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