This commit is contained in:
krahets
2023-10-09 05:05:19 +08:00
parent 2f761d9865
commit ec3f58fb70
7 changed files with 144 additions and 25 deletions

View File

@ -601,9 +601,66 @@ comments: true
=== "C"
```c title="n_queens.c"
[class]{}-[func]{backtrack}
/* 放置结果 */
struct result {
char ***data;
int size;
};
[class]{}-[func]{nQueens}
typedef struct result Result;
/* 回溯算法N 皇后 */
void backtrack(int row, int n, char state[MAX_N][MAX_N], Result *res,
bool cols[MAX_N], bool diags1[2 * MAX_N - 1], bool diags2[2 * MAX_N - 1]) {
// 当放置完所有行时,记录解
if (row == n) {
res->data[res->size] = (char **)malloc(sizeof(char *) * n);
for (int i = 0; i < n; ++i) {
res->data[res->size][i] = (char *)malloc(sizeof(char) * (n + 1));
strcpy(res->data[res->size][i], state[i]);
}
res->size++;
return;
}
// 遍历所有列
for (int col = 0; col < n; col++) {
// 计算该格子对应的主对角线和副对角线
int diag1 = row - col + n - 1;
int diag2 = row + col;
// 剪枝:不允许该格子所在列、主对角线、副对角线存在皇后
if (!cols[col] && !diags1[diag1] && !diags2[diag2]) {
// 尝试:将皇后放置在该格子
state[row][col] = 'Q';
cols[col] = diags1[diag1] = diags2[diag2] = true;
// 放置下一行
backtrack(row + 1, n, state, res, cols, diags1, diags2);
// 回退:将该格子恢复为空位
state[row][col] = '#';
cols[col] = diags1[diag1] = diags2[diag2] = false;
}
}
}
/* 求解 N 皇后 */
Result *nQueens(int n) {
char state[MAX_N][MAX_N];
// 初始化 n*n 大小的棋盘,其中 'Q' 代表皇后,'#' 代表空位
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
state[i][j] = '#';
}
state[i][n] = '\0';
}
bool cols[MAX_N] = {false}; // 记录列是否有皇后
bool diags1[2 * MAX_N - 1] = {false}; // 记录主对角线是否有皇后
bool diags2[2 * MAX_N - 1] = {false}; // 记录副对角线是否有皇后
Result *res = malloc(sizeof(Result));
res->data = (char ***)malloc(sizeof(char **) * MAX_RES);
res->size = 0;
backtrack(0, n, state, res, cols, diags1, diags2);
return res;
}
```
=== "Zig"