Sliding Window vs Prefix Sum: When to Use Which?

You see a problem about "Subarray Sums".
Do you use Sliding Window? Or Prefix Sums?

Both techniques optimize $O(N^2)$ brute force to $O(N)$. But they solve fundamentally different classes of problems. Using Sliding Window on a Prefix Sum problem is the most common way to fail a "Medium" interview question.

TL;DR — Cheat Sheet

• Sliding Window:
  • Vibe: Caterpillar moving forward.
  • Use for: Longest/Shortest valid subarray.
  • Requires: Positive numbers (Monotonicity).
• Prefix Sum:
  • Vibe: Time travel (jump between indices).
  • Use for: Counting subarrays, Negative numbers, Range Sum Queries.
  • Requires: $O(N)$ extra space.

What is prefix sum technique?

Prefix Sum involves pre-calculating the cumulative sum of the array up to each index.
P[i] = nums[0] + ... + nums[i].
This allows you to calculate the sum of any subarray nums[i...j] in $O(1)$ time using P[j] - P[i-1].

Why sliding window is more appropriate in streaming scenarios

Sliding Window is greedy and local. It maintains the state of the current window.

• Pros: $O(1)$ space (usually). No need to store an auxiliary array.
• Best for: Finding the "longest" or "shortest" subarray where the condition is monotonic (e.g., sum of positive numbers).

Cases where prefix sum still wins

Prefix Sum is global. It allows you to jump between any two points in history.

• Best for:
  1. Negative Numbers: Sliding Window fails here (See Why It Breaks). Prefix Sums work fine.
  2. "Count Subarrays with Sum = K": You need a Hash Map + Prefix Sum to find all occurrences efficiently. Sliding Window can't easily count combinations.
  3. Multiple Queries: If you need to answer 1000 queries about different ranges, Prefix Sum is unbeatable.

Comparative examples

1. Longest Subarray Sum <= K (Positive Numbers)

• Winner: Sliding Window.
• Why: We can greedily expand and shrink. $O(N)$ time, $O(1)$ space.

2. Count Subarrays with Sum = K (Any Numbers)

• Winner: Prefix Sum + Hash Map.
• Why: We need to find how many times CurrentSum - K appeared in the past. Sliding Window cannot look back at arbitrary past states.

Checklist: Problem features

FAQ

Q: Can I use both techniques together?
A: Yes, but it's rare. Sometimes you might compute a Prefix Sum array first, and then use a Sliding Window on the Prefix Sums to find a range with a specific property, though usually a Hash Map is preferred for the latter.

Q: Which is harder to implement?
A: Prefix Sum + Hash Map is generally trickier to get right. You have to handle the "0" case (empty subarray sum) and be careful with map lookups. Sliding Window is more visual and intuitive once you master the template.

Summary

• Use Sliding Window for optimization (longest/shortest) on positive data.
• Use Prefix Sum for counting or handling negative numbers.

Next Step:
Want to spot these patterns instantly? Check out How to Recognize Sliding Window Problems.