Weights change the frontier
BFS is insufficient when edges have different costs.
Advanced Graphs
5 chapters · 9 challenges · The Transit Nexus
Understand the idea, practise through play, then prove it in code. Choose your next quest below.
Visual introduction to this topic
Start here · 3 minute mental model
What makes a graph problem advanced?
Advanced graph algorithms add weights, negative edges, global connection cost, or route-use constraints. The traversal order must preserve a stronger guarantee than simple reachability.
Think of a transit control room. Reaching a station is not enough. You may need the cheapest route, a network connecting every station, or a trip that uses every ticket exactly once.
The frontier is ordered by the guarantee: distance, edge cost, or dependency.
Prove when a result is final
Dijkstra settles the nearest unsettled node only with non-negative edges.
Match the objective
Shortest path, spanning tree, and Eulerian route solve different questions.
What you will learn firstThe Cheapest Route
Begin the guided lesson Expand the lowest known distance
01
Dijkstra
0/2 completePractice Dijkstra through 2 visual expeditions.
02
Minimum Spanning Tree
0/2 completePractice minimum spanning tree through 2 visual expeditions.
03
Bellman Ford
0/2 completePractice Bellman Ford through 2 visual expeditions.
04
Floyd Warshall
0/2 completePractice Floyd Warshall through 2 visual expeditions.
05
Eulerian Path
0/1 completePractice Eulerian path through 1 visual expedition.
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