CS252 Algorithms
Wednesday, 10 April 2024

+ Questions

+ Studying for the exam
- My philosophy of in-class exams
- Read through Layla's review sheet (posted on our website)
- Topics
    - O, Ω, ϴ
        - definitions
        - simple O, Ω, ϴ proofs (e.g., polynomials)
        - arrange common functions in complexity order (e.g. n = O(n^2) but n^2 != O(n))
    - Stable matching and Gale-Shapley
        - inputs and outputs
        - stepping through a small example
        - arguments in the correctness proof
        - arguments in the runtime analysis
        - variants we have discussed
    - Graphs
        - basic vocabulary
        - BFS, DFS
        - [not topological sort, Dijkstra, etc. -- all of which are coming soon]
- Question types
    - Very simple proofs
    - Definitions of various terms
    - Short answer
    - Here's a specific graph or GS preference list set or whatever
        walk through algorithm X using this example
    - Here's a specific graph or ...
        does it have such and such a property? why or why not?
    - Questions about problem set problems
    - Questions about slight variations of problem set problems

+ BFS and DFS

BFS on graph g = (V, E)
    for v in g:
        v.visited = false

    q = queue()
    q.add(start_node)
    visit(start_node)
    while not q.empty()
        v = q.remove()
        for w in v.neighbors
            if not w.visited
                visit(w)
                q.add(w)

       B ---- C --- D
      /  ____/|   /  \
     /  /     |  /    \
    A --      | /      E
     \        |/      /
      F ----- G ---- H

THIS WAS DUMB
- Grab a partner. Each of you get a piece of paper. One of you is "queue" and one of you is "stack".
- Start at A
- We're gonna walk through BFS/DFS together.


+ Thinking about BFS & DFS
- Why do you want to traverse a graph?
    - compute shortest paths from start node (BFS)
    - look for cycles
    - traveling salesperson problem (lowest cost visit every node and come home)
    - is this graph connected? if not, which nodes are in A's connected component
    - find whether a particular piece of data / node is here at all
    - accumulate some statistics about the nodes
    - bfs could collect attributes of the 1-level, 2-level,...
    ...
- From Slack
    - "Both BFS and DFS feel like very brute force algorithms, it feels like
       there should be a clever, faster solution..."
    - "In real-world comp-sci applications of graph traversal, are
        'pure' BFS or 'pure' DFS ever the best option?"

+ Graph algorithm categories
- Traversal
- Topological sort
- [Greedy Algorithms, starting with interval scheduling]
- Shortest paths
- Spanning trees

+ Topological sort
- What is it?
- What's it for?