Make the XOR of All Segments Equal to Zero — LeetCode 1787 Python Solution

The problem

You are given an array nums​​​ and an integer k​​​​​. The XOR of a segment [left, right] where left <= right is the XOR of all the elements with indices between left and right, inclusive: nums[left] XOR nums[left+1] XOR ...

Example

Input

nums = [1,2,0,3,0], k = 1

Output

3

Explanation

Modify the array from [1,2,0,3,0] to from [0,0,0,0,0].

Python solution

class Solution:
    def minChanges(self, nums: List[int], k: int) -> int:
        n = 1 << 10
        cnt = [Counter() for _ in range(k)]
        size = [0] * k
        for i, v in enumerate(nums):
            cnt[i % k][v] += 1
            size[i % k] += 1
        f = [inf] * n
        f[0] = 0
        for i in range(k):
            g = [min(f) + size[i]] * n
            for j in range(n):
                for v, c in cnt[i].items():
                    g[j] = min(g[j], f[j ^ v] + size[i] - c)
            f = g
        return f[0]

Complexity

Pattern: Bit Manipulation

Use XOR, masks and the low-bit trick to replace whole data structures with an integer. LeetCode 1787. Make the XOR of All Segments Equal to Zero is filed here because LeetCode tags it Bit Manipulation, 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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