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The problem

An accounting audit scans a ledger of daily net movements (positive and negative) looking for the longest stretch of consecutive days where the books exactly balance, meaning the movements sum to zero. That's the "longest subarray with sum K" problem with K = 0, and it has a particularly clean interpretation: a subarray sums to zero exactly when the running total at its end equals the running total just before its start. So you're looking for the two furthest-apart positions with the same prefix sum.

Example: [15, -2, 2, -8, 1, 7, 10, 23] → 5 (the subarray [-2, 2, -8, 1, 7]).

Function signature

int maxLenZeroSum(const vector<int>& a);  // length of the longest subarray with sum 0, or 0

Test cases

Input a	Output	Explanation
[15, -2, 2, -8, 1, 7, 10, 23]	5	[-2, 2, -8, 1, 7]
[1, 2, 3]	0	No zero-sum subarray
[1, 0, 3]	1	[0]
[0, 0, 0]	3	The whole array
[-1, 1, -1, 1]	4	The whole array

(Confirm: values can be negative, zero or positive; return 0 if no subarray sums to 0.)

How interviewers phrase it

• "Find the length of the largest subarray with 0 sum" (GeeksforGeeks).
• "Does any subarray sum to 0?" (a yes/no version, same technique).

Clarifying questions to ask

1. Can values be negative or zero?
2. Length or the subarray itself?
3. What if there is no such subarray?

Follow-ups to expect

1. "Why do equal prefix sums mean a zero-sum subarray?"
2. "Why store the first occurrence?"
3. "How do you include subarrays starting at index 0?"
4. "How would you just check existence?"
5. "Complexity?"

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