Hash Map

Subtitle / Summary Clone Graph is not a traversal-only problem. The real challenge is preserving graph structure while avoiding duplicate copies in the presence of cycles. The stable solution is a traversal plus a hash map from original nodes to cloned nodes. Reading time: 12-15 min Tags: graph, dfs, bfs, hash map, deep copy SEO keywords: Clone Graph, graph deep copy, DFS, BFS, LeetCode 133 Meta description: Deep-copy an undirected graph with a node-to-node map, explaining why memoization is mandatory and how DFS/BFS versions work, with runnable code in six languages. Target Readers LeetCode learners practicing graph traversal and deep-copy patterns Engineers who duplicate object graphs, workflow graphs, or topology graphs Developers who want one reusable template for “clone with cycles” Background / Motivation Many “copy” problems are actually identity-preservation problems. ...

Subtitle / Summary This is not a memorization question. It is core cache-engineering practice: satisfy fast lookup and least-recently-used eviction at the same time, both in constant average time. We derive the optimal structure from naive approaches and provide runnable implementations. Reading time: 14-18 min Tags: LRU, hash map, doubly linked list, system design SEO keywords: LRU Cache, LeetCode 146, hash map, doubly linked list, O(1) Meta description: Build an LRU cache with hash map + doubly linked list to achieve O(1) average get/put, with engineering use cases, pitfalls, and six-language implementations. Target Readers LeetCode learners who want to master data-structure composition Backend/middleware engineers implementing local caches Interview candidates who know the answer headline but not the invariants Background / Motivation Caching trades space for time, but cache space is limited. When full, we must evict keys. LRU (Least Recently Used) assumes: ...

Subtitle / Summary This is Hot100 article #1 for the series: Subarray Sum Equals K. We reduce the naive O(n^2) approach to O(n) with prefix sum plus a frequency hash map, then map the same pattern to real engineering scenarios. Reading time: 12-15 min Tags: Hot100, prefix sum, hash map SEO keywords: Subarray Sum Equals K, prefix sum, hash map, O(n), Hot100 Meta description: O(n) counting of subarrays with sum k using prefix sum + hash map, with complexity analysis and runnable multi-language code. Target Readers Hot100 learners who want stable reusable templates Intermediate engineers who want to transfer counting patterns to real data pipelines Interview prep readers who want to master prefix sum + hash map Background / Motivation “Count subarrays whose sum equals k” is one of the most classic counting problems. It appears in log analytics, risk threshold hits, and transaction sequence statistics. The two-loop brute force method is straightforward, but slows down quickly as input grows. So we need an O(n) method that scales. ...

Subtitle / Summary The constraint “the path can start anywhere, but must go downward” makes root-to-leaf DP insufficient. This ACERS guide explains prefix sums on trees: convert any downward path into a difference of two prefix sums, maintain a frequency hash map during one DFS, and finish in O(n). Reading time: 12–15 min Tags: binary tree, prefix sum, DFS, hash map SEO keywords: Path Sum III, tree prefix sum, prefix-sum hash, LeetCode 437 Meta description: Count downward paths whose sum equals targetSum in O(n) via prefix sum + hash map, with derivation, tradeoffs, and multi-language implementations. Target Readers LeetCode learners who want a reusable “tree + hash map” template People who tend to write O(n²) when the path does not have to start at the root Engineers working with hierarchical data (call traces, org trees) who need “downward segment” statistics Background / Motivation Many “tree path” problems hide a trap: you naturally assume paths start at the root, or end at leaves — but this problem allows the path to start and end at any nodes, as long as the direction is downward (parent → child). ...