From ff58d4113cccc77fc7c341380004eb6524b40fe4 Mon Sep 17 00:00:00 2001 From: hpstory <33348162+hpstory@users.noreply.github.com> Date: Sun, 25 Jun 2023 20:54:58 +0800 Subject: [PATCH] feat(csharp/backtracking): add subset_sum_i, _ii, _i_naive (#567) --- .../chapter_backtracking/subset_sum_i.cs | 55 +++++++++++++++++ .../subset_sum_i_naive.cs | 53 ++++++++++++++++ .../chapter_backtracking/subset_sum_ii.cs | 60 +++++++++++++++++++ 3 files changed, 168 insertions(+) create mode 100644 codes/csharp/chapter_backtracking/subset_sum_i.cs create mode 100644 codes/csharp/chapter_backtracking/subset_sum_i_naive.cs create mode 100644 codes/csharp/chapter_backtracking/subset_sum_ii.cs diff --git a/codes/csharp/chapter_backtracking/subset_sum_i.cs b/codes/csharp/chapter_backtracking/subset_sum_i.cs new file mode 100644 index 000000000..1840e074a --- /dev/null +++ b/codes/csharp/chapter_backtracking/subset_sum_i.cs @@ -0,0 +1,55 @@ +/** +* File: subset_sum_i.cs +* Created Time: 2023-06-25 +* Author: hpstory (hpstory1024@163.com) +*/ + +namespace hello_algo.chapter_backtracking; + +public class subset_sum_i { + /* 回溯算法：子集和 I */ + public static void backtrack(List state, int target, int[] choices, int start, List> res) { + // 子集和等于 target 时，记录解 + if (target == 0) { + res.Add(new List(state)); + return; + } + // 遍历所有选择 + // 剪枝二：从 start 开始遍历，避免生成重复子集 + for (int i = start; i < choices.Length; i++) { + // 剪枝一：若子集和超过 target ，则直接结束循环 + // 这是因为数组已排序，后边元素更大，子集和一定超过 target + if (target - choices[i] < 0) { + break; + } + // 尝试：做出选择，更新 target, start + state.Add(choices[i]); + // 进行下一轮选择 + backtrack(state, target - choices[i], choices, i, res); + // 回退：撤销选择，恢复到之前的状态 + state.RemoveAt(state.Count - 1); + } + } + + /* 求解子集和 I */ + public static List> subsetSumI(int[] nums, int target) { + List state = new List(); // 状态（子集） + Array.Sort(nums); // 对 nums 进行排序 + int start = 0; // 遍历起始点 + List> res = new List>(); // 结果列表（子集列表） + backtrack(state, target, nums, start, res); + return res; + } + + [Test] + public void Test() { + int[] nums = { 3, 4, 5 }; + int target = 9; + List> res = subsetSumI(nums, target); + Console.WriteLine("输入数组 nums = " + string.Join(", ", nums) + ", target = " + target); + Console.WriteLine("所有和等于 " + target + " 的子集 res = "); + foreach (var subset in res) { + PrintUtil.PrintList(subset); + } + } +} diff --git a/codes/csharp/chapter_backtracking/subset_sum_i_naive.cs b/codes/csharp/chapter_backtracking/subset_sum_i_naive.cs new file mode 100644 index 000000000..6e16ed78c --- /dev/null +++ b/codes/csharp/chapter_backtracking/subset_sum_i_naive.cs @@ -0,0 +1,53 @@ +/** +* File: subset_sum_i_naive.cs +* Created Time: 2023-06-25 +* Author: hpstory (hpstory1024@163.com) +*/ + +namespace hello_algo.chapter_backtracking; + +public class subset_sum_i_naive { + /* 回溯算法：子集和 I */ + public static void backtrack(List state, int target, int total, int[] choices, List> res) { + // 子集和等于 target 时，记录解 + if (total == target) { + res.Add(new List(state)); + return; + } + // 遍历所有选择 + for (int i = 0; i < choices.Length; i++) { + // 剪枝：若子集和超过 target ，则跳过该选择 + if (total + choices[i] > target) { + continue; + } + // 尝试：做出选择，更新元素和 total + state.Add(choices[i]); + // 进行下一轮选择 + backtrack(state, target, total + choices[i], choices, res); + // 回退：撤销选择，恢复到之前的状态 + state.RemoveAt(state.Count - 1); + } + } + + /* 求解子集和 I（包含重复子集） */ + public static List> subsetSumINaive(int[] nums, int target) { + List state = new List(); // 状态（子集） + int total = 0; // 子集和 + List> res = new List>(); // 结果列表（子集列表） + backtrack(state, target, total, nums, res); + return res; + } + + [Test] + public void Test() { + int[] nums = { 3, 4, 5 }; + int target = 9; + List> res = subsetSumINaive(nums, target); + Console.WriteLine("输入数组 nums = " + string.Join(", ", nums) + ", target = " + target); + Console.WriteLine("所有和等于 " + target + " 的子集 res = "); + foreach (var subset in res) { + PrintUtil.PrintList(subset); + } + Console.WriteLine("请注意，该方法输出的结果包含重复集合"); + } +} diff --git a/codes/csharp/chapter_backtracking/subset_sum_ii.cs b/codes/csharp/chapter_backtracking/subset_sum_ii.cs new file mode 100644 index 000000000..dec1ef317 --- /dev/null +++ b/codes/csharp/chapter_backtracking/subset_sum_ii.cs @@ -0,0 +1,60 @@ +/** +* File: subset_sum_ii.cs +* Created Time: 2023-06-25 +* Author: hpstory (hpstory1024@163.com) +*/ + +namespace hello_algo.chapter_backtracking; + +public class subset_sum_ii { + /* 回溯算法：子集和 II */ + public static void backtrack(List state, int target, int[] choices, int start, List> res) { + // 子集和等于 target 时，记录解 + if (target == 0) { + res.Add(new List(state)); + return; + } + // 遍历所有选择 + // 剪枝二：从 start 开始遍历，避免生成重复子集 + // 剪枝三：从 start 开始遍历，避免重复选择同一元素 + for (int i = start; i < choices.Length; i++) { + // 剪枝一：若子集和超过 target ，则直接结束循环 + // 这是因为数组已排序，后边元素更大，子集和一定超过 target + if (target - choices[i] < 0) { + break; + } + // 剪枝四：如果该元素与左边元素相等，说明该搜索分支重复，直接跳过 + if (i > start && choices[i] == choices[i - 1]) { + continue; + } + // 尝试：做出选择，更新 target, start + state.Add(choices[i]); + // 进行下一轮选择 + backtrack(state, target - choices[i], choices, i + 1, res); + // 回退：撤销选择，恢复到之前的状态 + state.RemoveAt(state.Count - 1); + } + } + + /* 求解子集和 II */ + public static List> subsetSumII(int[] nums, int target) { + List state = new List(); // 状态（子集） + Array.Sort(nums); // 对 nums 进行排序 + int start = 0; // 遍历起始点 + List> res = new List>(); // 结果列表（子集列表） + backtrack(state, target, nums, start, res); + return res; + } + + [Test] + public void Test() { + int[] nums = { 4, 4, 5 }; + int target = 9; + List> res = subsetSumII(nums, target); + Console.WriteLine("输入数组 nums = " + string.Join(", ", nums) + ", target = " + target); + Console.WriteLine("所有和等于 " + target + " 的子集 res = "); + foreach (var subset in res) { + PrintUtil.PrintList(subset); + } + } +}