416. Partition Equal Subset Sum

Difficulty: Medium

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:

Each of the array element will not exceed 100.
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.

class Solution {
public:
bool canPartition(vector<int>& nums) {
int sum=0;
for(auto num:nums) sum+=num;
if(sum%2) return false; //if the sum is odd, the array can't be partitioned.
int half=sum/2;
vector<bool> canPartition(half+1, false);
canPartition[0]=1;
for(auto num:nums)
for(int i=half; i>=num; i--){
if(canPartition[i-num]==1) canPartition[i]=1; //DP: if we can get the sum i, then we can get the sum i+num;
}
return canPartition[half];
}
};

运用DP思路，如果和sum能够得到，那么和sum+num也一定能够得到。