Subtitle / Summary Detecting a cycle in a linked list is a pointer chasing problem, not a value comparison problem. This ACERS guide explains why Floyd’s fast/slow pointers must meet if a cycle exists, how to avoid null-pointer bugs, and how the same pattern maps to engineering checks. Reading time: 10-12 min Tags: Hot100, linked list, fast slow pointers, Floyd SEO keywords: Linked List Cycle, Floyd, fast slow pointers, LeetCode 141, Hot100 Meta description: O(n)/O(1) cycle detection in singly linked lists using Floyd fast/slow pointers, with alternatives, common mistakes, and runnable multi-language code. A - Algorithm (Problem and Algorithm) Problem Restatement Given head node head of a singly linked list, determine whether there is a cycle in the list. Return true if a cycle exists, else false. ...

Subtitle / Summary The core of palindrome validation is symmetric comparison, but a singly linked list cannot move backward. The most stable engineering template is: find middle -> reverse second half in-place -> compare -> reverse back to restore. Reading time: 10-14 min Tags: Hot100, linked list, fast slow pointers, in-place reverse SEO keywords: Palindrome Linked List, fast slow pointers, reverse second half, O(1) space, LeetCode 234 Meta description: O(n)/O(1) palindrome check for singly linked list with middle detection, second-half reversal, comparison, and full structure restoration. A - Algorithm (Problem and Algorithm) Problem Restatement Given the head of a singly linked list head, return true if it is a palindrome; otherwise return false. ...

Subtitle / Summary Reverse Linked List is the first serious pointer-rewiring exercise in Hot100. It looks simple, but most bugs come from broken links and wrong operation order. This ACERS guide explains the three-pointer iterative template thoroughly and compares it with recursion. Reading time: 10-12 min Tags: Hot100, linked list, pointer, iteration SEO keywords: Hot100, Reverse Linked List, three pointers, iterative, recursive, LeetCode 206 Meta description: Three-pointer iterative reversal in O(n)/O(1), with recursive contrast, common pitfalls, engineering mapping, and runnable multi-language implementations. A - Algorithm (Problem and Algorithm) Problem Restatement Given the head of a singly linked list, reverse the list and return the new head. ...

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. ...

This is a “graph algorithms topic navigation” page. The goal is not to stack articles together, but to give you an executable learning path from basic traversal to distributed graph computation. Current Directory Status (Topic Structuring Completed) The graph algorithms series has been migrated to: content/zh/dev/algorithm/graph/ It also uses two-digit prefixes (00/10/20...) to mark reading order, which makes it easier to: Browse in sequence within the file system Insert new articles incrementally later (while preserving numbering gaps) Locate stages quickly during batch maintenance Recommended Reading Order (By Capability Building) Stage 0: Traversal Fundamentals (Lay the Foundation First) BFS / DFS Engineering Intro: k-hop Queries, Subgraph Extraction, and Path Reachability Shortest Path in Practice: Engineering Selection of BFS, Dijkstra, and A* Goals: ...

A systematic walkthrough of Pregel (BSP) and GAS (Gather-Apply-Scatter), focused on execution paths, convergence strategies, and engineering trade-offs for PageRank, Connected Components, and parallel BFS.

Starting from Edge-cut/Vertex-cut objective functions, this article systematically explains METIS-style multilevel partitioning and production implementation, with emphasis on how partitioning affects query latency and cross-machine traffic.

Subtitle / Abstract In dynamic-graph workloads, the real pain point is not “do you know the algorithm,” but “can the system survive continuous updates.” Following the ACERS template, this article explains three engineering essentials: incremental shortest path, incremental PageRank, and connectivity maintenance, along with three practical strategies: local recomputation, lazy updates, and approximate results. Estimated reading time: 14-18 minutes Tags: dynamic graph, incremental computation, shortest path, PageRank, connectivity maintenance SEO keywords: dynamic graph, incremental shortest path, incremental PageRank, connectivity maintenance, local recomputation, lazy updates, approximate results Meta description: An engineering guide to dynamic graphs: how to control latency and cost in high-frequency update scenarios with incremental algorithms and practical system strategies. Target Audience Engineers building online services for graph databases, relationship graphs, and recommendation graphs Developers moving from offline graph computation to real-time incremental computation Tech leads who want to replace “full recomputation” with a production-ready update pipeline Background / Motivation Static graph algorithms look elegant in papers, but real production graphs are constantly changing: ...

Subtitle / Abstract Community detection is not just “splitting a graph into a few groups.” In production, you must balance accuracy, interpretability, speed, and maintainability. Following the ACERS structure, this article breaks down two of the most common engineering choices: Louvain (modularity optimization) and Label Propagation (LPA). Estimated reading time: 12-16 minutes Tags: Community Detection, Louvain, Label Propagation, Graph Partitioning SEO keywords: community detection, Louvain, Label Propagation, modularity, graph partition Meta description: Engineering primer for community detection: principles, complexity, algorithm selection, and implementation templates for Louvain and LPA across group discovery, graph partitioning, and cold start. Target Audience Engineers working on social graphs, risk-control graphs, or recommender-system graph analytics Developers who want to move community detection from paper concepts into production workflows Practitioners modeling group structure for graph partitioning and cold-start scenarios Background / Motivation Community detection appears frequently in production: ...

Subtitle / Abstract Subgraph matching is one of the hardest parts of graph querying: NP-hard in theory, but not automatically “too slow” in production. Following the ACERS template, this article explains VF2 and Ullmann clearly, and focuses on what actually decides performance: candidate generation and pruning strategy. Estimated reading time: 15-20 minutes Tags: Subgraph Matching, VF2, Ullmann, Graph Database SEO keywords: Subgraph Isomorphism, VF2, Ullmann, candidate pruning, graph pattern matching Meta description: Starting from NP-hard subgraph isomorphism, this article explains VF2/Ullmann mechanics and practical pruning strategies for constrained graph-database pattern queries. Target Audience Engineers building pattern queries, rule detection, or risk-relationship mining in graph databases Developers who already know BFS/DFS/connected components and want stronger graph-matching skills Algorithm practitioners balancing explainable rule matching against performance limits Background / Motivation In graph databases, you regularly face requirements like: ...