APS

Shortest path algorithms (Dijkstra, Bellman-Ford) and BFS-based state-space search illustrated with the sliding puzzle problem.

How a single depth-first walk unravels every cycle in a directed graph, without ever looking back.

From range minimum query to LCA in O(1): Segment Tree, Sparse Table, and Euler tour reduction.

From naïve O(nm) to KMP O(n+m): prefix function, rolling hash, and binary search on longest repeated substring.

From cross product to convex hull: a complete walkthrough of CCW, line segment intersection, and the Monotone Chain algorithm.