19 articles
Learn how to remove consecutive nodes that sum to zero from a linked list using a prefix sum hashmap in two passes. A tricky interview problem asked at Google and Amazon that combines linked list manipulation with the classic prefix sum technique.
LeetCode 1480 is the gateway to one of the most powerful patterns in competitive programming and FAANG interviews: prefix sums. Master the in-place O(1) space solution, understand why the prefix sum array unlocks O(1) range queries, and learn the real follow-up questions — range sum queries, subarray sum equals K, and 2D matrix prefix sums — that interviewers ask once you solve this problem in thirty seconds.
LeetCode 238 is one of the most frequently asked medium problems at Google and Meta. Learn why the no-division constraint is intentional, how the prefix × suffix insight unlocks the O(n) solution, and how a single running variable eliminates the extra O(n) space entirely.
LeetCode 560 is one of the most-asked FAANG problems because it teaches the prefix sum + hashmap pattern — a technique that handles negative numbers, generalizes to a dozen follow-ups, and cannot be replaced by sliding window. Learn the insight, the dry run, the common mistakes, and the O(n) solution in Python and JavaScript.
Master LeetCode 209 from first principles: understand why a variable-size shrinkable sliding window is the insight that cracks this problem in O(n), trace through every pointer movement on a real example, learn the three common interview mistakes, and be ready for the O(n log n) binary search follow-up that Amazon and Microsoft love to ask.
Negative numbers completely break the classic sliding window for minimum-length subarray problems. Learn exactly why, then master the only correct approach — a monotonic deque on prefix sums — with a step-by-step visual trace, the three mistakes every candidate makes, and every real interview follow-up with approach hints.
Master LeetCode 327 — Count of Range Sum — with deep intuition, a visual dry run, brute-force to O(n log n) merge sort progression, and real interview follow-ups covering BIT, LC 315, and LC 493.
Count subarrays whose sum lies in [lower, upper] using merge sort on prefix sums in O(n log n). Understand the divide-and-conquer counting trick that makes an O(n^2) brute-force drop to linearithmic time.
LC 974 Subarray Sum Divisible by K counts subarrays whose sum is divisible by K using prefix remainders and a frequency hash map — the canonical prefix mod pattern tested at Google, Amazon, and Facebook.
Count subarray sums in [lower, upper] using merge sort or Fenwick tree on prefix sums. The flagship Hard problem connecting prefix sums, divide-and-conquer counting, and BIT range queries.
Apply many range shift operations to a string in O(n + q) using a difference array. The textbook example of when a diff array beats a segment tree, and the canonical interview signal for offline range updates.
Master LeetCode 304 Range Sum Query 2D Immutable with 2D prefix sums, inclusion-exclusion, and the natural extension to 2D Fenwick tree (BIT) for the mutable variant.
Crack LeetCode 363 Max Sum of Rectangle No Larger Than K by fixing two row boundaries to collapse 2D into 1D, then using prefix sums plus a sorted set (or BIT/segment tree) to find the best subarray sum bounded above by K.
Find the longest contiguous subarray whose sum is at most K in linear time using prefix sums plus a decreasing monotonic stack, then learn the segment tree and BIT alternatives for streaming variants.
Solve LeetCode 862 Shortest Subarray with Sum At Least K in O(n) using a monotonic increasing deque on prefix sums. A FAANG hard interview classic.
LC 437 Path Sum III counts all paths in a binary tree summing to a target. The optimal O(n) solution mirrors the subarray sum equals k trick — use a prefix sum frequency map with DFS backtracking, a pattern tested at Amazon and Google.
LeetCode 1480 Running Sum of 1D Array introduces the prefix sum technique used in dozens of FAANG range query problems. Build the running sum in O(n) time and O(1) extra space and unlock LC 303, LC 560, and LC 974.
LC 974 counts subarrays whose sum is divisible by k using prefix sums modulo k and a frequency map of remainders. O(n) time, O(k) space. The standard FAANG pattern for all modular subarray problems.
Find the shortest subarray whose sum is at least k, even with negative numbers, using a monotone increasing deque on prefix sums — the canonical hard problem where a simple sliding window fails.