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tm4.c

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+
+#include <stdio.h>
+#include <stdbool.h>
+
+// 判断数字在行是否重复
+bool isRowValid(int matrix[9][9], int row, int num) {
+    for (int col = 0; col < 9; col++) {
+        if (matrix[row][col] == num) {
+            return false;
+        }
+    }
+    return true;
+}
+
+// 判断数字在列是否重复
+bool isColValid(int matrix[9][9], int col, int num) {
+    for (int row = 0; row < 9; row++) {
+        if (matrix[row][col] == num) {
+            return false;
+        }
+    }
+    return true;
+}
+
+// 判断数字在3x3的子矩阵是否重复
+bool isBlockValid(int matrix[9][9], int startRow, int startCol, int num) {
+    for (int row = 0; row < 3; row++) {
+        for (int col = 0; col < 3; col++) {
+            if (matrix[startRow + row][startCol + col] == num) {
+                return false;
+            }
+        }
+    }
+    return true;
+}
+
+// 判断是否满足数独矩阵的定义
+bool isValidSudoku(int matrix[9][9]) {
+    int sum = 0;
+
+    // 检查每行是否出现重复
+    for (int row = 0; row < 9; row++) {
+        sum = 0;
+        for (int col = 0; col < 9; col++) {
+            sum += matrix[row][col];
+            if (!isRowValid(matrix, row, matrix[row][col]) || !isColValid(matrix, col, matrix[row][col]) || !isBlockValid(matrix, row - row % 3, col - col % 3, matrix[row][col])) {
+                return false;
+            }
+        }
+        if (sum != 45) {
+            return false;
+        }
+    }
+
+    // 检查每列是否出现重复
+    for (int col = 0; col < 9; col++) {
+        sum = 0;
+        for (int row = 0; row < 9; row++) {
+            sum += matrix[row][col];
+            if (!isRowValid(matrix, row, matrix[row][col]) || !isColValid(matrix, col, matrix[row][col]) || !isBlockValid(matrix, row - row % 3, col - col % 3, matrix[row][col])) {
+                return false;
+            }
+        }
+        if (sum != 45) {
+            return false;
+        }
+    }
+
+    // 检查每个3x3子矩阵是否出现重复
+    for (int startRow = 0; startRow < 9; startRow += 3) {
+        for (int startCol = 0; startCol < 9; startCol += 3) {
+            sum = 0;
+            for (int row = 0; row < 3; row++) {
+                for (int col = 0; col < 3; col++) {
+                    sum += matrix[startRow + row][startCol + col];
+                    if (!isRowValid(matrix, startRow + row, matrix[startRow + row][startCol + col]) || !isColValid(matrix, startCol + col, matrix[startRow + row][startCol + col]) || !isBlockValid(matrix, startRow, startCol, matrix[startRow + row][startCol + col])) {
+                        return false;
+                    }
+                }
+            }
+            if (sum != 45) {
+                return false;
+            }
+        }
+    }
+
+    return true;
+}
+
+// 解数独
+bool solveSudoku(int matrix[9][9]) {
+    for (int row = 0; row < 9; row++) {
+        for (int col = 0; col < 9; col++) {
+            if (matrix[row][col] == 0) {
+                for (int num = 1; num <= 9; num++) {
+                    if (isRowValid(matrix, row, num) && isColValid(matrix, col, num) && isBlockValid(matrix, row - row % 3, col - col % 3, num)) {
+                        matrix[row][col] = num;
+                        if (solveSudoku(matrix)) {
+                            return true;
+                        }
+                        matrix[row][col] = 0; // 回溯
+                    }
+                }
+                return false;
+            }
+        }
+    }
+    return true;
+}
+
+// 打印数独矩阵
+void printMatrix(int matrix[9][9]) {
+    for (int row = 0; row < 9; row++) {
+        for (int col = 0; col < 9; col++) {
+            printf("%d ", matrix[row][col]);
+        }
+        printf("\n");
+    }
+}
+
+int main() {
+    int matrix[9][9] = {
+        {8, 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, 0},
+        {0, 0, 0, 0, 8, 0, 0, 7, 9}
+    };
+
+    printf("The original Sudoku matrix:\n");
+    printMatrix(matrix);
+
+    bool isSudokuValid = solveSudoku(matrix);
+
+    if (isSudokuValid) {
+        printf("True:Valid initial Sudoku matrix!\n");
+        printf("The solution of Sudoku matrix:\n");
+        printMatrix(matrix);
+    }
+    else {
+        printf("False:Invalid initial Sudoku matrix!\n");
+        printf("No solution!\n");
+    }
+
+    return 0;
+}