Maximum AND Sum of Array — LeetCode 2172 Python Solution

The problem

You are given an integer array nums of length n and an integer numSlots such that 2 * numSlots >= n. There are numSlots slots numbered from 1 to numSlots.

Example

Input

nums = [1,2,3,4,5,6], numSlots = 3

Output

9

Explanation

One possible placement is [1, 4] into slot 1, [2, 6] into slot 2, and [3, 5] into slot 3.

Python solution

class Solution:
    def maximumANDSum(self, nums: List[int], numSlots: int) -> int:
        n = len(nums)
        m = numSlots << 1
        f = [0] * (1 << m)
        for i in range(1 << m):
            cnt = i.bit_count()
            if cnt > n:
                continue
            for j in range(m):
                if i >> j & 1:
                    f[i] = max(f[i], f[i ^ (1 << j)] + (nums[cnt - 1] & (j // 2 + 1)))
        return max(f)

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 2172. Maximum AND Sum of Array 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.

Related problems