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47 lines
1.5 KiB
47 lines
1.5 KiB
/**
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* File: subset_sum_i.js
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* Created Time: 2023-07-30
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* Author: yuan0221 (yl1452491917@gmail.com)
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*/
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/* 回溯演算法：子集和 I */
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function backtrack(state, target, choices, start, res) {
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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.push([...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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for (let 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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// 嘗試：做出選擇，更新 target, start
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state.push(choices[i]);
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// 進行下一輪選擇
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backtrack(state, target - choices[i], choices, i, res);
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// 回退：撤銷選擇，恢復到之前的狀態
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state.pop();
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}
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}
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/* 求解子集和 I */
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function subsetSumI(nums, target) {
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const state = []; // 狀態（子集）
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nums.sort((a, b) => a - b); // 對 nums 進行排序
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const start = 0; // 走訪起始點
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const 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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const nums = [3, 4, 5];
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const target = 9;
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const res = subsetSumI(nums, target);
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console.log(`輸入陣列 nums = ${JSON.stringify(nums)}, target = ${target}`);
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console.log(`所有和等於 ${target} 的子集 res = ${JSON.stringify(res)}`);
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