feat(csharp/backtracking): add csharp code in permutations (#478)

* feat(csharp/backtracking): add csharp code in permutations

* Update permutations_i.cs

* Update permutations_ii.cs

* Update permutations_ii.cs

---------

Co-authored-by: Yudong Jin <krahets@163.com>

codes/csharp/chapter_backtracking/permutations_i.cs

@@ -0,0 +1,50 @@
+/**
+ * File: permutations_i.cs
+ * Created Time: 2023-04-24
+ * Author: hpstory (hpstory1024@163.com)
+ */
+
+using hello_algo.utils;
+using NUnit.Framework;
+
+namespace hello_algo.chapter_backtracking; 
+
+public class permutations_i {
+    /* 回溯算法：全排列 I */
+    public static void backtrack(List<int> state, int[] choices, bool[] selected, List<List<int>> res) {
+        // 当状态长度等于元素数量时，记录解
+        if (state.Count == choices.Length) {
+            res.Add(new List<int>(state));
+            return;
+        }
+        // 遍历所有选择
+        for (int i = 0; i < choices.Length; i++) {
+            int choice = choices[i];
+            // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
+            if (!selected[i]) {
+                // 尝试
+                selected[i] = true; // 做出选择
+                state.Add(choice); // 更新状态
+                backtrack(state, choices, selected, res);
+                // 回退
+                selected[i] = false; // 撤销选择
+                state.RemoveAt(state.Count - 1); // 恢复到之前的状态
+            }
+        }
+    }
+
+    [Test]
+    public void Test() {
+        int[] nums = { 1, 2, 3 };
+
+        // 回溯算法
+        List<List<int>> res = new List<List<int>>();
+        backtrack(new List<int>(), nums, new bool[nums.Length], res);
+
+        Console.WriteLine("输入数组 nums = " + string.Join(", ", nums));
+        Console.WriteLine("所有排列 res = ");
+        foreach (List<int> permutation in res) {
+            PrintUtil.PrintList(permutation);
+        }
+    }
+}

codes/csharp/chapter_backtracking/permutations_ii.cs

@@ -0,0 +1,52 @@
+/**
+ * File: permutations_ii.cs
+ * Created Time: 2023-04-24
+ * Author: hpstory (hpstory1024@163.com)
+ */
+
+using hello_algo.utils;
+using NUnit.Framework;
+
+namespace hello_algo.chapter_backtracking; 
+
+public class permutations_ii {
+    /* 回溯算法：全排列 II */
+    public static void backtrack(List<int> state, int[] choices, bool[] selected, List<List<int>> res) {
+        // 当状态长度等于元素数量时，记录解
+        if (state.Count == choices.Length) {
+            res.Add(new List<int>(state));
+            return;
+        }
+        // 遍历所有选择
+        ISet<int> duplicated = new HashSet<int>();
+        for (int i = 0; i < choices.Length; i++) {
+            int choice = choices[i];
+            // 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
+            if (!selected[i] && !duplicated.Contains(choice)) {
+                // 尝试
+                duplicated.Add(choice); // 记录选择过的元素值
+                selected[i] = true; // 做出选择
+                state.Add(choice); // 更新状态
+                backtrack(state, choices, selected, res);
+                // 回退
+                selected[i] = false; // 撤销选择
+                state.RemoveAt(state.Count - 1); // 恢复到之前的状态
+            }
+        }
+    }
+
+    [Test]
+    public void Test() {
+        int[] nums = { 1, 2, 2 };
+
+        // 回溯算法
+        List<List<int>> res = new List<List<int>>();
+        backtrack(new List<int>(), nums, new bool[nums.Length], res);
+
+        Console.WriteLine("输入数组 nums = " + string.Join(", ", nums));
+        Console.WriteLine("所有排列 res = ");
+        foreach (List<int> permutation in res) {
+            PrintUtil.PrintList(permutation);
+        }
+    }
+}

codes/csharp/chapter_backtracking/preorder_traversal_i_compact.cs

@@ -6,7 +6,6 @@
 
 using hello_algo.utils;
 using NUnit.Framework;
-using System.IO;
 
 namespace hello_algo.chapter_backtracking;