Split Array With Same Average — LeetCode 805 Python Solution

The problem

You are given an integer array nums. You should move each element of nums into one of the two arrays A and B such that A and B are non-empty, and average(A) == average(B).

Example

Input

nums = [1,2,3,4,5,6,7,8]

Output

true

Explanation

We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have an average of 4.5.

Python solution

class Solution:
    def splitArraySameAverage(self, nums: List[int]) -> bool:
        n = len(nums)
        if n == 1:
            return False
        s = sum(nums)
        for i, v in enumerate(nums):
            nums[i] = v * n - s
        m = n >> 1
        vis = set()
        for i in range(1, 1 << m):
            t = sum(v for j, v in enumerate(nums[:m]) if i >> j & 1)
            if t == 0:
                return True
            vis.add(t)
        for i in range(1, 1 << (n - m)):
            t = sum(v for j, v in enumerate(nums[m:]) if i >> j & 1)
            if t == 0 or (i != (1 << (n - m)) - 1 and -t in vis):
                return True
        return False

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 805. Split Array With Same Average is filed here because LeetCode tags it Bit Manipulation and Bitmask, which is the vocabulary this hub collects.

The bit manipulation guide has the Python template for the pattern and the 194 LeetCode problems that use it.

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