Set Split - Facebook Top Interview Questions


Problem Statement :


Given a list of positive integers nums, return whether you can divide the list into two groups a and b such that:

The sum of a and the sum of b are equal.

Every number in a is strictly less than every number in b.

Constraints

1 ≤ n ≤ 100,000 where n is the length of nums.

Example 1

Input

nums = [4, 9, 5]

Output

True

Explanation

We can have a = [4, 5] and b = [9] and both of their sums are 9.

Example 2

Input

nums = [9, 9]

Output

False


Explanation


We can have a = [9] and b = [9] but it doesn't meet this criteria: "Every number in a is strictly less than every number in b."



Solution :



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                        Solution in C++ :

bool solve(vector<int>& nums) {
    sort(nums.begin(), nums.end());
    int total_sum = accumulate(nums.begin(), nums.end(), 0);
    int running_sum = 0;

    for (int i = 0; i < nums.size() - 1; i++) {
        running_sum += nums[i];
        if (running_sum * 2 == total_sum && nums[i] < nums[i + 1]) return true;
    }
    return false;
}
                    


                        Solution in Java :

import java.util.*;

class Solution {
    public boolean solve(int[] A) {
        Arrays.sort(A);
        int sum = 0;
        for (int i : A) sum += i;
        int left = 0;
        for (int i = 0; i < A.length - 1; i++) {
            left += A[i];
            sum -= A[i];
            if (left == sum && A[i] < A[i + 1])
                return true;
        }

        return false;
    }
}
                    


                        Solution in Python : 
                            
class Solution:
    def solve(self, nums):
        s = sum(nums)
        if s & 1:
            return False
        target = s // 2
        nums.sort(reverse=True)
        i = 0
        while target - nums[i] >= 0:
            target -= nums[i]
            i += 1
        return not (nums[i - 1] == nums[i]) and target == 0
                    


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