Ways to Make a Fair Array

Problem Description

You are given an integer array nums. You can choose exactly one index (0-indexed) and remove the element. An array is fair if the sum of the odd-indexed values equals the sum of the even-indexed values. Return the number of indices that you could choose such that after the removal, nums is fair.

Key Insights

• The array can be split into two categories: even-indexed and odd-indexed values.
• The removal of an element changes the index positions of the remaining elements.
• We can use a prefix sum approach to efficiently calculate the sums of even and odd indexed elements as we consider removing each index.
• We need to maintain the running totals of the sums to quickly determine if the remaining array is fair after each removal.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we can use a prefix sum technique to keep track of the cumulative sums of even and odd indexed elements. For each index, we can calculate the new sums of even and odd indexed elements after the removal and check if they are equal. We maintain a count of indices that result in a fair array.

1. Initialize two variables for the even and odd indexed sums.
2. Iterate through the array to calculate the total sums for even and odd indexed positions.
3. For each index, calculate the potential new sums after removing the element at that index.
4. Check if the new sums are equal, and if so, increment the count.

Code Solutions