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;
+}

codes/java/chapter_backtracking/permutations_i.java

@@ -0,0 +1,45 @@
+/**
+ * File: permutations_i.java
+ * Created Time: 2023-04-24
+ * Author: Krahets (krahets@163.com)
+ */
+
+package chapter_backtracking;
+
+import java.util.*;
+
+public class permutations_i {
+    /* 回溯算法：全排列 I */
+    public static void backtrack(List<Integer> state, int[] choices, boolean[] selected, List<List<Integer>> res) {
+        // 当状态长度等于元素数量时，记录解
+        if (state.size() == choices.length) {
+            res.add(new ArrayList<Integer>(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.remove(state.size() - 1); // 恢复到之前的状态
+            }
+        }
+    }
+
+    public static void main(String[] args) {
+        int[] nums = { 1, 2, 3 };
+        List<List<Integer>> res = new ArrayList<List<Integer>>();
+
+        // 回溯算法
+        backtrack(new ArrayList<Integer>(), nums, new boolean[nums.length], res);
+        
+        System.out.println("输入数组 nums = " + Arrays.toString(nums));
+        System.out.println("所有排列 res = " + res);
+    }
+}

codes/java/chapter_backtracking/permutations_ii.java

@@ -0,0 +1,47 @@
+/**
+ * File: permutations_ii.java
+ * Created Time: 2023-04-24
+ * Author: Krahets (krahets@163.com)
+ */
+
+package chapter_backtracking;
+
+import java.util.*;
+
+public class permutations_ii {
+    /* 回溯算法：全排列 II */
+    public static void backtrack(List<Integer> state, int[] choices, boolean[] selected, List<List<Integer>> res) {
+        // 当状态长度等于元素数量时，记录解
+        if (state.size() == choices.length) {
+            res.add(new ArrayList<Integer>(state));
+            return;
+        }
+        // 遍历所有选择
+        Set<Integer> duplicated = new HashSet<Integer>();
+        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.remove(state.size() - 1); // 恢复到之前的状态
+            }
+        }
+    }
+
+    public static void main(String[] args) {
+        int[] nums = { 1, 2, 2 };
+        List<List<Integer>> res = new ArrayList<List<Integer>>();
+
+        // 回溯算法
+        backtrack(new ArrayList<Integer>(), nums, new boolean[nums.length], res);
+
+        System.out.println("输入数组 nums = " + Arrays.toString(nums));
+        System.out.println("所有排列 res = " + res);
+    }
+}

codes/python/chapter_array_and_linkedlist/array.py

@@ -54,6 +54,9 @@ def traverse(nums: list[int]) -> None:
     # 直接遍历数组
     for num in nums:
         count += 1
+    # 同时遍历数据索引和元素
+    for i, num in enumerate(nums):
+        count += 1
 
 
 def find(nums: list[int], target: int) -> int:

codes/python/chapter_backtracking/permutations_i.py

@@ -0,0 +1,43 @@
+"""
+File: permutations_i.py
+Created Time: 2023-04-15
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from modules import *
+
+
+def backtrack(
+    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]
+):
+    """回溯算法：全排列 I"""
+    # 当状态长度等于元素数量时，记录解
+    if len(state) == len(choices):
+        res.append(list(state))
+        return
+    # 遍历所有选择
+    for i, choice in enumerate(choices):
+        # 剪枝：不允许重复选择元素
+        if not selected[i]:
+            # 尝试
+            selected[i] = True  # 做出选择
+            state.append(choice)  # 更新状态
+            backtrack(state, choices, selected, res)
+            # 回退
+            selected[i] = False  # 撤销选择
+            state.pop()  # 恢复到之前的状态
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    nums = [1, 2, 3]
+    res = []
+
+    # 回溯算法
+    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)
+
+    print(f"输入数组 nums = {nums}")
+    print(f"所有排列 res = {res}")

codes/python/chapter_backtracking/permutations_ii.py

@@ -0,0 +1,45 @@
+"""
+File: permutations_ii.py
+Created Time: 2023-04-15
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from modules import *
+
+
+def backtrack(
+    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]
+):
+    """回溯算法：全排列 II"""
+    # 当状态长度等于元素数量时，记录解
+    if len(state) == len(choices):
+        res.append(list(state))
+        return
+    # 遍历所有选择
+    duplicated = set[int]()
+    for i, choice in enumerate(choices):
+        # 剪枝：不允许重复选择元素 且 不允许重复选择相等元素
+        if not selected[i] and choice not in duplicated:
+            # 尝试
+            duplicated.add(choice)  # 记录选择过的元素值
+            selected[i] = True  # 做出选择
+            state.append(choice)  # 更新状态
+            backtrack(state, choices, selected, res)
+            # 回退
+            selected[i] = False  # 撤销选择
+            state.pop()  # 恢复到之前的状态
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    nums = [1, 2, 2]
+    res = []
+
+    # 回溯算法
+    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)
+
+    print(f"输入数组 nums = {nums}")
+    print(f"所有排列 res = {res}")