.state[4] && initial.state[5] == board.state[1] &&
initial.state[6] == board.state[6] && initial.state[7] == board.state[3] &&
initial.state[8] == board.state[0])
return true;
// rotations
if (initial.state[0] == board.state[6] && initial.state[1] == board.state[3] &&
initial.state[2] == board.state[0] && initial.state[3] == board.state[7] &&
initial.state[4] == board.state[4] && initial.state[5] == board.state[1] &&
initial.state[6] == board.state[8] && initial.state[7] == board.state[5] &&
initial.state[8] == board.state[2])
return true;
if (initial.state[0] == board.state[8] && initial.state[1] == board.state[7] &&
initial.state[2] == board.state[6] && initial.state[3] == board.state[5] &&
initial.state[4] == board.state[4] && initial.state[5] == board.state[3] &&
initial.state[6] == board.state[2] && initial.state[7] == board.state[1] &&
initial.state[8] == board.state[0])
return true;
if (initial.state[0] == board.state[2] && initial.state[1] == board.state[5] &&
initial.state[2] == board.state[8] && initial.state[3] == board.state[1] &&
initial.state[4] == board.state[4] && initial.state[5] == board.state[7] &&
initial.state[6] == board.state[0] && initial.state[7] == board.state[3] &&
initial.state[8] == board.state[6])
return true;
// equal
return initial == board;
}
bool Win(const Board b, char winner[8]) {
bool win = false;
for (int i = 0; i < 8; i++)
winner[i] = Board::CharS;
if (b.board[0][0] == b.board[0][1] && b.board[0][0] ==
b.board[0][2] && b.board[0][0] != Board::CharS) {
winner[0] = b.board[0][0];
win = true;
}
if (b.board[1][0] == b.board[1][1] && b.board[1][0] ==
b.board[1][2] && b.board[1][0] != Board::CharS) {
winner[1] = b.board[1][0];
win = true;
}
if (b.board[2][0] == b.board[2][1] && b.board[2][0] ==
b.board[2][2] && b.board[2][0] != Board::CharS) {
winner[2] = b.board[2][0];
win = true;
}
if (b.board[0][0] == b.board[1][0] && b.board[0][0] ==
b.board[2][0] && b.board[0][0] != Board::CharS) {
winner[3] = b.board[0][0];
win = true;
}
if (b.board[0][1] == b.board[1][1] && b.board[0][1] ==
b.board[2][1] && b.board[0][1] != Board::CharS) {
winner[4] = b.board[0][1];
win = true;
}
if (b.board[0][2] == b.board[1][2] && b.board[0][2] ==
b.board[2][2] && b.board[0][2] != Board::CharS) {
winner[5] = b.board[0][2];
win = true;
}
if (b.board[0][0] == b.board[1][1] && b.board[0][0] ==
b.board[2][2] && b.board[0][0] != Board::CharS) {
winner[6] = b.board[0][0];
win = true;
}
if (b.board[0][2] == b.board[1][1] && b.board[0][2] ==
b.board[2][0] && b.board[0][2] != Board::CharS) {
winner[7] = b.board[0][2];
win = true;
}
return win;
}
void PrintBoard(char board[3][3], int number) {
std::cout << "number = " << number << std::endl;
std::cout << std::endl;
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++)
std::cout << board[i][j];
std:: cout << std::endl;
}
std::cout << std::endl;
}
bool LegalBoard(
bool &legal, bool &won, char &whoWon, const Board b) {
bool winO, winX;
char winner[8];
int countO = 0, countS = 0, countX = 0;
int i, j, oWins = 0, xWins = 0;
legal = won = false;
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
if (b.board[i][j] == Board::CharO)
countO++;
else if (b.board[i][j] == Board::CharX)
countX++;
else if (b.board[i][j] == Board::CharS)
countS++;
}
}
if ((countX >= 3 || countO >= 3) && Win(b, winner)) {
for (i = 0; i < 8; i++) {
if (winner[i] == Board::CharX)
xWins++;
else if (winner[i] == Board::CharO)
oWins++;
}
winX = (xWins >= 1 && oWins == 0) &&
(countX <= 5 && countO <= 4 && countX == countO + 1);
winO = (xWins == 0 && oWins >= 1) &&
(countO <= 5 && countX <= 4 && countO == countX + 1);
legal = won = winX || winO;
if (won && winX)
whoWon = Board::CharX;
else if (won && winO)
whoWon = Board::CharO;
}
else
legal = (countX <= 5 && countO <= 4 && countX == countO + 1) ||
(countO <= 5 && countX <= 4 && countO == countX + 1);
return legal;
}
#define _WriteBV_
#include <algorithm>
#ifdef _WriteBV_
#include <fstream>
#endif
#include <iomanip>
#include <iostream>
#include <vector>
#include "Board.h"
static int Compare(const void *vPtr1, const void *vPtr2) {
char *cPtr1 = (char *) vPtr1;
char *cPtr2 = (char *) vPtr2;
return strcmp(cPtr1, cPtr2);
}
static void EnumerateTicTacToe(void) {
bool legal, won;
char b[3][3], whoWon;
char tree[3][3][3][3][3][3][3][3][3];
int i0, i1, i2, i3, i4, i5, i6, i7, i8;
int legals = 0, number = 0, wCount = 0;
int xCount = 0, oCount = 0;
int bvSize, i, j;
std::vector<Board> boardVector;
for (i0 = 0; i0 < 3; i0++) {
for (i1 = 0; i1 < 3; i1++) {
for (i2 = 0; i2 < 3; i2++) {
for (i3 = 0; i3 < 3; i3++) {
for (i4 = 0; i4 < 3; i4++) {
for (i5 = 0; i5 < 3; i5++) {
for (i6 = 0; i6 < 3; i6++) {
for (i7 = 0; i7 < 3; i7++) {
for (i8 = 0; i8 < 3; i8++) {
if (i0 == 0)
b[0][0] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharX;
else if (i0 == 1)
b[0][0] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharO;
else if (i0 == 2)
b[0][0] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharS;
if (i1 == 0)
b[0][1] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharX;
else if (i1 == 1)
b[0][1] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharO;
else if (i1 == 2)
b[0][1] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharS;
if (i2 == 0)
b[0][2] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharX;
else if (i2 == 1)
b[0][2] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharO;
else if (i2 == 2)
b[0][2] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharS;
if (i3 == 0)
b[1][0] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharX;
else if (i3 == 1)
b[1][0] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharO;
else if (i3 == 2)
b[1][0] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharS;
if (i4 == 0)
b[1][1] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharX;
else if (i4 == 1)
b[1][1] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharO;
else if (i4 == 2)
b[1][1] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharS;
if (i5 == 0)
b[1][2] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharX;
else if (i5 == 1)
b[1][2] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharO;
else if (i5 == 2)
b[1][2] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharS;
if (i6 == 0)
b[2][0] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharX;
else if (i6 == 1)
b[2][0] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharO;
else if (i6 == 2)
b[2][0] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharS;
if (i7 == 0)
b[2][1] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharX;
else if (i7 == 1)
b[2][1] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharO;
else if (i7 == 2)
b[2][1] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharS;
if (i8 == 0)
b[2][2] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharX;
else if (i8 == 1)
b[2][2] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharO;
else if (i8 == 2)
b[2][2] = tree[i0][i1][i2][i3][i4][i5][i6][i7][i8] = Board::CharS;
Board bb(b);
if (LegalBoard(legal, won, whoWon, bb)) {
Board board(b);
legals++;
if (won) {
wCount++;
if (whoWon == Board::CharX)
xCount++;
else if (whoWon == Board::CharO)
oCount++;
}
boardVector.push_back(board);
}
number++;
}}}}}}}}}
for (i = 0; i < boardVector.size() - 1; i++)
for (j = i; j < boardVector.size(); j++)
if (Found(boardVector[i], boardVector[j]))
boardVector.erase(boardVector.begin() + j);
bvSize = (int)boardVector.size();
std::cout << std::setw(4) << "legal total = " << legals << std::endl;
std::cout << std::setw(4) << "xWins total = " << xCount << std::endl;
std::cout << std::setw(4) << "oWins total = " << xCount << std::endl;
std::cout << std::setw(4) << "oxWin total = " << xCount + oCount << std::endl;
std::cout << std::setw(4) << "unique size = " << boardVector.size();
std::cout << std::endl;
#ifdef _WriteBV_
std::cout << std::endl;
std::ofstream outFile("Tic TacToe Game Tree Enumeration.txt");
std::cout << std::endl;
for (i = 0; i < bvSize; i++) {
boardVector[i].PrintBoard(i + 1);
boardVector[i].WriteBoard(outFile);
}
#endif
}
int main (int argc, char * const argv[]) {
EnumerateTicTacToe();
return 0;
}
Author: jamespatewilliamsjr
My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.
View all posts by jamespatewilliamsjr
Numerical Explorations 