416. Partition Equal Subset Sum

• Difficulty: Medium

• Topics: Dynamic Programming

• Similar Questions:

  • Partition to K Equal Sum Subsets

Problem:

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.

Solutions:

class Solution {
public:
    bool canPartition(vector<int>& nums) {
        bitset<10001> bits;
        bits[0] = 1;
        int sum = 0;
        for (auto& num : nums) {
            bits |= bits << num;
            sum += num;
        }

        return sum % 2 == 0 && bits[sum>>1] == 1;
    }
};