Concepts8
Pigeonhole Principle Applications
The Pigeonhole Principle says if you put more items than boxes, at least one box must contain two or more items; this simple idea powers many algorithmic guarantees.
Functional Graph
A functional graph is a directed graph where every node has exactly one outgoing edge, so repeatedly following edges from any start eventually loops into a cycle.
Pollard's Rho Factorization
Pollard's Rho is a randomized algorithm that finds a non-trivial factor of a composite integer by walking a pseudorandom sequence modulo n and extracting a factor with a gcd.
Strongly Connected Components
Strongly Connected Components (SCCs) partition a directed graph into maximal groups where every vertex can reach every other vertex in the group.
DFS - Tree and Graph Properties
Depth-First Search (DFS) assigns each vertex a discovery time and a finish time that capture a neat nesting structure of recursion.
Topological Sort
Topological sort orders the nodes of a directed acyclic graph (DAG) so every edge points from left to right in the order.
Depth-First Search (DFS)
Depth-First Search (DFS) explores a graph by going as deep as possible along each path before backtracking.
Disjoint Set Union (Union-Find)
Disjoint Set Union (Union-Find) maintains a collection of non-overlapping sets and supports fast merging and membership queries.