Count All Subarrays with Zero Sum

The problem. Given an array arr of integers, return how many subarrays (runs of consecutive elements) add up to 0. Overlapping subarrays count separately.

The array 15, -2, 2, -8, 1, 7, 10, 23 has three zero-sum subarrays: -2, 2; -8, 1, 7; and -2, 2, -8, 1, 7. The answer is 3.

Example

arr = [15, -2, 2, -8, 1, 7, 10, 23]  ->  3
arr = [0, 0, 5, 5, 0, 0]             ->  6     ([0], [0], [0, 0], and the same three on the right)
arr = [1, 2, 3]                      ->  0

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Still to come

1. Brute force: add up every subarray
2. Optimal: a running sum for every start
The key idea: every earlier equal sum is one subarray
3. Best solution: prefix sums + how often each sum appeared
Comparing the approaches
Edge cases to test
Variations

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Count All Subarrays with Zero Sum

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