Minimum Seconds to Equalize a Circular Array

Problem Description

You are given a 0-indexed array nums containing n integers. At each second, you can perform an operation on the array where each element can be replaced by itself or its two neighbors (considering the array as circular). Your task is to return the minimum number of seconds needed to make all elements in the array equal.

Key Insights

• The operation allows replacing any element with itself or its immediate neighbors.
• The goal is to find the most frequent element in the array as it will take the least time to convert all other elements to this value.
• The number of seconds required to equalize the array will depend on the number of elements that are different from the most frequent element.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(n)

Solution

To solve the problem, we will use the following approach:

1. Count Frequencies: Utilize a hash table (or dictionary) to count the frequency of each number in the array.
2. Find Maximum Frequency: Identify the maximum frequency among the counted elements, which represents the most common element in the array.
3. Calculate Seconds: The minimum number of seconds required will be equal to the total number of elements minus the maximum frequency. This is because all other elements need to be transformed to this most frequent element.

This algorithm runs in linear time relative to the size of the input array, making it efficient for large inputs.

Code Solutions