CS252 Algorithms
Friday, 12 April 2024

+ Whatever you want to talk about

+ DFS and BFS
- Let's do an example of each

- Storage of G
    - n = |V|
    - how big can m = |E| be? how small?
    - adjacency lists: space = O(m + n), i.e. O(|E| + |V|)
    - adjacency matrix: space = O(n^2)

- Runtime complexity of BFS (w/ adjacency lists)

    BFS(s):
        visited[s] = true                                O(1)
        visited[v] = false for all other v               O(n)
        L[0] = [s] # using python list notation []       O(1)
        i = 0 # layer counter                            O(1)
        while L[i] is not empty
            L[i+1] = []
            for u in L[i]
                for v in neighbors(u)     <-- how many iterations of this loop, total?
                                                 2m, because we do this twice per edge
                    if not visited[v]      O(1)
                        visited[v] = true  O(1)
                        L[i+1].add(v)      O(1)
            i++

Runtime = O(n + m) = O(|V| + |E|)
 
+ What would you change about this algorithm to
- compute the spanning tree?
- determine whether G is connected?
- compute G's diameter?

+ Worksheet for more practice