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x4.cpp

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+#include <stdio.h>
+#include <stdbool.h>
+
+// 打印数独函数
+void x1(int m[9][9])
+{
+  int i,j;
+  for(i=0;i<9;i++)
+  {
+    if(i%3==0)printf("-------------\n");
+    for(j=0;j<9;j++)
+    {
+      if(j%3==0)printf("|");
+      printf("%d",m[i][j]);
+    }
+    printf("|\n");
+  }
+  printf("-------------\n");
+}
+
+// 检查行是否有效
+bool hang(int m[9][9], int i, int num) {
+    for (int j = 0; j < 9; j++) {
+        if (m[j][i] == num) {
+            return false;
+        }
+    }
+    return true;
+}
+
+// 检查列是否有效
+bool lie(int m[9][9], int j, int num) {
+    for (int i = 0; i < 9; i++) {
+        if (m[i][j] == num) {
+            return false;
+        }
+    }
+    return true;
+}
+
+// 检查3x3子矩阵是否有效
+bool o3(int board[9][9], int starti, int startj, int num) {
+    for (int i = 0; i < 3; i++) {
+        for (int j = 0; j < 3; j++) {
+            if (board[starti + i][startj + j] == num) {
+                return false;
+            }
+        }
+    }
+    return true;
+}
+
+// 检查某个位置是否可以放置某个数字
+bool check(int m[9][9], int i, int j, int num) {
+    return hang(m, i, j) &&
+           lie(m, i, j) &&
+           o3(m, i - i % 3, j - j % 3, num);
+}
+
+// 解数独
+bool solve(int m[9][9]) {
+    for (int i = 0; i < 9; i++) {
+        for (int j = 0; j < 9; j++) {
+            if (m[i][j] == 0) {
+                for (int num = 1; num <= 9; num++) {
+                    if (check(m, i, j, num)) {
+                        m[i][j] = num;
+                        if (solve(m)) {
+                            return true;
+                        }
+                        m[i][j] = 0; // 回溯
+                    }
+                }
+                return false; // 无法填充，回溯
+            }
+        }
+    }
+    return true; // 数独已解
+}
+
+// 检查整个数独矩阵是否有效
+bool judge(int m[9][9]) {
+    for (int i = 0; i < 9; i++) {
+        for (int j = 0; j < 9; j++) {
+            if (m[i][j] != 0) {
+                int num = m[i][j];
+                m[i][j] = 0;
+                if (!check(m, i, j, num)) {
+                    printf("The number %d in the row %d has been used!\n", num, i + 1);
+                    m[i][j] = num;
+                    return false;
+                }
+                m[i][j] = num;
+            }
+        }
+    }
+    return true;
+}
+
+int main() {
+    int m[9][9] ={{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");
+    x1(m);
+
+    if (judge(m)) {
+        printf("True: Valid initial Sudoku matrix!\n");
+        if (solve(m)) {
+            printf("The solution of Sudoku matrix:\n");
+            x1(m);
+        } else {
+            printf("No solution!\n");
+        }
+    } else {
+        printf("False: Invalid initial Sudoku matrix!\n");
+        printf("No solution!\n");
+    }
+
+    return 0;
+}