# 1787. Make the XOR of All Segments Equal to Zero import collections """ 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 ... xor nums[right]'. return the minimum number of elements to change in the array such that the 'xor' of all segments of size 'k' is equal to zero """ class Solution(object): def minChanges(self, nums, k): """ :type nums: List[int] :type k: int :rtype: int """ m = 1 << 10 freq = collections.defaultdict(collections.Counter) for i, n in enumerate(nums): freq[i % k][n] += 1 dp = [[0] * m for _ in range(k + 1)] for i in range(1, m): dp[0][i] = -float("inf") for i in range(1, k + 1): max_row = max(dp[i - 1]) for j in range(m): for mask in freq[i - 1]: dp[i][j] = max( dp[i][j], max_row, dp[i - 1][j ^ mask] + freq[i - 1][mask] ) return len(nums) - dp[-1][0] if __name__ == "__main__": obj = Solution() print(obj.minChanges(nums=[1, 2, 0, 3, 0], k=1)) print(obj.minChanges(nums=[3, 4, 5, 2, 1, 7, 3, 4, 7], k=3)) print(obj.minChanges(nums=[1, 2, 4, 1, 2, 5, 1, 2, 6], k=3))