Is Reduction Operations to Make the Array Elements Equal easy or hard?

LeetCode classifies this problem as Medium. The challenge is recognizing that each distinct value level contributes reductions for all larger elements. Once that pattern is identified, the implementation becomes a straightforward sorting and counting pass.

Reduction Operations to Make the Array Elements Equal Python/Java solution

In Python or Java, the standard solution sorts the array and iterates once. Whenever nums[i] differs from nums[i-1], add i to the operation count. This concise logic works the same across languages like Python, Java, C++, and JavaScript.

What is the best approach for Reduction Operations to Make the Array Elements Equal?

The most common approach sorts the array and scans it once. Every time a new distinct value appears at index i, you add i operations because all larger elements must eventually be reduced through this level. This produces an O(n log n) time solution with O(1) extra space and is the method most interviewers expect.

Is Reduction Operations to Make the Array Elements Equal asked at Google/Amazon/Meta?

This problem reflects common interview patterns around sorting and counting reductions across value groups. Similar problems appear in interviews at companies like Amazon and Google where candidates must recognize patterns involving sorted arrays and cumulative operations.

What data structure is used in Reduction Operations to Make the Array Elements Equal?

The primary data structures are arrays and optionally a hash map for counting frequencies. The sorting-based approach works directly on the array, while the counting approach stores value frequencies before aggregating operations across distinct numbers.

What is the time complexity of Reduction Operations to Make the Array Elements Equal?

The typical solution runs in O(n log n) time due to sorting the array. After sorting, the algorithm performs a single linear scan to accumulate operations. Space complexity is O(1) if sorting is done in place, aside from the input array.

Description Hints 2 Solution Video 13:54

1887. Reduction Operations to Make the Array Elements Equal

Q: How to solve Reduction Operations to Make the Array Elements Equal in O(n)?

An almost linear approach uses a frequency map to count occurrences of each value, then processes unique values in sorted order. Building the map is O(n), and operations are aggregated using counts of larger elements. The total complexity becomes O(n + k log k), where k is the number of distinct values.

Medium72.7% acceptance1 company

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

Asked at 1 company

Microsoft

Topics

Array Sorting

Hints open one at a time

Hint 1

Sort the array.

Hint 2

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

13:54

Still stuck?Read 3 approaches, or watch a walkthrough.

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1class Solution:
2    def reductionOperations(self, nums: List[int]) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[5,1,3]

Input

[1,1,1]

Input

[1,1,2,2,3]

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