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task 4.c

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+#include <stdio.h>
+#include <stdbool.h>
+
+#define SIZE 9
+
+// 打印数独矩阵
+void printSudoku(int board[SIZE][SIZE]) {
+	int row,col; 
+    for (row = 0; row < SIZE; row++) {
+        for (col = 0; col < SIZE; col++) {
+            printf("%d ", board[row][col]);
+        }
+        printf("\n");
+    }
+}
+
+// 检查当前位置是否安全
+bool isSafe(int board[SIZE][SIZE], int row, int col, int num) {
+    // 检查行
+    int x;
+    for (x = 0; x < SIZE; x++) {
+        if (board[row][x] == num) {
+            return false;
+        }
+    }
+
+    // 检查列
+    for (x = 0; x < SIZE; x++) {
+        if (board[x][col] == num) {
+            return false;
+        }
+    }
+
+    // 检查 3x3 子网格
+    int startRow = row - row % 3;
+    int startCol = col - col % 3;
+    int i,j;
+    for (i = 0; i < 3; i++) {
+        for (j = 0; j < 3; j++) {
+            if (board[i + startRow][j + startCol] == num) {
+                return false;
+            }
+        }
+    }
+
+    return true;
+}
+
+// 解决数独的回溯算法
+bool solveSudoku(int board[SIZE][SIZE]) {
+    // 遍历整个数独矩阵
+    int row,col;
+    for (row = 0; row < SIZE; row++) {
+        for (col = 0; col < SIZE; col++) {
+            // 如果当前位置是空的
+            if (board[row][col] == 0) {
+                // 尝试填充 1 到 9
+                int num;
+                for (num = 1; num <= 9; num++) {
+                    if (isSafe(board, row, col, num)) {
+                        // 放置数字
+                        board[row][col] = num;
+
+                        // 递归调用解决数独
+                        if (solveSudoku(board)) {
+                            return true;
+                        }
+
+                        // 如果失败，回溯
+                        board[row][col] = 0;
+                    }
+                }
+
+                // 如果 1 到 9 都不能放置，返回 false
+                return false;
+            }
+        }
+    }
+
+    // 如果所有位置都填充完毕，返回 true
+    return true;
+}
+
+// 检查数独矩阵的有效性
+bool isValidSudoku(int board[SIZE][SIZE]) {
+    // 检查行和列是否有重复的数字
+    int row,col;
+    for (row = 0; row < SIZE; row++) {
+        int rowSet[10] = {0};
+        int colSet[10] = {0};
+        for (col = 0; col < SIZE; col++) {
+            int num = board[row][col];
+            if (num != 0) {
+                if (rowSet[num]) {
+                    printf("Row %d has duplicate number %d\n", row, num);
+                    return false;
+                }
+                rowSet[num] = 1;
+
+                if (colSet[num]) {
+                    printf("Column %d has duplicate number %d\n", col, num);
+                    return false;
+                }
+                colSet[num] = 1;
+            }
+        }
+    }
+
+    // 检查 3x3 子网格是否有重复的数字
+    int block;
+    for (block = 0; block < 9; block++) {
+        int blockSet[10] = {0};
+        int startRow = block / 3 * 3;
+        int startCol = block % 3 * 3;
+        int i,j;
+        for (i = 0; i < 3; i++) {
+            for (j = 0; j < 3; j++) {
+                int num = board[startRow + i][startCol + j];
+                if (num != 0) {
+                    if (blockSet[num]) {
+                        printf("3x3 block starting at (%d, %d) has duplicate number %d\n", startRow, startCol, num);
+                        return false;
+                    }
+                    blockSet[num] = 1;
+                }
+            }
+        }
+    }
+
+    return true;
+}
+
+int main() {
+    int board[SIZE][SIZE] = {
+        {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}
+    };
+
+    printf("The original Sudoku matrix:\n");
+    printSudoku(board);
+
+    if (isValidSudoku(board)) {
+        printf("True:Valid initial Sudoku matrix!\n");
+        if (solveSudoku(board)) {
+            printf("The solution of Sudoku matrix:\n");
+            printSudoku(board);
+        } else {
+            printf("No solution!\n");
+        }
+    } else {
+        printf("False:Invalid initial Sudoku matrix!\n");
+        printf("No solution!\n");
+    }
+
+    return 0;
+}