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62 lines
1.8 KiB
62 lines
1.8 KiB
8 months ago
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/**
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* File: subset_sum_ii.dart
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* Created Time: 2023-08-10
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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/* 回溯演算法：子集和 II */
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void backtrack(
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List<int> state,
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int target,
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List<int> choices,
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int start,
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List<List<int>> res,
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) {
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// 子集和等於 target 時，記錄解
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if (target == 0) {
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res.add(List.from(state));
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return;
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}
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// 走訪所有選擇
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// 剪枝二：從 start 開始走訪，避免生成重複子集
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// 剪枝三：從 start 開始走訪，避免重複選擇同一元素
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for (int i = start; i < choices.length; i++) {
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// 剪枝一：若子集和超過 target ，則直接結束迴圈
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// 這是因為陣列已排序，後邊元素更大，子集和一定超過 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：如果該元素與左邊元素相等，說明該搜尋分支重複，直接跳過
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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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// 嘗試：做出選擇，更新 target, start
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state.add(choices[i]);
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// 進行下一輪選擇
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backtrack(state, target - choices[i], choices, i + 1, res);
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// 回退：撤銷選擇，恢復到之前的狀態
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state.removeLast();
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}
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}
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/* 求解子集和 II */
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List<List<int>> subsetSumII(List<int> nums, int target) {
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List<int> state = []; // 狀態（子集）
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nums.sort(); // 對 nums 進行排序
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int start = 0; // 走訪起始點
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List<List<int>> res = []; // 結果串列（子集串列）
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backtrack(state, target, nums, start, res);
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return res;
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}
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/* Driver Code */
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void main() {
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List<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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print("輸入陣列 nums = $nums, target = $target");
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print("所有和等於 $target 的子集 res = $res");
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}
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