From 704b638d895b9bbb819d39d85ff860b4e32b5ae7 Mon Sep 17 00:00:00 2001 From: lucas Date: Mon, 9 Oct 2023 01:42:32 +0800 Subject: [PATCH] feat: n_queens.c translation (#774) * feat: tranlating n_queens.c * Reference to c++ code with additional comments * Update n_queens.c * Update n_queens.c * Format n_queens.c * Update n_queens.c keep the file header information format consistent with others * fine tune * fine tune * Delete mkdocs-en.yml * Update README.md --------- Co-authored-by: krahets --- codes/c/chapter_backtracking/CMakeLists.txt | 3 +- codes/c/chapter_backtracking/n_queens.c | 103 ++++++++++++++++++++ 2 files changed, 105 insertions(+), 1 deletion(-) create mode 100644 codes/c/chapter_backtracking/n_queens.c diff --git a/codes/c/chapter_backtracking/CMakeLists.txt b/codes/c/chapter_backtracking/CMakeLists.txt index 87538d37..8d768be3 100644 --- a/codes/c/chapter_backtracking/CMakeLists.txt +++ b/codes/c/chapter_backtracking/CMakeLists.txt @@ -5,4 +5,5 @@ add_executable(preorder_traversal_iii_compact preorder_traversal_iii_compact.c) add_executable(preorder_traversal_iii_template preorder_traversal_iii_template.c) add_executable(subset_sum_i_naive subset_sum_i_naive.c) add_executable(subset_sum_i subset_sum_i.c) -add_executable(subset_sum_ii subset_sum_ii.c) \ No newline at end of file +add_executable(subset_sum_ii subset_sum_ii.c) +add_executable(n_queens n_queens.c) \ No newline at end of file diff --git a/codes/c/chapter_backtracking/n_queens.c b/codes/c/chapter_backtracking/n_queens.c new file mode 100644 index 00000000..c5997d92 --- /dev/null +++ b/codes/c/chapter_backtracking/n_queens.c @@ -0,0 +1,103 @@ +/** + * File : n_queens.c + * Created Time: 2023-09-25 + * Author : lucas (superrat6@gmail.com) + */ + +#include "../utils/common.h" + +#define MAX_N 100 +#define MAX_RES 1000 + +struct result { + char ***data; + int size; +}; + +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; +} + +/* Driver Code */ +int main() { + int n = 4; + Result *res = nQueens(n); + + printf("输入棋盘长宽为%d\n", n); + printf("皇后放置方案共有 %d 种\n", res->size); + for (int i = 0; i < res->size; ++i) { + for (int j = 0; j < n; ++j) { + printf("["); + for (int k = 0; res->data[i][j][k] != '\0'; ++k) { + printf("%c", res->data[i][j][k]); + if (res->data[i][j][k + 1] != '\0') { + printf(", "); + } + } + printf("]\n"); + } + printf("---------------------\n"); + } + + // 释放内存 + for (int i = 0; i < res->size; ++i) { + for (int j = 0; j < n; ++j) { + free(res->data[i][j]); + } + free(res->data[i]); + } + free(res->data); + + return 0; +}