Tag: coding
Blog Entry © Sunday, November 30, 2025, by James Pate Williams, Jr. and the Microsoft Artificially Intelligent Agent, the Copilot
Blog Entry © Saturday, November 28, 2025, by James Pate Williams, Jr. Fair Coin and Fair Dice Probabilities
Blog Entry © Tuesday 25, 2025, by James Pate Williams, Jr. Enumeration of the Tic-Tac-Toe Game Tree
/*
* 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;
}
Blog Entry © Monday, November 24, 2025, by James Pate Williams, Jr., A* Informed Search Application to Solve the 15-Tile Puzzle
Blog Entry © Sunday, November 23, 2025, by James Pate Williams, Jr. Modification of My A* Informed Search Solver for the 8-Tile Puzzle
Blog Entry © Friday, November 21, 2025, by James Pate Williams, Jr., Win32 C/C++ Desktop GUI Solution of the 15-Tile Puzzle Using Iterative Deepening A* Informed Seach Algorithm
Blog Entry © Monday, November 17, 2025, by James Pate Williams, Jr. An Elitist Evolutionary Hill Climber to Solve the 8-Tile Puzzle
Blog Entry © Wednesday, September 3, 2025, by James Pate Williams, Jr. Solution of Exercise 1.11 in Modern Quantum Chemistry an Introduction to Advanced Electronic Structure Theory © 1996 by Attila Szabo and Neil S. Ostlund
// EigenVV2x2.cpp (c) Wednesday, September 3, 2025
// by James Pate Williams, Jr., BA, BS, MSwE, PhD
// Solution to Exercise 1.11 in "Quantum Chemistry
// an Introduction to Advanced Electronic Structure
// Theory (c) 1996 by Attila Szabo and Neil S. Ostlund
#include "pch.h"
#include "framework.h"
#include "EigenVV2x2.h"
#define MAX_LOADSTRING 100
// Global Variables:
HINSTANCE hInst; // current instance
WCHAR szTitle[MAX_LOADSTRING]; // The title bar text
WCHAR szWindowClass[MAX_LOADSTRING]; // the main window class name
std::wstring text; // output wide string
// Forward declarations of functions included in this code module:
ATOM MyRegisterClass(HINSTANCE hInstance);
BOOL InitInstance(HINSTANCE, int);
LRESULT CALLBACK WndProc(HWND, UINT, WPARAM, LPARAM);
INT_PTR CALLBACK About(HWND, UINT, WPARAM, LPARAM);
int APIENTRY wWinMain(_In_ HINSTANCE hInstance,
_In_opt_ HINSTANCE hPrevInstance,
_In_ LPWSTR lpCmdLine,
_In_ int nCmdShow)
{
UNREFERENCED_PARAMETER(hPrevInstance);
UNREFERENCED_PARAMETER(lpCmdLine);
// TODO: Place code here.
// Initialize global strings
LoadStringW(hInstance, IDS_APP_TITLE, szTitle, MAX_LOADSTRING);
LoadStringW(hInstance, IDC_EIGENVV2X2, szWindowClass, MAX_LOADSTRING);
MyRegisterClass(hInstance);
// Perform application initialization:
if (!InitInstance (hInstance, nCmdShow))
{
return FALSE;
}
HACCEL hAccelTable = LoadAccelerators(hInstance, MAKEINTRESOURCE(IDC_EIGENVV2X2));
MSG msg;
// Main message loop:
while (GetMessage(&msg, nullptr, 0, 0))
{
if (!TranslateAccelerator(msg.hwnd, hAccelTable, &msg))
{
TranslateMessage(&msg);
DispatchMessage(&msg);
}
}
return (int) msg.wParam;
}
//
// FUNCTION: MyRegisterClass()
//
// PURPOSE: Registers the window class.
//
ATOM MyRegisterClass(HINSTANCE hInstance)
{
WNDCLASSEXW wcex;
wcex.cbSize = sizeof(WNDCLASSEX);
wcex.style = CS_HREDRAW | CS_VREDRAW;
wcex.lpfnWndProc = WndProc;
wcex.cbClsExtra = 0;
wcex.cbWndExtra = 0;
wcex.hInstance = hInstance;
wcex.hIcon = LoadIcon(hInstance, MAKEINTRESOURCE(IDI_EIGENVV2X2));
wcex.hCursor = LoadCursor(nullptr, IDC_ARROW);
wcex.hbrBackground = (HBRUSH)(COLOR_WINDOW+1);
wcex.lpszMenuName = MAKEINTRESOURCEW(IDC_EIGENVV2X2);
wcex.lpszClassName = szWindowClass;
wcex.hIconSm = LoadIcon(wcex.hInstance, MAKEINTRESOURCE(IDI_SMALL));
return RegisterClassExW(&wcex);
}
//
// FUNCTION: InitInstance(HINSTANCE, int)
//
// PURPOSE: Saves instance handle and creates main window
//
// COMMENTS:
//
// In this function, we save the instance handle in a global variable and
// create and display the main program window.
//
BOOL InitInstance(HINSTANCE hInstance, int nCmdShow)
{
hInst = hInstance; // Store instance handle in our global variable
HWND hWnd = CreateWindowW(szWindowClass, szTitle, WS_OVERLAPPEDWINDOW,
CW_USEDEFAULT, 0, CW_USEDEFAULT, 0, nullptr, nullptr, hInstance, nullptr);
if (!hWnd)
{
return FALSE;
}
ShowWindow(hWnd, nCmdShow);
UpdateWindow(hWnd);
return TRUE;
}
#define IDC_STATIC1 1000
#define IDC_STATIC2 1010
#define IDC_STATIC3 1020
#define IDC_STATIC4 1030
#define IDC_EDIT_A11 2000
#define IDC_EDIT_A12 2010
#define IDC_EDIT_A21 2020
#define IDC_EDIT_A22 2030
#define IDC_EDIT_MULTILINE 3000
#define IDC_BUTTON_COMPUTE 4000
#define IDC_BUTTON_CANCEL 4010
//
// FUNCTION: WndProc(HWND, UINT, WPARAM, LPARAM)
//
// PURPOSE: Processes messages for the main window.
//
// WM_COMMAND - process the application menu
// WM_PAINT - Paint the main window
// WM_DESTROY - post a quit message and return
//
//
LRESULT CALLBACK WndProc(HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam)
{
static HFONT hFont = { };
static HWND hEditMultiline = { };
static HWND hEditA11 = { };
static HWND hEditA12 = { };
static HWND hEditA21 = { };
static HWND hEditA22 = { };
switch (message)
{
case WM_CREATE:
{
hFont = CreateFont(16, 0, 0, 0, FW_NORMAL, FALSE, FALSE, FALSE,
ANSI_CHARSET, OUT_DEFAULT_PRECIS, CLIP_DEFAULT_PRECIS,
DEFAULT_QUALITY, DEFAULT_PITCH | FF_SWISS, L"Courier New Bold");
CreateWindowEx(0, L"STATIC", L"A[1][1]:", WS_CHILD | WS_VISIBLE,
10, 10, 80, 20, hWnd, (HMENU)IDC_STATIC1, hInst, NULL);
CreateWindowEx(0, L"STATIC", L"A[1][2]:", WS_CHILD | WS_VISIBLE,
10, 40, 80, 20, hWnd, (HMENU)IDC_STATIC2, hInst, NULL);
CreateWindowEx(0, L"STATIC", L"A[2][1]:", WS_CHILD | WS_VISIBLE,
10, 70, 80, 20, hWnd, (HMENU)IDC_STATIC3, hInst, NULL);
CreateWindowEx(0, L"STATIC", L"A[2][2]:", WS_CHILD | WS_VISIBLE,
10, 100, 80, 20, hWnd, (HMENU)IDC_STATIC4, hInst, NULL);
hEditA11 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
100, 10, 200, 20, hWnd, (HMENU)IDC_EDIT_A11, hInst, NULL);
hEditA12 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
100, 40, 200, 20, hWnd, (HMENU)IDC_EDIT_A12, hInst, NULL);
hEditA21 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
100, 70, 200, 20, hWnd, (HMENU)IDC_EDIT_A21, hInst, NULL);
hEditA22 = CreateWindowEx(0, L"EDIT", NULL, WS_CHILD | WS_VISIBLE | WS_BORDER,
100, 100, 200, 20, hWnd, (HMENU)IDC_EDIT_A22, hInst, NULL);
hEditMultiline = CreateWindowEx(
WS_EX_CLIENTEDGE, // Extended style for sunken border
TEXT("EDIT"), // Class name
TEXT(""), // Initial text (can be blank)
WS_CHILD | WS_VISIBLE | WS_VSCROLL | ES_AUTOHSCROLL |
ES_LEFT | ES_MULTILINE | ES_AUTOVSCROLL | WS_HSCROLL | WS_VSCROLL,
310, 10, 300, 300, // Position and size
hWnd, // Parent window handle
(HMENU)IDC_EDIT_MULTILINE, // Unique control ID
hInst, // Application instance
NULL // Extra parameter
);
CreateWindowEx(0, L"BUTTON", L"Compute", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
10, 130, 80, 30, hWnd, (HMENU)IDC_BUTTON_COMPUTE, hInst, NULL);
CreateWindowEx(0, L"BUTTON", L"Cancel", WS_CHILD | WS_VISIBLE | BS_PUSHBUTTON,
220, 130, 80, 30, hWnd, (HMENU)IDC_BUTTON_CANCEL, hInst, NULL);
SendMessage(hEditMultiline, WM_SETFONT, (WPARAM)hFont, TRUE);
SetDlgItemText(hWnd, IDC_EDIT_A11, L"3");
SetDlgItemText(hWnd, IDC_EDIT_A12, L"1");
SetDlgItemText(hWnd, IDC_EDIT_A21, L"1");
SetDlgItemText(hWnd, IDC_EDIT_A22, L"3");
}
break;
case WM_COMMAND:
{
int wmId = LOWORD(wParam);
// Parse the menu selections:
switch (wmId)
{
case IDM_ABOUT:
DialogBox(hInst, MAKEINTRESOURCE(IDD_ABOUTBOX), hWnd, About);
break;
case IDC_BUTTON_COMPUTE:
{
WCHAR line[128] = L"";
text = L"";
// eigenvalues
std::vector<double> omega(3);
// matrix
std::vector<std::vector<double>> A(3,
std::vector<double>(3));
std::vector<std::vector<double>> B(3,
std::vector<double>(3));
// eigenvectors
std::vector<std::vector<double>> c(3,
std::vector<double>(3));
GetWindowText(hEditA11, line, 128);
std::wstring A11Str(line);
A[1][1] = std::stod(A11Str);
GetWindowText(hEditA12, line, 128);
std::wstring A12Str(line);
A[1][2] = std::stod(A12Str);
GetWindowText(hEditA21, line, 128);
std::wstring A21Str(line);
A[2][1] = std::stod(A21Str);
GetWindowText(hEditA22, line, 128);
std::wstring A22Str(line);
A[2][2] = std::stod(A22Str);
double term1 = A[1][1] + A[2][2];
double term2 = pow(A[2][2] - A[1][1], 2.0);
double term3 = 4.0 * A[1][2] * A[2][1];
// compute eigenvalues
omega[1] = 0.5 * (term1 - sqrt(term2 + term3));
omega[2] = 0.5 * (term1 + sqrt(term2 + term3));
swprintf_s(line, L"Eigenvalues:\r\n\r\n");
text += std::wstring(line);
swprintf_s(line, L"omega 1 = %13.10lf\r\n", omega[1]);
text += std::wstring(line);
swprintf_s(line, L"omega 2 = %13.10lf\r\n\r\n", omega[2]);
text += std::wstring(line);
// compute eigenvalues using a unitary transformation
// matrix A must be symmetric
double theta0 = 0.0;
if (A[1][1] == A[2][2])
{
theta0 = 0.5 * acos(0.0);
}
else
{
theta0 = 0.5 * atan(2.0 * A[1][2] /
(A[1][1] - A[2][2]));
}
// compute the eigenvalues
omega[1] = A[1][1] * pow(cos(theta0), 2.0) +
A[2][2] * pow(sin(theta0), 2.0) +
A[1][2] * sin(2.0 * theta0);
omega[2] = A[1][1] * pow(cos(theta0), 2.0) +
A[2][2] * pow(sin(theta0), 2.0) -
A[1][2] * sin(2.0 * theta0);
swprintf_s(line, L"Eigenvalues:\r\n\r\n");
text += std::wstring(line);
swprintf_s(line, L"omega 1 = %13.10lf\r\n", omega[1]);
text += std::wstring(line);
swprintf_s(line, L"omega 2 = %13.10lf\r\n\r\n", omega[2]);
text += std::wstring(line);
// compute eigenvectors
c[1][1] = cos(theta0);
c[1][2] = sin(theta0);
c[2][1] = sin(theta0);
c[2][2] = -cos(theta0);
swprintf_s(line, L"Eigenvectors:\r\n\r\n");
text += std::wstring(line);
swprintf_s(line, L"c 11 = %13.10lf\r\n", c[1][1]);
text += std::wstring(line);
swprintf_s(line, L"c 12 = %13.10lf\r\n", c[1][2]);
text += std::wstring(line);
swprintf_s(line, L"c 21 = %13.10lf\r\n", c[2][1]);
text += std::wstring(line);
swprintf_s(line, L"c 22 = %13.10lf\r\n", c[2][2]);
text += std::wstring(line);
SetWindowText(hEditMultiline, text.c_str());
break;
}
case IDC_BUTTON_CANCEL:
{
PostQuitMessage(0);
break;
}
break;
case IDM_EXIT:
DestroyWindow(hWnd);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
}
break;
case WM_PAINT:
{
PAINTSTRUCT ps;
HDC hdc = BeginPaint(hWnd, &ps);
// TODO: Add any drawing code that uses hdc here...
EndPaint(hWnd, &ps);
}
break;
case WM_DESTROY:
PostQuitMessage(0);
break;
default:
return DefWindowProc(hWnd, message, wParam, lParam);
}
return 0;
}
// Message handler for about box.
INT_PTR CALLBACK About(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam)
{
UNREFERENCED_PARAMETER(lParam);
switch (message)
{
case WM_INITDIALOG:
return (INT_PTR)TRUE;
case WM_COMMAND:
if (LOWORD(wParam) == IDOK || LOWORD(wParam) == IDCANCEL)
{
EndDialog(hDlg, LOWORD(wParam));
return (INT_PTR)TRUE;
}
break;
}
return (INT_PTR)FALSE;
}
Blog Entry © Sunday, March 29, 2025, by James Pate Williams, Jr., BA, BS, Master of Software Engineering, PhD Slater Determinant Coefficients for Z = 2 to 4
Enter the atomic number Z (2 to 6 or 0 to quit): 2
2 1 1 + a(1)b(2)
1 0 0 - a(2)b(1)
# Even Permutations = 1
Enter the atomic number Z (2 to 6 or 0 to quit): 3
6 3 1 + a(1)b(2)c(3)
5 2 0 - a(1)b(3)c(2)
4 2 0 - a(2)b(1)c(3)
3 1 1 + a(2)b(3)c(1)
2 1 1 + a(3)b(1)c(2)
1 0 0 - a(3)b(2)c(1)
# Even Permutations = 3
Enter the atomic number Z (2 to 6 or 0 to quit): 4
24 12 0 + a(1)b(2)c(3)d(4)
23 11 1 - a(1)b(2)c(4)d(3)
22 11 1 - a(1)b(3)c(2)d(4)
21 10 0 + a(1)b(3)c(4)d(2)
20 10 0 + a(1)b(4)c(2)d(3)
19 9 1 - a(1)b(4)c(3)d(2)
18 9 1 - a(2)b(1)c(3)d(4)
17 8 0 + a(2)b(1)c(4)d(3)
16 8 0 + a(2)b(3)c(1)d(4)
15 7 1 - a(2)b(3)c(4)d(1)
14 7 1 - a(2)b(4)c(1)d(3)
13 6 0 + a(2)b(4)c(3)d(1)
12 6 0 + a(3)b(1)c(2)d(4)
11 5 1 - a(3)b(1)c(4)d(2)
10 5 1 - a(3)b(2)c(1)d(4)
9 4 0 + a(3)b(2)c(4)d(1)
8 4 0 + a(3)b(4)c(1)d(2)
7 3 1 - a(3)b(4)c(2)d(1)
6 3 1 - a(4)b(1)c(2)d(3)
5 2 0 + a(4)b(1)c(3)d(2)
4 2 0 + a(4)b(2)c(1)d(3)
3 1 1 - a(4)b(2)c(3)d(1)
2 1 1 - a(4)b(3)c(1)d(2)
1 0 0 + a(4)b(3)c(2)d(1)
# Even Permutations = 12
Enter the atomic number Z (2 to 6 or 0 to quit):
// AOPermutations.cpp : This file contains the 'main' function.
// Program execution begins and ends there.
// Copyright (c) Saturday, March 29, 2025
// by James Pate Williams, Jr., BA, BS, MSwE, PhD
// Signs of the atomic orbitals in a Slater Determinant
#include <algorithm>
#include <iostream>
#include <string>
#include <vector>
int main()
{
char alpha[] = { 'a', 'b', 'c', 'd', 'e', 'f' }, line[128] = {};
int factorial[7] = { 1, 1, 2, 6, 24, 120, 720 };
while (true)
{
int col = 0, counter = 0, row = 0, sign = 1, t = 0, Z = 0, zfact = 0;
int numberEven = 0;
std::cout << "Enter the atomic number Z (2 to 6 or 0 to quit): ";
std::cin.getline(line, 127);
std::string str(line);
Z = std::stoi(str);
if (Z == 0)
{
break;
}
if (Z < 2 || Z > 6)
{
std::cout << "Illegal Z, please try again" << std::endl;
continue;
}
zfact = factorial[Z];
std::vector<char> orb(Z);
std::vector<int> tmp(Z), vec(Z);
for (int i = 0; i < Z; i++)
{
orb[i] = alpha[i];
vec[i] = i + 1;
}
do
{
for (int i = 0; i < (int)vec.size(); i++)
{
tmp[i] = vec[i];
}
t = 0;
do
{
t++;
} while (std::next_permutation(tmp.begin(), tmp.end()));
std::cout << t << '\t' << t / 2 << '\t';
std::cout << (t / 2 & 1) << '\t';
if (Z == 2 || Z == 3)
{
if ((t / 2 & 1) == 0)
{
std::cout << "-\t";
}
else
{
std::cout << "+\t";
numberEven++;
}
}
else
{
if ((t / 2 & 1) == 1)
{
std::cout << "-\t";
}
else
{
std::cout << "+\t";
numberEven++;
}
}
for (int i = 0; i < Z; i++)
{
std::cout << orb[i] << '(' << vec[i] << ')';
}
row++;
std::cout << std::endl;
if (zfact != 2 && row == zfact)
{
std::cout << std::endl;
break;
}
row %= Z;
} while (std::next_permutation(vec.begin(), vec.end()));
std::cout << "# Even Permutations = ";
std::cout << numberEven << std::endl;
}
return 0;
}
Numerical Explorations 