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4047. Minimum Operations to Make XOR of All Elements Zero 🔒
Description
You are given an integer array nums consisting of positive integers.
You may perform the following operation any number of times:
- Choose two distinct indices
iandjsuch thatnums[i] != nums[j], and replace eithernums[i]ornums[j]withnums[i] ^ nums[j], where^denotes the bitwise XOR.
Return the minimum number of operations required to make the bitwise XOR of all elements in nums equal to 0. If it is impossible, return -1.
Example 1:
Input: nums = [8,1,4,8,2]
Output: 3
Explanation:
One optimal sequence of operations is:
- Choose indices 0 and 1, and replace
nums[0]with8 ^ 1 = 9. The array becomes[9, 1, 4, 8, 2]. - Choose indices 2 and 3, and replace
nums[3]with4 ^ 8 = 12. The array becomes[9, 1, 4, 12, 2]. - Choose indices 0 and 4, and replace
nums[0]with9 ^ 2 = 11. The array becomes[11, 1, 4, 12, 2].
The XOR of all elements of nums is 11 ^ 1 ^ 4 ^ 12 ^ 2 = 0, so the answer is 3.
Example 2:
Input: nums = [1,2,3]
Output: 0
Explanation:
The XOR of all elements of nums is 1 ^ 2 ^ 3 = 0, so no operations are required.
Example 3:
Input: nums = [1,2,4]
Output: -1
Explanation:
It is impossible to make the XOR of all elements of nums equal to 0, so the answer is -1.
Constraints:
2 <= nums.length <= 1051 <= nums[i] <= 2000