Minimum Moves to Equal Array Elements
Medium · Math · Array · Math
Problem
You are given an integer array nums of length n. In one move you choose n - 1 of the elements and increase each of them by 1.
Return the fewest moves needed to make all the elements equal. The answer fits in a 32-bit integer.
Examples
Input: nums = [2,5,3] Output: 4
Relative to the minimum 2, the others are 3 and 1 above it: 3 + 1 = 4 moves.
Input: nums = [6,6,6,6] Output: 0
Nothing to do.
Input: nums = [-1,4] Output: 5
Each move raises -1 by one relative to 4, and they are 5 apart.
Constraints
- n == len(nums)
- 1 <= n <= 10^5
- -10^9 <= nums[i] <= 10^9
- The answer fits in a 32-bit integer
Approaches
- Sort and level the top step by step — time O(n log n), space O(n) for the sorted copy
Follow-up
If a move may instead add or subtract 1 on a single element, the best common value is the median, and the answer is the sum of distances to it. Different move, different target: here the minimum, there the median.
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