416. Partition Equal Subset Sum

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: true

Explanation: The array can be partitioned as [1, 5, 5] and [11].

 

Example 2:

Input: [1, 2, 3, 5]

Output: false

Explanation: The array cannot be partitioned into equal sum subsets.

数组是否可分为两个子集，使得两个子集的元素和相等

看成一个背包大小为 sum/2 的 0-1 背包问题。

C++：

class Solution {
public:
    bool canPartition(vector<int>& nums) {
        int sum = 0 ;
        for(int num : nums){
            sum += num ;
        }
        if (sum%2!=0){
            return false ;
        }
        int W = sum/2 ;
        vector<bool> dp(W+1,false) ;
        dp[0] = true ;
        for(int num : nums){
            for(int i = W ; i >= num ; i--){
                dp[i] = (dp[i] || dp[i-num]) ;
            }
        }
        return dp[W] ;
    }
};