Maximum Equal Frequency

Problem Description

Given an array nums of positive integers, return the longest possible length of an array prefix of nums, such that it is possible to remove exactly one element from this prefix so that every number that has appeared in it will have the same number of occurrences. If after removing one element there are no remaining elements, it's still considered that every appeared number has the same number of occurrences (0).

Key Insights

• The goal is to determine a prefix of the array where, after removing one element, all remaining elements have the same frequency.
• We can track the frequency of each number and how many numbers have each frequency.
• The solution involves checking possible conditions for equal frequencies after removing one element.

Space and Time Complexity

Time Complexity: O(n), where n is the length of the nums array. Space Complexity: O(n), for storing the frequency counts and occurrence counts.

Solution

To solve this problem, we can use a hash table (dictionary) to keep track of the frequency of each number in the array. We will also maintain another hash table to count how many numbers have each frequency. As we iterate through the array, we will update these tables accordingly.

1. For each number in the array, update its frequency.
2. Update the count of how many numbers have each frequency.
3. Check various cases to determine if removing one element can lead to a valid configuration where all remaining frequencies are equal.
4. Keep track of the maximum valid prefix length found.

Code Solutions