Step-by-step guide to solving LeetCode 560 Subarray Sum Equals K in interviews, with clear explanation and tips.
What is 560. subarray sum equals k and can you see examples of it
560. subarray sum equals k asks you to count contiguous, non-empty subarrays whose elements sum to k. The input allows negative numbers, so sliding-window alone won't work reliably. A clear example from practice: nums = [2, -1, 1, 2], k = 2 has four valid subarrays (indices are inclusive):
- [2] (index 0)
- [2, -1, 1] (indices 0–2)
- [1, 2] (indices 2–3)
- [2] (index 3)
Another example: nums = [1, 1, 1], k = 2 has two subarrays: [1,1] at indices (0–1) and (1–2). Constraints you should call out in interviews: n ≤ 20,000 and nums[i] ∈ [-1000, 1000], so aim for an O(n) solution where possible (neetcode, GeeksforGeeks).
How does the brute force approach for 560. subarray sum equals k work and why is it slow
Brute force makes the problem obvious but inefficient:
- O(n³): three nested loops that enumerate every start, end, and recompute sum — easy to write, rarely acceptable.
- O(n²): improve by precomputing prefix sums so each subarray sum becomes O(1), but enumerating all start/end pairs still takes O(n²). This will TLE on n up to 20k (interviewing.io, dev.to).
In interviews, state the brute idea succinctly, then propose a faster approach: count prior prefix sums that differ from current by k using a hashmap.
How does the optimal hashmap solution for 560. subarray sum equals k work conceptually
The optimal pattern is prefix-sum + hashmap. Let prefixsum[i] be the sum of nums[0..i]. For a subarray (j+1..i) to sum to k we need: prefixsum[i] - prefixsum[j] = k => prefixsum[j] = prefix_sum[i] - k
So at each index i you:
1. Compute current prefix_sum.
2. Add to your answer the number of times prefix_sum[i] - k has appeared before (lookup in hashmap).
3. Then record prefix_sum[i] into the hashmap.
Key implementation details interviewers expect:
- Initialize the hashmap with {0: 1} so subarrays that start at index 0 are counted.
- Lookup before incrementing the current prefix count to avoid counting the current index as a prior prefix. This technique yields O(n) time and O(n) space and is standard for this problem (neetcode, GeeksforGeeks, interviewing.io).
How can I implement 560. subarray sum equals k in Python and JavaScript with clear comments
Below are compact, interview-ready implementations that follow the safe pattern: lookup then update.
Python (readable for a whiteboard-to-code transition): ```python def subarraySum(nums, k): count = 0 prefix = 0 freq = {0: 1} # prefix sum 0 seen once to count subarrays starting at index 0
for x in nums: prefix += x # How many prior prefixes would make a subarray ending here sum to k? count += freq.get(prefix - k, 0) # Record this prefix for future indices freq[prefix] = freq.get(prefix, 0) + 1
return count ```
JavaScript (ES6, same logic): ```javascript function subarraySum(nums, k) { let count = 0; let prefix = 0; const freq = new Map([[0, 1]]); // prefix sum 0 seen once
for (const x of nums) { prefix += x; const need = prefix - k; if (freq.has(need)) count += freq.get(need); freq.set(prefix, (freq.get(prefix) || 0) + 1); }
return count; } ```
Explain choices while coding: "I initialize {0:1} so subarrays that begin at index 0 are counted. For each element I check prefix - k in the map, add that frequency to answer, then increment the prefix count."
What is the time and space complexity for 560. subarray sum equals k and how does it compare to brute force
- Optimal hashmap approach: O(n) time (single pass) and O(n) extra space (hashmap of distinct prefix sums). With n ≤ 20k this is safe and typical in interviews (neetcode).
- Brute approaches: O(n³) naive, O(n²) with prefix sums — both often unacceptable for worst-case inputs and will hit time limits on large tests (interviewing.io, dev.to).
Note: The hashmap size is bounded by the number of distinct prefix sums (≤ n+1). Use it early in interviews to avoid time-limit pitfalls.
What are common pitfalls and edge cases for 560. subarray sum equals k and how do you fix them
Common pitfalls
- Forgetting {0:1} initialization — you miss subarrays that begin at index 0. Fix: always seed the map with 0 → 1.
- Updating the map before lookup — this can incorrectly count the current prefix as a prior one. Fix: lookup first, then increment.
- Mishandling k = 0 — zeros and negatives can yield many valid subarrays; handled naturally by the prefix approach when map usage is correct.
- Off-by-one / indexing errors when translating math to code — draw a small array and trace prefix sums on paper.
- Memory worry about hashmap growth — although possible, with n ≤ 20k it's acceptable for interviews (GeeksforGeeks, neetcode).
Test cases to try in interview or practice:
- Empty array or single-element arrays.
- All positives, all negatives, mixtures.
- k = 0 and arrays with multiple zeros (ensure counts include overlapping zero-sum subarrays).
- Large arrays with repeating cumulative patterns.
How should I explain 560. subarray sum equals k under interview pressure and what variations should I mention
Interview pitch sequence (60–120 seconds):
1. Restate problem and constraints (mention negatives permitted).
2. Offer brute force (O(n²) with prefix sums) quickly to show correctness baseline.
3. Present prefix sum + hashmap idea: "Count prior prefix sums equal to current_prefix - k; initialize map {0:1}."
4. Outline complexity O(n) time, O(n) space and note tradeoffs.
5. If time, code the loop and narrate key checks (lookup then update).
Variations to mention to show depth:
- Count subarrays with sum > k or closest to k — these require different techniques (two pointers/monotonic structures or transforms).
- Continuous Subarray Sum with modulo (sum % k) where modulo logic is used instead of direct difference — similar hashmap idea but with mods (YouTube discussions of variants, neetcode).
- Maximum subarray sum (Kadane’s algorithm) — related family but different objective.
Communication tips:
- Use a simple analogy: "track cumulative spend and count how many earlier balances are exactly current minus target" — that maps to prefix_sum logic and helps non-technical interviewers follow.
- Draw the array, prefix sums, and pointers on the board. Mark prefix values and show how previous equalities correspond to valid subarrays.
- Practice saying "lookup then update" as a guardrail phrase during the code walkthrough.
What follow-up practice and drills should I do after solving 560. subarray sum equals k
Practice drills to cement the pattern:
- Implement the solution in two languages (Python + JavaScript/Java) until fluent.
- Trace by hand 5 arrays (include negatives and zeros).
- Solve related problems: Continuous Subarray Sum, subarray sum equals k with modulo, count subarrays with sum less than k, and maximum subarray sum (Kadane).
- Mock interview: explain to a peer or record yourself explaining the prefix+hashmap idea in under 90 seconds.
- Time-boxed practice: be able to explain O(n²) fallback and justify moving to O(n) within 2 minutes of reading the problem.
Suggested resources to study and cross-check solutions:
- NeetCode solution notes and walkthroughs: https://neetcode.io/solutions/subarray-sum-equals-k
- GeeksforGeeks explanation and examples: https://www.geeksforgeeks.org/dsa/number-subarrays-sum-exactly-equal-k/
- First-hand interview question reference: https://interviewing.io/questions/subarray-sum-equals-k
- Developer diary and community explanations: https://dev.to/kevin074/leetcode-diary-560-subarray-sum-equals-k-55i4
How Can Verve AI Copilot Help You With 560. subarray sum equals k
Verve AI Interview Copilot can simulate interview prompts for 560. subarray sum equals k, give instant feedback on your explanation, and generate step-by-step hints when you’re stuck. Use Verve AI Interview Copilot to rehearse your 90-second pitch, ask for targeted follow-ups, and grade your code clarity. Verve AI Interview Copilot also produces focused practice drills and debugging tips, and you can try it at https://vervecopilot.com
What Are the Most Common Questions About 560. subarray sum equals k
Q: What is the simplest optimal approach for 560. subarray sum equals k A: Use prefix sums + hashmap: count occurrences of prefix_sum - k while scanning left to right.
Q: Why do we initialize freq with {0:1} for 560. subarray sum equals k A: It counts subarrays starting at index 0 by treating an empty prefix as seen once.
Q: When does the hashmap method for 560. subarray sum equals k fail A: It doesn’t fail logically; but forgetting lookup-before-update or {0:1} breaks counts.
Q: How do negatives affect 560. subarray sum equals k solutions A: Negatives invalidate sliding-window; prefix-sum + hashmap handles negatives fine.
Q: What complexity should I claim for 560. subarray sum equals k in interviews A: O(n) time and O(n) space with explanation of the hashmap of prefix counts.
Final checklist for interview-ready delivery of 560. subarray sum equals k
- State problem and constraints, give one example (walk it).
- Offer brute idea, then present prefix-sum + hashmap in plain English.
- Code the loop with comment "lookup then update" and initialize {0:1}.
- Run a couple of edge-case mental tests (k=0, negatives, starts-at-zero).
- Mention complexity and possible follow-ups or variations.
References
- NeetCode solution notes and walkthrough: https://neetcode.io/solutions/subarray-sum-equals-k
- GeeksforGeeks explanation: https://www.geeksforgeeks.org/dsa/number-subarrays-sum-exactly-equal-k/
- Interview question example: https://interviewing.io/questions/subarray-sum-equals-k
- Developer walkthrough: https://dev.to/kevin074/leetcode-diary-560-subarray-sum-equals-k-55i4
- Variant discussion videos and deeper walkthroughs: https://www.youtube.com/watch?v=rsDvhHiAe1E, https://www.youtube.com/watch?v=fFVZt-6sgyo
Good luck — practice the pitch and the prefix intuition until saying it aloud is automatic, then code confidently and explain clearly.
Kevin Durand
Career Strategist
