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pj4.c

@@ -0,0 +1,134 @@
+#include <stdio.h>
+#include <stdbool.h>
+
+#define SIZE 9
+
+void printMatrix(int matrix[SIZE][SIZE]);
+bool isValidSudoku(int matrix[SIZE][SIZE]);
+bool solveSudoku(int matrix[SIZE][SIZE]);
+bool isSafe(int matrix[SIZE][SIZE], int row, int col, int num);
+bool findUnassignedLocation(int matrix[SIZE][SIZE], int *row, int *col);
+
+int main() {
+    int board1[SIZE][SIZE] = {
+        {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}
+    };
+
+    printf("The original Sudoku matrix:\n");
+    printMatrix(board1);
+
+    if (!isValidSudoku(board1)) {
+        printf("False: Invalid initial Sudoku matrix!\nNo solution!\n");
+    } else {
+        printf("True: Valid initial Sudoku matrix!\n");
+
+        if (solveSudoku(board1)) {
+            printf("The solution of Sudoku matrix:\n");
+            printMatrix(board1);
+        } else {
+            printf("No solution!\n");
+        }
+    }
+
+    return 0;
+}
+
+void printMatrix(int matrix[SIZE][SIZE]) {
+    printf("|-------|-------|-------|\n");
+    for (int i = 0; i < SIZE; i++) {
+        for (int j = 0; j < SIZE; j++) {
+            if (j % 3 == 0) printf("| ");
+            if (matrix[i][j] == 0) {
+                printf(". ");
+            } else {
+                printf("%d ", matrix[i][j]);
+            }
+        }
+        printf("|\n");
+        if (i % 3 == 2) printf("|-------|-------|-------|\n");
+    }
+}
+
+bool isValidSudoku(int matrix[SIZE][SIZE]) {
+    bool rowUsed[SIZE][SIZE + 1] = {false};  
+    bool colUsed[SIZE][SIZE + 1] = {false};  
+    bool blockUsed[SIZE][SIZE + 1] = {false};  
+
+    for (int row = 0; row < SIZE; row++) {
+        for (int col = 0; col < SIZE; col++) {
+            int num = matrix[row][col];
+            if (num != 0) {
+                int blockIndex = (row / 3) * 3 + (col / 3);
+                if (rowUsed[row][num] || colUsed[col][num] || blockUsed[blockIndex][num]) {
+                    printf("False: Invalid initial Sudoku matrix!\n");
+                    if (rowUsed[row][num]) {
+                        printf("The number %d in the row %d has been used!\n", num, row + 1);
+                    } else if (colUsed[col][num]) {
+                        printf("The number %d in the col %d has been used!\n", num, col + 1);
+                    } else if (blockUsed[blockIndex][num]) {
+                        printf("The number %d in the block %d has been used!\n", num, blockIndex + 1);
+                    }
+                    return false;
+                }
+                rowUsed[row][num] = colUsed[col][num] = blockUsed[blockIndex][num] = true;
+            }
+        }
+    }
+    return true;
+}
+
+
+bool solveSudoku(int matrix[SIZE][SIZE]) {
+    int row, col;
+
+    if (!findUnassignedLocation(matrix, &row, &col)) {
+        return true; 
+    }
+
+    for (int num = 1; num <= SIZE; num++) {
+        if (isSafe(matrix, row, col, num)) {
+            matrix[row][col] = num;
+            if (solveSudoku(matrix)) {
+                return true;
+            }
+            matrix[row][col] = 0; 
+        }
+    }
+    return false;  
+}
+
+bool findUnassignedLocation(int matrix[SIZE][SIZE], int *row, int *col) {
+    for (*row = 0; *row < SIZE; (*row)++) {
+        for (*col = 0; *col < SIZE; (*col)++) {
+            if (matrix[*row][*col] == 0) {
+                return true;
+            }
+        }
+    }
+    return false;
+}
+
+bool isSafe(int matrix[SIZE][SIZE], int row, int col, int num) {
+    for (int x = 0; x < SIZE; x++) {
+        if (matrix[row][x] == num || matrix[x][col] == num) {
+            return false;
+        }
+    }
+    int startRow = row - row % 3, startCol = col - col % 3;
+    for (int i = 0; i < 3; i++) {
+        for (int j = 0; j < 3; j++) {
+            if (matrix[i + startRow][j + startCol] == num) {
+                return false;
+            }
+        }
+    }
+    return true;
+}