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feat(csharp/backtracking): add csharp code in n queens (#485)

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* feat(csharp/backtracking): add csharp code in n queens

* fix format

* Update n_queens.cs

---------

Co-authored-by: Yudong Jin <krahets@163.com>
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hpstory 2023-05-05 03:34:52 +08:00 committed by GitHub
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codes/csharp/chapter_backtracking/n_queens.cs Normal file
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/**
* File: n_queens.cs
* Created Time: 2023-05-04
* Author: hpstory (hpstory1024@163.com)
*/
using hello_algo.utils;
using NUnit.Framework;
namespace hello_algo.chapter_backtracking;
public class n_queens {
/* 回溯算法：N 皇后 */
static void backtrack(int row, int n, List<List<string>> state, List<List<List<string>>> res,
bool[] cols, bool[] diags1, bool[] diags2) {
// 当放置完所有行时，记录解
if (row == n) {
List<List<string>> copyState = new List<List<string>>();
foreach (List<string> sRow in state) {
copyState.Add(new List<string>(sRow));
}
res.Add(copyState);
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 或 主对角线 或 副对角线) 包含皇后
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 */
static List<List<List<string>>> nQueens(int n) {
// 初始化 n*n 大小的棋盘，其中 'Q' 代表皇后，'#' 代表空位
List<List<string>> state = new List<List<string>>();
for (int i = 0; i < n; i++) {
List<string> row = new List<string>();
for (int j = 0; j < n; j++) {
row.Add("#");
}
state.Add(row);
}
bool[] cols = new bool[n]; // 记录列是否有皇后
bool[] diags1 = new bool[2 * n - 1]; // 记录主对角线是否有皇后
bool[] diags2 = new bool[2 * n - 1]; // 记录副对角线是否有皇后
List<List<List<string>>> res = new List<List<List<string>>>();
backtrack(0, n, state, res, cols, diags1, diags2);
return res;
}
[Test]
public void Test() {
int n = 4;
List<List<List<string>>> res = nQueens(n);
Console.WriteLine("输入棋盘长宽为 " + n);
Console.WriteLine("皇后放置方案共有 " + res.Count + " 种");
foreach (List<List<string>> state in res) {
Console.WriteLine("--------------------");
foreach (List<string> row in state) {
PrintUtil.PrintList(row);
}
}
}
}