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feat(csharp/backtracking): add subset_sum_i, _ii, _i_naive (#567)
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55
codes/csharp/chapter_backtracking/subset_sum_i.cs
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codes/csharp/chapter_backtracking/subset_sum_i.cs
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/**
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* File: subset_sum_i.cs
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* Created Time: 2023-06-25
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* Author: hpstory (hpstory1024@163.com)
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*/
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namespace hello_algo.chapter_backtracking;
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public class subset_sum_i {
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/* 回溯算法:子集和 I */
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public static void backtrack(List<int> state, int target, int[] choices, int start, List<List<int>> res) {
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// 子集和等于 target 时,记录解
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if (target == 0) {
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res.Add(new List<int>(state));
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return;
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}
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// 遍历所有选择
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// 剪枝二:从 start 开始遍历,避免生成重复子集
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for (int i = start; i < choices.Length; i++) {
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// 剪枝一:若子集和超过 target ,则直接结束循环
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// 这是因为数组已排序,后边元素更大,子集和一定超过 target
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if (target - choices[i] < 0) {
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break;
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}
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// 尝试:做出选择,更新 target, start
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state.Add(choices[i]);
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// 进行下一轮选择
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backtrack(state, target - choices[i], choices, i, res);
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// 回退:撤销选择,恢复到之前的状态
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state.RemoveAt(state.Count - 1);
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}
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}
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/* 求解子集和 I */
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public static List<List<int>> subsetSumI(int[] nums, int target) {
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List<int> state = new List<int>(); // 状态(子集)
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Array.Sort(nums); // 对 nums 进行排序
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int start = 0; // 遍历起始点
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List<List<int>> res = new List<List<int>>(); // 结果列表(子集列表)
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backtrack(state, target, nums, start, res);
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return res;
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}
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[Test]
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public void Test() {
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int[] nums = { 3, 4, 5 };
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int target = 9;
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List<List<int>> res = subsetSumI(nums, target);
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Console.WriteLine("输入数组 nums = " + string.Join(", ", nums) + ", target = " + target);
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Console.WriteLine("所有和等于 " + target + " 的子集 res = ");
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foreach (var subset in res) {
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PrintUtil.PrintList(subset);
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}
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}
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}
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53
codes/csharp/chapter_backtracking/subset_sum_i_naive.cs
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codes/csharp/chapter_backtracking/subset_sum_i_naive.cs
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/**
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* File: subset_sum_i_naive.cs
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* Created Time: 2023-06-25
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* Author: hpstory (hpstory1024@163.com)
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*/
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namespace hello_algo.chapter_backtracking;
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public class subset_sum_i_naive {
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/* 回溯算法:子集和 I */
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public static void backtrack(List<int> state, int target, int total, int[] choices, List<List<int>> res) {
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// 子集和等于 target 时,记录解
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if (total == target) {
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res.Add(new List<int>(state));
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return;
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}
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// 遍历所有选择
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for (int i = 0; i < choices.Length; i++) {
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// 剪枝:若子集和超过 target ,则跳过该选择
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if (total + choices[i] > target) {
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continue;
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}
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// 尝试:做出选择,更新元素和 total
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state.Add(choices[i]);
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// 进行下一轮选择
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backtrack(state, target, total + choices[i], choices, res);
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// 回退:撤销选择,恢复到之前的状态
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state.RemoveAt(state.Count - 1);
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}
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}
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/* 求解子集和 I(包含重复子集) */
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public static List<List<int>> subsetSumINaive(int[] nums, int target) {
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List<int> state = new List<int>(); // 状态(子集)
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int total = 0; // 子集和
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List<List<int>> res = new List<List<int>>(); // 结果列表(子集列表)
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backtrack(state, target, total, nums, res);
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return res;
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}
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[Test]
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public void Test() {
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int[] nums = { 3, 4, 5 };
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int target = 9;
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List<List<int>> res = subsetSumINaive(nums, target);
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Console.WriteLine("输入数组 nums = " + string.Join(", ", nums) + ", target = " + target);
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Console.WriteLine("所有和等于 " + target + " 的子集 res = ");
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foreach (var subset in res) {
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PrintUtil.PrintList(subset);
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}
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Console.WriteLine("请注意,该方法输出的结果包含重复集合");
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}
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}
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60
codes/csharp/chapter_backtracking/subset_sum_ii.cs
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60
codes/csharp/chapter_backtracking/subset_sum_ii.cs
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/**
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* File: subset_sum_ii.cs
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* Created Time: 2023-06-25
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* Author: hpstory (hpstory1024@163.com)
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*/
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namespace hello_algo.chapter_backtracking;
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public class subset_sum_ii {
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/* 回溯算法:子集和 II */
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public static void backtrack(List<int> state, int target, int[] choices, int start, List<List<int>> res) {
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// 子集和等于 target 时,记录解
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if (target == 0) {
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res.Add(new List<int>(state));
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return;
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}
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// 遍历所有选择
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// 剪枝二:从 start 开始遍历,避免生成重复子集
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// 剪枝三:从 start 开始遍历,避免重复选择同一元素
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for (int i = start; i < choices.Length; i++) {
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// 剪枝一:若子集和超过 target ,则直接结束循环
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// 这是因为数组已排序,后边元素更大,子集和一定超过 target
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if (target - choices[i] < 0) {
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break;
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}
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// 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
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if (i > start && choices[i] == choices[i - 1]) {
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continue;
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}
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// 尝试:做出选择,更新 target, start
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state.Add(choices[i]);
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// 进行下一轮选择
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backtrack(state, target - choices[i], choices, i + 1, res);
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// 回退:撤销选择,恢复到之前的状态
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state.RemoveAt(state.Count - 1);
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}
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}
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/* 求解子集和 II */
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public static List<List<int>> subsetSumII(int[] nums, int target) {
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List<int> state = new List<int>(); // 状态(子集)
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Array.Sort(nums); // 对 nums 进行排序
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int start = 0; // 遍历起始点
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List<List<int>> res = new List<List<int>>(); // 结果列表(子集列表)
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backtrack(state, target, nums, start, res);
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return res;
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}
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[Test]
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public void Test() {
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int[] nums = { 4, 4, 5 };
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int target = 9;
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List<List<int>> res = subsetSumII(nums, target);
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Console.WriteLine("输入数组 nums = " + string.Join(", ", nums) + ", target = " + target);
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Console.WriteLine("所有和等于 " + target + " 的子集 res = ");
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foreach (var subset in res) {
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PrintUtil.PrintList(subset);
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}
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}
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}
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