Number of Ways to Split Array

Problem Description

You are given a 0-indexed integer array nums of length n. nums contains a valid split at index i if the following are true:

• The sum of the first i + 1 elements is greater than or equal to the sum of the last n - i - 1 elements.
• There is at least one element to the right of i. That is, 0 <= i < n - 1.

Return the number of valid splits in nums.

Key Insights

• The problem requires calculating the prefix sum of the array to determine valid splits.
• For each index, we need to compare the sum of elements on the left with the sum of elements on the right.
• Optimal traversal of the array can help maintain performance, given that the maximum length can be 100,000.

Space and Time Complexity

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

Solution

To solve the problem, we use a prefix sum approach. We calculate the total sum of the array once and then maintain a running sum of the left partition as we check for valid splits. For each index i, we determine if the left sum is greater than or equal to the right sum by using the formula:

left_sum = prefix_sum[i]
right_sum = total_sum - left_sum

We iterate through the array up to the second-to-last index and count how many times the condition holds true. This approach is efficient, as it only requires a single pass through the array.

Code Solutions