From c6eecfd0dc29e3393a1e749ef5e1fe047ad59452 Mon Sep 17 00:00:00 2001 From: Yudong Jin Date: Mon, 24 Apr 2023 03:33:30 +0800 Subject: [PATCH] feat: Add the section of permutations problem. (#476) * Add the section of permutations problem. * Update permutations_problem.md --- .../chapter_backtracking/permutations_i.cpp | 48 +++++ .../chapter_backtracking/permutations_ii.cpp | 50 +++++ .../chapter_backtracking/permutations_i.java | 45 +++++ .../chapter_backtracking/permutations_ii.java | 47 +++++ .../chapter_array_and_linkedlist/array.py | 3 + .../chapter_backtracking/permutations_i.py | 43 +++++ .../chapter_backtracking/permutations_ii.py | 45 +++++ .../permutations_i.png | Bin 0 -> 55917 bytes .../permutations_i_pruning.png | Bin 0 -> 90253 bytes .../permutations_ii.png | Bin 0 -> 62284 bytes .../permutations_ii_pruning.png | Bin 0 -> 80436 bytes .../permutations_ii_pruning_summary.png | Bin 0 -> 74933 bytes .../permutations_problem.md | 180 ++++++++++++++++++ mkdocs.yml | 1 + 14 files changed, 462 insertions(+) create mode 100644 codes/cpp/chapter_backtracking/permutations_i.cpp create mode 100644 codes/cpp/chapter_backtracking/permutations_ii.cpp create mode 100644 codes/java/chapter_backtracking/permutations_i.java create mode 100644 codes/java/chapter_backtracking/permutations_ii.java create mode 100644 codes/python/chapter_backtracking/permutations_i.py create mode 100644 codes/python/chapter_backtracking/permutations_ii.py create mode 100644 docs/chapter_backtracking/permutations_problem.assets/permutations_i.png create mode 100644 docs/chapter_backtracking/permutations_problem.assets/permutations_i_pruning.png create mode 100644 docs/chapter_backtracking/permutations_problem.assets/permutations_ii.png create mode 100644 docs/chapter_backtracking/permutations_problem.assets/permutations_ii_pruning.png create mode 100644 docs/chapter_backtracking/permutations_problem.assets/permutations_ii_pruning_summary.png create mode 100644 docs/chapter_backtracking/permutations_problem.md diff --git a/codes/cpp/chapter_backtracking/permutations_i.cpp b/codes/cpp/chapter_backtracking/permutations_i.cpp new file mode 100644 index 000000000..1f268fc60 --- /dev/null +++ b/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 &state, const vector &choices, vector &selected, vector> &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 nums = {1, 2, 3}; + + // 回溯算法 + vector state; + vector selected(nums.size(), false); + vector> res; + backtrack(state, nums, selected, res); + + cout << "输入数组 nums = "; + printVector(nums); + cout << "所有排列 res = "; + printVectorMatrix(res); + + return 0; +} diff --git a/codes/cpp/chapter_backtracking/permutations_ii.cpp b/codes/cpp/chapter_backtracking/permutations_ii.cpp new file mode 100644 index 000000000..b06b34fa3 --- /dev/null +++ b/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 &state, const vector &choices, vector &selected, vector> &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 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 nums = {1, 1, 2}; + + // 回溯算法 + vector state; + vector selected(nums.size(), false); + vector> res; + backtrack(state, nums, selected, res); + + cout << "输入数组 nums = "; + printVector(nums); + cout << "所有排列 res = "; + printVectorMatrix(res); + + return 0; +} diff --git a/codes/java/chapter_backtracking/permutations_i.java b/codes/java/chapter_backtracking/permutations_i.java new file mode 100644 index 000000000..340fb4766 --- /dev/null +++ b/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 state, int[] choices, boolean[] selected, List> 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(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> res = new ArrayList>(); + + // 回溯算法 + backtrack(new ArrayList(), 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); + } +} diff --git a/codes/java/chapter_backtracking/permutations_ii.java b/codes/java/chapter_backtracking/permutations_ii.java new file mode 100644 index 000000000..f48f75c48 --- /dev/null +++ b/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 state, int[] choices, boolean[] selected, List> 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(state)); + return; + } + // 遍历所有选择 + Set duplicated = new HashSet(); + 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> res = new ArrayList>(); + + // 回溯算法 + backtrack(new ArrayList(), 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); + } +} diff --git a/codes/python/chapter_array_and_linkedlist/array.py b/codes/python/chapter_array_and_linkedlist/array.py index 7bbccd42b..bee5b1e36 100644 --- a/codes/python/chapter_array_and_linkedlist/array.py +++ b/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: diff --git a/codes/python/chapter_backtracking/permutations_i.py b/codes/python/chapter_backtracking/permutations_i.py new file mode 100644 index 000000000..aaaa77a47 --- /dev/null +++ b/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}") diff --git a/codes/python/chapter_backtracking/permutations_ii.py b/codes/python/chapter_backtracking/permutations_ii.py new file mode 100644 index 000000000..1aa9e84b2 --- /dev/null +++ b/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, 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