416. Partition Equal Subset Sum

Problem Link

Description

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Given an integer array nums, return true if you can partition the array into two subsets such that the sum of the elements in both subsets is equal or false otherwise.

 

Example 1:

Input: nums = [1,5,11,5]
Output: true
Explanation: The array can be partitioned as [1, 5, 5] and [11].

Example 2:

Input: nums = [1,2,3,5]
Output: false
Explanation: The array cannot be partitioned into equal sum subsets.

 

Constraints:

• 1 <= nums.length <= 200
• 1 <= nums[i] <= 100

Solution

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Python3

class Solution:
    def canPartition(self, nums: List[int]) -> bool:
        n = len(nums)
        total = sum(nums)
        target = total // 2
        if total & 1: return False
        
        bits = 1
        
        for x in nums:
            bits |= (bits << x)
        
        return (bits & (1 << target)) > 0

C++

class Solution {
public:
    bool canPartition(vector<int>& nums) {
        bitset<10001> bits(1);
        int total = 0;
        
        for (auto n:nums)
            bits |= bits << n, total += n;
        
        return !(total&1) && bits[total / 2];
    }
};