Minimum Operations to Make Array Equal II

Problem Description

Ah, the classic dilemma of making two arrays equal! It’s like trying to convince your cat and dog to share the same bed—good luck with that! The problem, “Minimum Operations to Make Array Equal II,” is a delightful exercise in mathematical manipulation. You have two integer arrays, nums1 and nums2, and a magical integer k. Your mission, should you choose to accept it, is to determine the minimum number of operations required to make these two arrays equal.

An operation consists of either incrementing or decrementing an element in one of the arrays by k. If k is zero, you might as well throw in the towel if the arrays aren’t already equal.

Code Solution


class Solution:
    def minOperations(self, nums1: list[int], nums2: list[int], k: int) -> int:
        if k == 0:
            return 0 if nums1 == nums2 else -1

        ans = 0
        opsDiff = 0  # the number of increments - number of decrements

        for num1, num2 in zip(nums1, nums2):
            diff = num1 - num2
            if diff == 0:
                continue
            if diff % k != 0:
                return -1
            ops = diff // k
            opsDiff += ops
            ans += abs(ops)

        return ans // 2 if opsDiff == 0 else -1

Approach Explanation

The approach here is as straightforward as a Sunday morning. First, we check if k is zero. If it is, we simply compare the two arrays. If they’re not equal, we return -1 because, let’s face it, you can’t change anything with a zero increment.

Next, we loop through both arrays simultaneously, calculating the difference between corresponding elements. If the difference isn’t divisible by k, we return -1 because that’s just not going to work. We keep track of the total operations needed and the net difference between increments and decrements. Finally, if everything balances out, we return half the total operations (because each operation affects two elements).

Time and Space Complexity

Complexity Type	Complexity
Time Complexity	O(n), where n is the length of the arrays. We traverse both arrays once.
Space Complexity	O(1), as we are using a constant amount of space for our variables.

Real-World Example

Imagine you and your friend are trying to synchronize your playlists. You have a few extra songs, and your friend has a few less. You can only add or remove songs in batches of k. The goal is to make your playlists identical with the least amount of effort. This problem is a mathematical representation of that scenario!