453. Minimum Moves to Equal Array Elements

1. Description

Given an integer array nums of length n, make every element equal using as few moves as possible.
Each move selects exactly n - 1 elements and increases each selected element by 1. Return the minimum number of moves.

2. Example

Example 1

Input: nums = [1,2,3]
Output: 3
Explanation: Three moves suffice: [1,2,3] → [2,3,3] → [3,4,3] → [4,4,4]. Each step increases two elements by 1.

Example 2

Input: nums = [1,1,1]
Output: 0
Explanation: All elements already have the same value.

3. Constraints

• n == nums.length
• 1 <= nums.length <= 10$^5$
• -10$^9$ <= nums[i] <= 10$^9$
• The minimum move count fits in a signed 32-bit integer.

4. Solutions

Math

n = nums.size()
Time complexity: O(n)
Space complexity: O(1)

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class Solution {
public:
    int minMoves(const vector<int> &nums) {
        int min_value = *min_element(nums.begin(), nums.end());
        int count = 0;
        for (int num : nums) {
            count += num - min_value;
        }

        return count;
    }
};