Concepts4

Proof Techniques for Greedy Algorithms

Greedy algorithm correctness is usually proved with patterns like exchange argument, stays-ahead, structural arguments, cut-and-paste, and contradiction.

#greedy algorithms#exchange argument#stays ahead+12

⚙️AlgorithmIntermediate

MST Properties and Applications

An MST minimizes total edge weight over all spanning trees and has powerful properties such as the cut and cycle properties that guide correct, greedy construction.

#minimum spanning tree#kruskal#prim+12

⚙️AlgorithmIntermediate

Minimum Spanning Tree - Prim

Prim's algorithm builds a Minimum Spanning Tree (MST) by growing a tree from an arbitrary start vertex, always adding the lightest edge that connects the tree to a new vertex.

#prim#minimum spanning tree#mst+12

⚙️AlgorithmIntermediate

Minimum Spanning Tree - Kruskal

Kruskal’s algorithm builds a minimum spanning tree (MST) by sorting all edges by weight and greedily picking the next lightest edge that does not form a cycle.

#kruskal#minimum spanning tree#mst+11