Add 4

4

@@ -0,0 +1,122 @@
+void printBoard(int board[N][N]) {
+    for (int i = 0; i < N; i++) {
+        for (int j = 0; j < N; j++) {
+            printf("%2d", board[i][j]);
+            if (j < N - 1) {
+                printf(" ");
+            }
+        }
+        printf("\n");
+    }
+}
+// 检查数独矩阵的有效性
+int isValid(int board[N][N], int row, int col, int num) {
+    // 检查行
+    for (int i = 0; i < N; i++) {
+        if (board[row][i] == num) {
+            return 0;
+        }
+    }
+    // 检查列
+    for (int j = 0; j < N; j++) {
+        if (board[j][col] == num) {
+            return 0;
+        }
+    }
+    // 检查3x3子矩阵
+    int startRow = row - row % 3;
+    int startCol = col - col % 3;
+    for (int m = 0; m < 3; m++) {
+        for (int n = 0; n < 3; n++) {
+            if (board[m + startRow][n + startCol] == num) {
+                return 0;
+            }
+        }
+    }
+    return 1;
+}
+// 检查数独矩阵的定义是否满足
+int checkBoardDefinition(int board[N][N]) {
+    int rowUsed[N][N] = { 0 };
+    int colUsed[N][N] = { 0 };
+    int blockUsed[N][N] = { 0 };
+
+    for (int row = 0; row < N; row++) {
+        for (int col = 0; col < N; col++) {
+            int num = board[row][col];
+            if (num != 0) {
+                if (rowUsed[row][num - 1]) {
+                    printf("False: Invalid initial Sudoku matrix!\n");
+                    printf("The number %d in the row %d has been used!\n", num, row + 1);
+                    printf("No solution!\n");
+                    return 0;
+                }
+                if (colUsed[col][num - 1]) {
+                    printf("False: Invalid initial Sudoku matrix!\n");
+                    printf("The number %d in the col %d has been used!\n", num, col + 1);
+                    printf("No solution!\n");
+                    return 0;
+                }
+                int blockIndex = (row / 3) * 3 + (col / 3);
+                if (blockUsed[blockIndex][num - 1]) {
+                    printf("False: Invalid initial Sudoku matrix!\n");
+                    printf("The number %d in the block %d has been used!\n", num, blockIndex + 1);
+                    printf("No solution!\n");
+                    return 0;
+                }
+                rowUsed[row][num - 1] = 1;
+                colUsed[col][num - 1] = 1;
+                blockUsed[blockIndex][num - 1] = 1;
+            }
+        }
+    }
+    return 1;
+}
+// 解数独
+int solveBoard(int board[N][N]) {
+    for (int row = 0; row < N; row++) {
+        for (int col = 0; col < N; col++) {
+            if (board[row][col] == 0) {
+                for (int num = 1; num <= 9; num++) {
+                    if (isValid(board, row, col, num)) {
+                        board[row][col] = num;
+                        if (solveBoard(board)) {
+                            return 1;
+                        }
+                        board[row][col] = 0;
+                    }
+                }
+                return 0;
+            }
+        }
+    }
+    return 1;
+}
+int main() {
+    int board[N][N] = { {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,  5},
+                        {0,  0,  0,  0,  8,  0,  0,  7,  9} };
+    //可以替换成不同的不完整数独矩阵，这里用了任务描述中的例子 
+    printf("The original Sudoku matrix:\n");
+    printBoard(board);
+    int initialIsValid = checkBoardDefinition(board); // 检查数独矩阵的定义
+    if (!initialIsValid) {
+    }
+    else {
+        if (solveBoard(board)) {
+            printf("True: Valid initial Sudoku matrix!\n");
+            printf("The solution of Sudoku matrix:\n");
+            printBoard(board);
+        }
+        else {
+            printf("True: Valid initial Sudoku matrix, but no solution!\n");
+        }
+    }
+    return 0;
+}