87 lines
1.8 KiB
Markdown
87 lines
1.8 KiB
Markdown
## 题目地址
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https://leetcode.com/problems/partition-equal-subset-sum/description/
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## 题目描述
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```
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Given a non-empty array containing only positive integers, find if the array can be partitioned into two subsets such that the sum of elements in both subsets is equal.
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Note:
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Each of the array element will not exceed 100.
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The array size will not exceed 200.
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Example 1:
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Input: [1, 5, 11, 5]
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Output: true
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Explanation: The array can be partitioned as [1, 5, 5] and [11].
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Example 2:
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Input: [1, 2, 3, 5]
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Output: false
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Explanation: The array cannot be partitioned into equal sum subsets.
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```
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## 思路
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题目要求给定一个数组， 问是否能划分为和相等的两个数组。
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这是一个典型的背包问题，我们可以遍历数组，对于每一个，我们都分两种情况考虑，拿或者不拿。
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背包问题处理这种离散的可以划分子问题解决的问题很有用。
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如果能够识别出这是一道背包问题，那么就相对容易了。
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## 关键点解析
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- 背包问题
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## 代码
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```js
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/**
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* @param {number[]} nums
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* @return {boolean}
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*/
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var canPartition = function(nums) {
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let sum = 0;
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for(let num of nums) {
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sum += num;
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}
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if (sum & 1 === 1) return false;
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const half = sum >> 1;
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let dp = Array(half);
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dp[0] = [true, ...Array(nums.length).fill(false)];
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for(let i = 1; i < nums.length + 1; i++) {
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dp[i] = [true, ...Array(half).fill(false)];
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for(let j = 1; j < half + 1; j++) {
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if (j >= nums[i - 1]) {
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dp[i][j] = dp[i - 1][j] || dp[i - 1][j - nums[i - 1]];
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}
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}
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}
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return dp[nums.length][half]
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};
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```
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