Bfs

Given a weighted graph $G$ with $V$ vertices and $E$ edges where all the weights are non-negative and given a source vertex $s$, the single source shortest path problem consists in finding the distance from $s$ to all the other vertices.

In this article I describe the problem in a weighted and unweighted graph as well as implementations using BFS for unweighted graphs and Dijkstra's algorithm for weighted graphs using an array and a priority queue.

There are many ways to traverse a graph. For example through breadth-first search and depth-first search. Exploring it with a breadth-first search has interesting properties like implicitly computing the distance from a source $s$ to all the reachable vertices. Exploring it with a depth-first search has properties about edges like finding back edges, forward edges and cross edges.

This article has implementations for both BFS and DFS.