Here's what you'll learn:
Bridge finding identifies edges whose removal disconnects the graph. Use it for network reliability problems.
Segment tree Dijkstra handles graphs with edges to ranges of nodes in .
LCA (Lowest Common Ancestor) answers tree path queries. Combine with binary lifting for queries.
MST properties let you answer queries about minimum spanning trees efficiently using LCA on the MST.
Shortest path DAGs count paths and handle BFS tree problems.