使用C++实现数独求解器：解密数独的算法之美
引言：
int board[9][9] = {
{5, 3, 0, 0, 7, 0, 0, 0, 0},
{6, 0, 0, 1, 9, 5, 0, 0, 0},
{0, 9, 8, 0, 0, 0, 0, 6, 0},
{8, 0, 0, 0, 6, 0, 0, 0, 3},
{4, 0, 0, 8, 0, 3, 0, 0, 1},
{7, 0, 0, 0, 2, 0, 0, 0, 6},
{0, 6, 0, 0, 0, 0, 2, 8, 0},
{0, 0, 0, 4, 1, 9, 0, 0, 5},
{0, 0, 0, 0, 8, 0, 0, 7, 9}
};
bool solveSudoku(int row, int col) {
if (row == 9) {
// 数独已解决
return true;
}
if (col == 9) {
// 当前行已填充完毕，进入下一行
return solveSudoku(row + 1, 0);
}
if (board[row][col] != 0) {
// 当前格子已填充数字，进入下一列
return solveSudoku(row, col + 1);
}
for (int num = 1; num <= 9; num++) {
if (isValid(row, col, num)) {
// 填充数字并进入下一列
board[row][col] = num;
if (solveSudoku(row, col + 1)) {
return true;
}
// 回溯，尝试其他数字
board[row][col] = 0;
}
}
return false;
}
bool isValid(int row, int col, int num) {
// 判断当前数字是否已存在于同一行或同一列
for (int i = 0; i < 9; i++) {
if (board[row][i] == num || board[i][col] == num) {
return false;
}
}
// 判断当前数字是否已存在于同一个3x3的小方格内
int startRow = (row / 3) * 3;
int startCol = (col / 3) * 3;
for (int i = startRow; i < startRow + 3; i++) {
for (int j = startCol; j < startCol + 3; j++) {
if (board[i][j] == num) {
return false;
}
}
}
return true;
}
#include <IOStream>
using namespace std;
int board[9][9] = {
{5, 3, 0, 0, 7, 0, 0, 0, 0},
{6, 0, 0, 1, 9, 5, 0, 0, 0},
{0, 9, 8, 0, 0, 0, 0, 6, 0},
{8, 0, 0, 0, 6, 0, 0, 0, 3},
{4, 0, 0, 8, 0, 3, 0, 0, 1},
{7, 0, 0, 0, 2, 0, 0, 0, 6},
{0, 6, 0, 0, 0, 0, 2, 8, 0},
{0, 0, 0, 4, 1, 9, 0, 0, 5},
{0, 0, 0, 0, 8, 0, 0, 7, 9}
};
bool isValid(int row, int col, int num) {
// 判断当前数字是否已存在于同一行或同一列
for (int i = 0; i < 9; i++) {
if (board[row][i] == num || board[i][col] == num) {
return false;
}
}
// 判断当前数字是否已存在于同一个3x3的小方格内
int startRow = (row / 3) * 3;
int startCol = (col / 3) * 3;
for (int i = startRow; i < startRow + 3; i++) {
for (int j = startCol; j < startCol + 3; j++) {
if (board[i][j] == num) {
return false;
}
}
}
return true;
}
bool solveSudoku(int row, int col) {
if (row == 9) {
// 数独已解决
return true;
}
if (col == 9) {
// 当前行已填充完毕，进入下一行
return solveSudoku(row + 1, 0);
}
if (board[row][col] != 0) {
// 当前格子已填充数字，进入下一列
return solveSudoku(row, col + 1);
}
for (int num = 1; num <= 9; num++) {
if (isValid(row, col, num)) {
// 填充数字并进入下一列
board[row][col] = num;
if (solveSudoku(row, col + 1)) {
return true;
}
// 回溯，尝试其他数字
board[row][col] = 0;
}
}
return false;
}
void printBoard() {
for (int i = 0; i < 9; i++) {
for (int j = 0; j < 9; j++) {
cout << board[i][j] << " ";
}
cout << endl;
}
}
int mAIn() {
if (solveSudoku(0, 0)) {
cout << "数独已解决：" << endl;
printBoard();
} else {
cout << "数独无解" << endl;
}
return 0;
}
