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program4.c

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+#include <stdio.h>
+#include <stdbool.h>
+#include <stdlib.h>
+#include <time.h>
+
+void printMatrix(int matrix[9][9]) {
+    for (int i = 0; i < 9; i++) {
+        if (i == 0 || i == 3 || i == 6) {
+            printf("|-----------------------|\n");
+        }
+        for (int j = 0; j < 9; j++) {
+            if (j == 0 || j == 3 || j == 6) {
+                printf("| ");
+            }
+            if (matrix[i][j] == 0) {
+                printf(". ");
+            }
+            else {
+                printf("%d ", matrix[i][j]);
+            }
+            printf("|\n");
+        }
+        printf("|-----------------------|\n");
+    }
+}
+
+
+bool usedInRow(int matrix[9][9], int row, int num) {
+    for (int col = 0; col < 9; col++) {
+        if (matrix[row][col] == num) {
+            return true;
+        }
+    }
+    return false;
+}
+bool usedInCol(int matrix[9][9], int col, int num) {
+    for (int row = 0; row < 9; row++) {
+        if (matrix[row][col] == num) {
+            return true;
+        }
+    }
+    return false;
+}
+
+bool usedInBox(int matrix[9][9], int boxStartRow, int boxStartCol, int num) {
+    for (int row = 0; row < 3; row++) {
+        for (int col = 0; col < 3; col++) {
+            if (matrix[row + boxStartRow][col + boxStartCol] == num) {
+                return true;
+            }
+        }
+    }
+    return false;
+}bool isSafe(int matrix[9][9], int row, int col, int num) {
+    return!usedInRow(matrix, row, num) &&!usedInCol(matrix, col, num) &&!usedInBox(matrix, row - row % 3, col - col % 3, num);
+}
+bool findEmptyLocation(int matrix[9][9], int *row, int *col) {
+    for (*row = 0; *row < 9; (*row)++) {
+        for (*col = 0; *col < 9; (*col)++) {
+            if (matrix[*row][*col] == 0) {
+                return true;
+            }
+        }
+    }
+    return false;
+}
+
+bool solveSudoku(int matrix[9][9]) {
+    int row, col;
+    if (!findEmptyLocation(matrix, &row, &col)) {
+        return true; // Êý¶ÀÒѽâ¾ö
+    }
+    for (int num = 1; num <= 9; num++) {
+        if (isSafe(matrix, row, col, num)) {
+            matrix[row][col] = num;
+            if (solveSudoku(matrix)) {
+                return true;
+            }
+            matrix[row][col] = 0; // »ØËÝ
+        }
+    }
+    return false;
+}
+
+bool checkRows(int matrix[9][9]) {
+    for (int i = 0; i < 9; i++) {
+        int count[9] = {0};
+        for (int j = 0; j < 9; j++) {
+            if (matrix[i][j] > 0 && matrix[i][j] <= 9) {
+                int num = matrix[i][j] - 1;
+                if (count[num] > 0) {
+                    return false;
+                }
+                count[num]++;
+            }
+        }
+    }
+    return true;
+}
+
+bool checkColumns(int matrix[9][9]) {
+    for (int j = 0; j < 9; j++) {
+        int count[9] = {0};
+        for (int i = 0; i < 9; i++) {
+            if (matrix[i][j] > 0 && matrix[i][j] <= 9) {
+                int num = matrix[i][j] - 1;
+                if (count[num] > 0) {
+                    return false;
+                }
+                count[num]++;
+            }
+        }
+    }
+    return true;
+}
+
+bool checkSubMatrices(int matrix[9][9]) {
+    for (int row = 0; row < 9; row += 3) {
+        for (int col = 0; col < 9; col += 3) {
+            int count[9] = {0};
+            for (int i = row; i < row + 3; i++) {
+                for (int j = col; j < col + 3; j++) {
+                    if (matrix[i][j] > 0 && matrix[i][j] <= 9) {
+                        int num = matrix[i][j] - 1;
+                        if (count[num] > 0) {
+                            return false;
+                        }
+                        count[num]++;
+                    }
+                }
+            }
+        }
+    }
+    return true;
+}
+
+bool isSudokuMatrix(int matrix[9][9]) {
+    return checkRows(matrix) && checkColumns(matrix) && checkSubMatrices(matrix);
+}
+
+int main() {
+    printf("The original Sudoku matrix: \n");
+    int matrix[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}
+    };
+    printMatrix(matrix);
+    bool valid = isSudokuMatrix(matrix);
+    if (valid) {
+        printf("True:Valid initial Sudoku matrix!\n");
+        if (solveSudoku(matrix)) {
+            printf("The solution of Sudoku matrix:\n");
+            printMatrix(matrix);
+        } else {
+            printf("No solution!\n");
+        }
+    } else {
+        printf("False:Invalid initial Sudoku matrix!\n");
+        for (int j = 0; j < 9; j++) {
+            int count[9] = {0};
+            for (int i = 0; i < 9; i++) {
+                if (matrix[i][j] > 0 && matrix[i][j] <= 9) {
+                    int num = matrix[i][j] - 1;
+                    if (count[num] > 0) {
+                        printf("The number %d in the col %d has been used!\n", matrix[i][j], j);
+                        break;
+                    }
+                    count[num]++;
+                }
+            }
+        }
+        printf("No solution!\n");
+    }
+    return 0;
+}