Lecture 12 - cse.buffalo.eduerdem/cse331/spring20/lectures/lect12.pdf · Lecture 12 CSE 331 Feb21,...

Lecture 12

CSE 331Feb 21, 2020

Mini Project group due next Friday!

124 of you still need to do this!

Connectivity Problem

Input: Graph G = (V,E) and s in V

Output: All t connected to s in G

Breadth First Search (BFS)

Build layers of vertices connected to s

L0 = {s}

Assume L0,..,Lj have been constructed

Lj+1 is the set of vertices not chosen yet but are connected by an edge to Lj

Stop when new layer is empty

BFS TreeBFS naturally defines a tree rooted at s

Lj forms the jth �level� in the tree

u in Lj+1 is child of v in Lj from which it was �discovered�

1

2 3

4 5

6

7

8

1

2 3

L0

L1

4 5 7 8 L2

6 L3

Add non-tree edges

9

0

Two facts about BFS trees

All non-tree edges are in the same or consecutive layer

If u is in Li then dist(s,u) = i

Today’s agenda

Computing Connected component

Computing Connected Component

Start with R = {s}

Explore(s)

While there is an edge (u,v) whereu in R and v not in R

Add v to ROutput R* = R

kobe bryantsteve nash

shaq o’neal

anthony davis

lebron james

kyrie irving

kevin love

michael jordan scottie pippen

Questions?