LeetCode #1887 — MEDIUM

Reduction Operations to Make the Array Elements Equal

Move from brute-force thinking to an efficient approach using array strategy.

The Problem

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.

Example 1:

Input: nums = [5,1,3]
Output: 3
Explanation: 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
Explanation: All elements in nums are already equal.

Example 3:

Input: nums = [1,1,2,2,3]
Output: 4
Explanation: 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 * 10⁴
1 <= nums[i] <= 5 * 10⁴

Step 01

Brute Force Baseline

Problem summary: 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.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array

Example 1

[5,1,3]

Example 2

[1,1,1]

Example 3

[1,1,2,2,3]

Step 02

Core Insight

What unlocks the optimal approach

Sort the array.
Try to reduce all elements with maximum value to the next maximum value in one operation.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1887: Reduction Operations to Make the Array Elements Equal
class Solution {
    public int reductionOperations(int[] nums) {
        Arrays.sort(nums);
        int ans = 0, cnt = 0;
        for (int i = 1; i < nums.length; ++i) {
            if (nums[i] != nums[i - 1]) {
                ++cnt;
            }
            ans += cnt;
        }
        return ans;
    }
}

// Accepted solution for LeetCode #1887: Reduction Operations to Make the Array Elements Equal
func reductionOperations(nums []int) (ans int) {
	sort.Ints(nums)
	cnt := 0
	for i, x := range nums[1:] {
		if x != nums[i] {
			cnt++
		}
		ans += cnt
	}
	return
}

# Accepted solution for LeetCode #1887: Reduction Operations to Make the Array Elements Equal
class Solution:
    def reductionOperations(self, nums: List[int]) -> int:
        nums.sort()
        ans = cnt = 0
        for a, b in pairwise(nums):
            if a != b:
                cnt += 1
            ans += cnt
        return ans

// Accepted solution for LeetCode #1887: Reduction Operations to Make the Array Elements Equal
/**
* [1887] Reduction Operations to Make the Array Elements Equal
*
* Given an integer array nums, your goal is to make all elements in nums equal. To complete one operation, follow these steps:
* <ol>
* 	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.
*
* Example 1:
*
* Input: nums = [5,1,3]
* Output: 3
* Explanation: 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 = [<u>3</u>,1,3].
* 2. largest = 3 at index 0. nextLargest = 1. Reduce nums[0] to 1. nums = [<u>1</u>,1,3].
* 3. largest = 3 at index 2. nextLargest = 1. Reduce nums[2] to 1. nums = [1,1,<u>1</u>].
*
* Example 2:
*
* Input: nums = [1,1,1]
* Output: 0
* Explanation: All elements in nums are already equal.
*
* Example 3:
*
* Input: nums = [1,1,2,2,3]
* Output: 4
* Explanation: 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,<u>2</u>].
* 2. largest = 2 at index 2. nextLargest = 1. Reduce nums[2] to 1. nums = [1,1,<u>1</u>,2,2].
* 3. largest = 2 at index 3. nextLargest = 1. Reduce nums[3] to 1. nums = [1,1,1,<u>1</u>,2].
* 4. largest = 2 at index 4. nextLargest = 1. Reduce nums[4] to 1. nums = [1,1,1,1,<u>1</u>].
*
*
* Constraints:
*
* 	1 <= nums.length <= 5 * 10^4
* 	1 <= nums[i] <= 5 * 10^4
*
*/
pub struct Solution {}

// problem: https://leetcode.com/problems/reduction-operations-to-make-the-array-elements-equal/
// discuss: https://leetcode.com/problems/reduction-operations-to-make-the-array-elements-equal/discuss/?currentPage=1&orderBy=most_votes&query=

// submission codes start here

impl Solution {
    pub fn reduction_operations(nums: Vec<i32>) -> i32 {
        0
    }
}

// submission codes end

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    #[ignore]
    fn test_1887_example_1() {
        let nums = vec![5, 1, 3];

        let result = 3;

        assert_eq!(Solution::reduction_operations(nums), result);
    }

    #[test]
    #[ignore]
    fn test_1887_example_2() {
        let nums = vec![1, 1, 1];

        let result = 0;

        assert_eq!(Solution::reduction_operations(nums), result);
    }

    #[test]
    #[ignore]
    fn test_1887_example_3() {
        let nums = vec![1, 1, 2, 2, 3];

        let result = 4;

        assert_eq!(Solution::reduction_operations(nums), result);
    }
}

// Accepted solution for LeetCode #1887: Reduction Operations to Make the Array Elements Equal
function reductionOperations(nums: number[]): number {
    nums.sort((a, b) => a - b);
    let [ans, cnt] = [0, 0];
    for (let i = 1; i < nums.length; ++i) {
        if (nums[i] !== nums[i - 1]) {
            ++cnt;
        }
        ans += cnt;
    }
    return ans;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n × log n)

Space

O(log n)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.