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.

class Solution {
public:

    bool canPartition(vector<int> & nums)
    {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        int target = sum>>1;
        if(sum&1) return false;
        vector<int> dp(target+1, 0);
        dp[0] = 1;
        for(auto num : nums)
            for(int i = target; i>=num; i--)
                dp[i] = dp[i] || dp[i-num];
        return dp[target];
    }
};

class Solution {
public:
    bool backtrack(vector<int>& nums, int start, int target) {
        if (target <= 0) return target == 0;
        for (int i = start; i < nums.size(); i++) 
            if (backtrack(nums, i + 1, target - nums[i])) return true;
        return false;
    }
    
    bool canPartition(vector<int>& nums) {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        return !(sum & 1) && backtrack(nums, 0, sum >> 1);
    }
};