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complement.c

@@ -0,0 +1,146 @@
+#include <stdio.h>
+#include <stdbool.h>
+bool check(int matrix[9][9]) {
+
+    for (int i = 0; i < 9; i++) {
+        int count[10] = {0}; 
+        for (int j = 0; j < 9; j++) {
+            int num = matrix[i][j];
+            if (num != 0) {
+                count[num]++;
+                if (count[num] > 1) {
+                    printf("False: The number %d in the row %d has been used!\n", num, i + 1);
+                    return false;
+                }
+            }
+        }
+    }
+
+
+    for (int j = 0; j < 9; j++) {
+        int count[10] = {0};
+        for (int i = 0; i < 9; i++) {
+            int num = matrix[i][j];
+            if (num != 0) {
+                count[num]++;
+                if (count[num] > 1) {
+                    printf("False: The number %d in the col %d has been used!\n", num, j + 1);
+                    return false;
+                }
+            }
+        }
+    }
+
+    for (int block = 0; block < 9; block++) {
+        int count[10] = {0};
+        int startRow = (block / 3) * 3;
+        int startCol = (block % 3) * 3;
+        for (int i = startRow; i < startRow + 3; i++) {
+            for (int j = startCol; j < startCol + 3; j++) {
+                int num = matrix[i][j];
+                if (num != 0) {
+                    count[num]++;
+                    if (count[num] > 1) {
+                        printf("False: The number %d in the block %d has been used!\n", num, block + 1);
+                        return false;
+                    }
+                }
+            }
+        }
+    }
+
+    printf("True: Valid initial Sudoku matrix!\n");
+}
+
+
+bool complement(int board[9][9], int row, int col) {
+    if (row == 9) {
+        return true;
+    }
+    if (board[row][col] != 0) {
+        if (col == 8) {
+            return complement(board, row + 1, 0);
+        } else {
+            return complement(board, row, col + 1);
+        }
+    }
+    for (int num = 1; num <= 9; num++) {
+        bool valid = true;
+        for (int i = 0; i < 9; i++) {
+            if (board[row][i] == num || board[i][col] == num ||
+                board[(row / 3) * 3 + i / 3][(col / 3) * 3 + i % 3] == num) {
+                valid = false;
+                break;
+            }
+        }
+        if (valid) {
+            board[row][col] = num;
+            if (col == 8) {
+                if (complement(board, row + 1, 0)) {
+                    return true;
+                }
+            } else {
+                if (complement(board, row, col + 1)) {
+                    return true;
+                }
+            }
+            board[row][col] = 0;
+        }
+    }
+    return false;
+}
+
+
+void printSudokuSolution(int matrix[9][9]) {
+    printf("The solution of Sudoku matrix:\n");
+    for (int i = 0; i < 9; i++) {
+        for (int j = 0; j < 9; j++) {
+            printf("%d ", matrix[i][j]);
+        }
+        printf("\n");
+    }
+}
+
+
+void output(int board[9][9]){
+    int i;
+    for(i = 0;i < 9 ;i++){
+        if(i %3 == 0){
+            printf("|-----------------------|\n");
+        }
+        printf("| %d %d %d | %d %d %d | %d %d %d |\n",
+        board[i][0],board[i][1],board[i][2],board[i][3],board[i][4],board[i][5],board[i][6],board[i][7],board[i][8]);
+    }
+    printf("|-----------------------|\n");
+}
+
+
+
+
+int main() {
+    // 示例矩阵
+    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}
+    };
+    printf("The original Sudoku matrix:\n ");
+    output(board);
+    if (check(board)) {
+        if (complement(board, 0, 0)) {
+            printSudokuSolution(board);
+        } else {
+            printf("No solution!\n");
+        }
+    } else {
+        printf("No solution!\n");
+    }
+
+    return 0;
+}