Minimum Operations to Make Array Equal II is a variation where you are given two arrays, nums1 and nums2, and an integer k. You want to make nums1 equal to nums2 by performing operations: choose two indices i and j, add k to nums1[i], and subtract k from nums1[j]. The problem asks for the minimum number of such operations, or -1 if it's impossible. If k=0, the arrays must already be identical.
Walmart Labs and similar companies use this problem to evaluate a candidate's grasp of Greedy algorithms and constraints. It requires checking several conditions for feasibility: the total sum of differences must be zero (conservation of mass), and each individual difference must be a multiple of k. It tests your ability to handle edge cases like k=0 and ensures you can correctly balance additions and subtractions.
This is a Greedy problem. The core idea is that every operation balances an increase in one position with a decrease in another. We iterate through both arrays simultaneously and calculate the difference diff = nums1[i] - nums2[i]. We keep track of the total positive differences and total negative differences. If at any point a diff is not divisible by k, it's impossible. Finally, if the sum of positive differences equals the absolute sum of negative differences, the answer is total_positive_diff / k.
nums1 = [4, 3, 1], nums2 = [2, 3, 3], k = 2.
4 - 2 = +2. (Difference is 2, which is 1 * k). Positives = 2, Negatives = 0.3 - 3 = 0. (No change needed).1 - 3 = -2. (Difference is -2, which is -1 * k). Positives = 2, Negatives = 2.
Total positive (2) equals absolute total negative (2). Operations = 2 / 2 = 1.Candidates often forget to handle the k=0 case, which requires a simple equality check of the two arrays. Another common mistake is not checking if each diff is divisible by k. Some also fail to verify that the total net change is zero; if you have more "additions" than "subtractions" needed, you can't balance them because each operation must do both.
When a problem involves "shifting" values between elements (like adding to one and subtracting from another), always check for invariants. Usually, the sum of the array remains constant. Tracking "balance" (the sum of required changes) is a common pattern in these types of greedy problems. Practice identifying these invariants early in your thought process.