【leetcode】416. Partition Equal Subset Sum

一、题目描述

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.

Note:

1. Each of the array element will not exceed 100.
2. The array size will not exceed 200.

Example 1:

Input: [1, 5, 11, 5]Output: trueExplanation: The array can be partitioned as [1, 5, 5] and [11].

Example 2:

Input: [1, 2, 3, 5]Output: falseExplanation: The array cannot be partitioned into equal sum subsets.

思路：用了一个最笨的方法，先算出来数组中所有数的总和sum，如果sum不能被2除断那么很明显无法分成两个和都相同的两组。如果能除断，那么就看数组中是否有和加起来等于sum/2 的组合了，用dp[i] 表示当前数组中加起来和等于i 的数的和。如果dp[sum/2] == sum/2，那么说明有组合加起来等于sum/2。

c++代码（312ms）

class Solution {public:    bool canPartition(vector<int>& nums) {        int len=nums.size();        int sum=0;        for(int i=0; i<len; i++){            sum += nums[i];        }                if((sum%2)==1)            return false;        sum = sum/2;        vector<int> dp(sum+1, 0);        for(int i=0; i<len; i++){            for(int j=sum; j>=1; j--){                if(j>=nums[i]){                    dp[j] = max(dp[j], nums[i]+dp[j-nums[i]]);                }            }        }        return dp[sum]==sum;    }};