Reduction Operations to Make the Array Elements Equal

arraysorting

Problem Statement

Given an integer array nums , your goal is to make all elements in nums equal. To complete one operation, follow these steps:

Find the largest value in nums . Let its index be i ( 0-indexed ) and its value be largest . If there are multiple elements with the largest value, pick the smallest i .

Find the next largest value in nums strictly smaller than largest . Let its value be nextLargest .

Reduce nums[i] to nextLargest .

Return the number of operations to make all elements in nums equal .

Examples

Example 1

Input: nums = [5,1,3]
Output: 3
It takes 3 operations to make all elements in nums equal:
1. largest = 5 at index 0. nextLargest = 3. Reduce nums[0] to 3. nums = [ 3 ,1,3].
2. largest = 3 at index 0. nextLargest = 1. Reduce nums[0] to 1. nums = [ 1 ,1,3].
3. largest = 3 at index 2. nextLargest = 1. Reduce nums[2] to 1. nums = [1,1, 1 ].

Example 2

Input: nums = [1,1,1]
Output: 0
All elements in nums are already equal.

Example 3

Input: nums = [1,1,2,2,3]
Output: 4
It takes 4 operations to make all elements in nums equal:
1. largest = 3 at index 4. nextLargest = 2. Reduce nums[4] to 2. nums = [1,1,2,2, 2 ].
2. largest = 2 at index 2. nextLargest = 1. Reduce nums[2] to 1. nums = [1,1, 1 ,2,2].
3. largest = 2 at index 3. nextLargest = 1. Reduce nums[3] to 1. nums = [1,1,1, 1 ,2].
4. largest = 2 at index 4. nextLargest = 1. Reduce nums[4] to 1. nums = [1,1,1,1, 1 ].

Constraints

1 <= nums.length <= 5 * 10 ^4

1 <= nums[i] <= 5 * 10 ^4

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicSorting