feat: Add the section of permutations problem. (#476)

* Add the section of permutations problem.

* Update permutations_problem.md

codes/cpp/chapter_backtracking/permutations_i.cpp

@@ -0,0 +1,48 @@
+/**
+ * File: permutations_i.cpp
+ * Created Time: 2023-04-24
+ * Author: Krahets (krahets@163.com)
+ */
+
+#include "../include/include.hpp"
+
+/* 回溯算法：全排列 I */
+void backtrack(vector<int> &state, const vector<int> &choices, vector<bool> &selected, vector<vector<int>> &res) {
+    // 当状态长度等于元素数量时，记录解
+    if (state.size() == choices.size()) {
+        res.push_back(state);
+        return;
+    }
+    // 遍历所有选择
+    for (int i = 0; i < choices.size(); 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.push_back(choice); // 更新状态
+            backtrack(state, choices, selected, res);
+            // 回退
+            selected[i] = false; // 撤销选择
+            state.pop_back();    // 恢复到之前的状态
+        }
+    }
+}
+
+/* Driver Code */
+int main() {
+    vector<int> nums = {1, 2, 3};
+
+    // 回溯算法
+    vector<int> state;
+    vector<bool> selected(nums.size(), false);
+    vector<vector<int>> res;
+    backtrack(state, nums, selected, res);
+
+    cout << "输入数组 nums = ";
+    printVector(nums);
+    cout << "所有排列 res = ";
+    printVectorMatrix(res);
+
+    return 0;
+}

codes/cpp/chapter_backtracking/permutations_ii.cpp

@@ -0,0 +1,50 @@
+/**
+ * File: permutations_ii.cpp
+ * Created Time: 2023-04-24
+ * Author: Krahets (krahets@163.com)
+ */
+
+#include "../include/include.hpp"
+
+/* 回溯算法：全排列 II */
+void backtrack(vector<int> &state, const vector<int> &choices, vector<bool> &selected, vector<vector<int>> &res) {
+    // 当状态长度等于元素数量时，记录解
+    if (state.size() == choices.size()) {
+        res.push_back(state);
+        return;
+    }
+    // 遍历所有选择
+    unordered_set<int> duplicated;
+    for (int i = 0; i < choices.size(); 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.find(choice) == duplicated.end()) {
+            // 尝试
+            duplicated.emplace(choice); // 记录选择过的元素值
+            selected[i] = true;         // 做出选择
+            state.push_back(choice);    // 更新状态
+            backtrack(state, choices, selected, res);
+            // 回退
+            selected[i] = false; // 撤销选择
+            state.pop_back();    // 恢复到之前的状态
+        }
+    }
+}
+
+/* Driver Code */
+int main() {
+    vector<int> nums = {1, 1, 2};
+
+    // 回溯算法
+    vector<int> state;
+    vector<bool> selected(nums.size(), false);
+    vector<vector<int>> res;
+    backtrack(state, nums, selected, res);
+
+    cout << "输入数组 nums = ";
+    printVector(nums);
+    cout << "所有排列 res = ";
+    printVectorMatrix(res);
+
+    return 0;
+}