Problem Description
Given an integer array nums, a split at index i (0 <= i < n-1) is considered valid if the sum of the first i+1 elements is greater than or equal to the sum of the remaining elements. The task is to count the number of such valid splits in the array.
Key Insights
- Calculate the total sum of the array to determine the sum of the right part for any split.
- Use a prefix sum to incrementally compute the sum of the left segment.
- For each possible split position (from index 0 to n-2), check if the left sum is at least as large as the right sum (totalSum - leftSum).
- Iterating only once through the array leads to an optimal solution.
Space and Time Complexity
Time Complexity: O(n) because we iterate through the array once to compute the prefix sum and check each split. Space Complexity: O(1), aside from the input array, as we only use a few extra variables.
Solution
We begin by computing the total sum of the array. Then, maintain a running prefix sum as we iterate over the array (up to the second-to-last element). At each iteration, the right part's sum is computed as totalSum - leftSum. If leftSum >= rightSum, we increment our count of valid splits. This approach uses a single pass through the array, making it efficient in both time and space. The key data structure is the array itself, and the algorithm leverages the prefix sum method.