Prefix Sum Pattern: LeetCode Guide & Problems
Precompute cumulative sums to answer range queries in O(1).
Problems (9)
| Problem | Solution | Link | |
|---|---|---|---|
| Subarray Sum Equals K
#Array
#Hash Map
#Prefix Sum | Solution | ||
| Product of Array Except Self
#Array
#Prefix Product | Solution | ||
| Range Sum Query - Immutable
#Array
#Design
#Prefix Sum | Solution | ||
| Contiguous Array
#Array
#Hash Map
#Prefix Sum | Solution | ||
| Find Pivot Index
#Array
#Prefix Sum | Solution | ||
| Running Sum of 1D Array
#Array
#Prefix Sum | Solution | ||
| Minimum Average Difference
#Array
#Prefix Sum | Solution | ||
| Max Chunks To Make Sorted
#Array | Solution | ||
| Max Chunks To Make Sorted II
#Array | Solution |
Mastering the Prefix Sum Pattern for Coding Interviews
1. Mental Model & Visual Intuition
The Prefix Sum pattern is designed to eliminate redundant work and reduce search spaces. Rather than evaluating every possible state using a naive brute-force approach, this pattern relies on an invariant that allows you to safely discard subproblems that cannot lead to an optimal answer. When encountering an interview question, look for core triggers such as monotonicity, contiguous constraints, optimal substructure, or overlapping subproblems.
2. Algorithmic Invariants & Step-by-Step Execution
To implement this pattern flawlessly under interview conditions, structure your thought process into three discrete steps:
- State Initialization: Define your boundaries, pointers, or memoization tables clearly before entering loops.
- State Transition: Update tracking variables incrementally as new elements enter or leave your active evaluation window.
- Feasibility Check: When constraints are violated, systematically shrink or adjust your state until the valid invariant is restored.
3. Time and Space Complexity Trade-Offs
In top-tier technical interviews at Google, Meta, and Amazon, arriving at a working solution is only half the battle. You must explicitly justify why your approach achieves optimal Big-O bounds. For Prefix Sum, the target time complexity is typically O(n) build, O(1) per query while maintaining an auxiliary space complexity of O(n). Always discuss whether an in-place modification or two-pass traversal can save memory.
4. Common Interview Edge Cases to Test
Before informing your interviewer that you have completed coding, trace your logic against these standard high-failure test cases:
- Empty inputs, single-element collections, or all-identical values.
- Inputs with negative numbers, duplicates, or extreme values that could cause integer overflow.
- Odd versus even length inputs when dealing with pointer convergence or tree midpoints.
Related Guide
Prefix Sum Complete Guide — Range Queries and Subarray Problems for Interviews →Master prefix sums for coding interviews: O(1) range sum queries, subarray sum detection with hash m…