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52 lines
1.8 KiB
52 lines
1.8 KiB
/**
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* File: subset_sum_ii.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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/* 回溯算法：子集和 II */
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function backtrack(state, target, choices, start, 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.push([...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 (let 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.push(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.pop();
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}
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}
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/* 求解子集和 II */
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function subsetSumII(nums, target) {
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const state = []; // 状态（子集）
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nums.sort((a, b) => a - b); // 对 nums 进行排序
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const start = 0; // 遍历起始点
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const res = []; // 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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/* Driver Code */
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const nums = [4, 4, 5];
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const target = 9;
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const res = subsetSumII(nums, target);
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console.log(`输入数组 nums = ${JSON.stringify(nums)}, target = ${target}`);
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console.log(`所有和等于 ${target} 的子集 res = ${JSON.stringify(res)}`);
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