My first instinct was prefix sums with a hash set, which works when you have negative numbers in the mix.
Start by clarifying constraints (e.g., array size, whether negative numbers are allowed) and then propose an efficient solution using a hash map to track prefix sums, achieving O(n) time. Explain the algorithm step-by-step, handle edge cases, and analyze time and space complexity.
Pro tip: Mention that if the array contains only non-negative numbers, a sliding window approach works, but the prefix sum method is more general and handles negative numbers too. This shows you understand trade-offs and can adapt to variations.
Ask about constraints: array size, range of values, whether negative numbers are allowed, and if the subarray must be non-empty. This ensures you understand the problem fully before coding.
Mention the O(n^2) brute force method, then propose the O(n) prefix sum with hash map approach. Explain why it's more efficient and how it works.
Describe maintaining a running sum and a hash map of prefix sums to their earliest index. For each element, check if (current_sum - target) exists in the map; if so, return true. Otherwise, store the current sum if not already present.
Choose a small example (e.g., [1,2,3], target=5) and trace the algorithm step-by-step to demonstrate correctness and clarity.
State time complexity O(n) and space complexity O(n). Discuss edge cases: empty array, target=0, all zeros, and large arrays.
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