Concepts7
Problem Classification Patterns
Many competitive programming problems map to a small set of classic patterns; recognizing keywords and constraints lets you pick the right tool fast.
Minimum Cost Maximum Flow
Minimum Cost Maximum Flow (MCMF) finds the maximum possible flow from a source to a sink while minimizing the total cost paid per unit of flow along edges.
Johnson's Algorithm
Johnson's Algorithm computes all-pairs shortest paths on sparse graphs by first removing negative edges via reweighting, then running Dijkstra from every vertex.
Dijkstra's Algorithm
Dijkstra's algorithm finds shortest path distances from one source to all vertices when all edge weights are non-negative.
Dijkstra - Variations and Applications
Dijkstra’s algorithm can be adapted to track the second shortest path by keeping the best and second-best distances per vertex.
Greedy Algorithms
Greedy algorithms build a solution step by step by always taking the best local choice available.
Priority Queue (Heap)
A priority queue returns the highest-priority element first and is efficiently implemented by a binary heap.