DSA interview question

Longest Subarray with Sum K (Positive Numbers)

Medium · Algorithms · Topics: array, prefix sum, sliding window

The problem

A delivery driver logs the kilometres covered on each leg of a route, all positive. Head office wants the longest sequence of consecutive legs that adds up to exactly K kilometres, to plan a standard shift. Checking every subarray is O(n²). Because every value is positive, a much faster idea works: a sliding window. Growing the window can only increase its sum and shrinking it can only decrease the sum, so one pass with two pointers finds the answer in O(n).

Example: [1, 2, 3, 1, 1, 1, 1, 4, 2, 3], K = 3 → 3 (the subarray [1, 1, 1]).

Function signature

int longestSubarrayWithSumK(const vector<int>& a, long long k);  // a has positive values; 0 if none

Test cases

Input `(a, k)`	Output	Explanation
`([1, 2, 3, 1, 1, 1, 1, 4, 2, 3], 3)`	3	`[1, 1, 1]` beats `[1, 2]` and `[3]`
`([10, 5, 2, 7, 1, 9], 15)`	4	`[5, 2, 7, 1]`
`([2, 3, 5], 5)`	2	`[2, 3]` is longer than `[5]`
`([1, 1, 1, 1], 2)`	2
`([5], 3)`	0	No subarray sums to 3

(Confirm: every value is positive (non-negative also works); return 0 if no subarray has sum K. Arrays with negative numbers need the prefix-sum method in S.No 75.)

How interviewers phrase it

"Find the length of the longest subarray with sum K" (GeeksforGeeks, Coding Ninjas), with the constraint that all elements are positive.
The same technique solves "minimum size subarray sum ≥ target" (LeetCode 209).
Interviewers often follow up with "What if the array can contain negatives?" (S.No 75).

Clarifying questions to ask

Are all the values positive? (That's what makes the sliding window valid.)
Should I return the length or the subarray itself?
What if no subarray matches: return 0?
How large can the sums get? (Use 64-bit.)

Follow-ups to expect

"Why does the sliding window need positive numbers?"
"Why is it O(n) with a nested while loop?"
"What's the brute-force approach?"
"What if there are negative numbers?"
"Complexity?"

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