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.

Approach #1: DP. [C++]

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

　　

Analysis:

dp[i][j] : whether we can sum to j using first i numbers.

dp[i][j] = true if dp[i-1][j-num]

check dp[n-1][sum/2]

init dp[-1][0] = true

Time complexity: O(n^2*sum) -> O(n*sum)

Space complexity: O(sum)