CS252 Algorithms
Wednesday, 24 April 2024

+ Questions

+ Today
- Priority queues
    - Interface / Abstract Data Type
    - Objects w/ key + other stuff
    - Implementation with unsorted array; runtimes of operations
    - Implementation with heap; runtimes of operations

+ Dijkstra's Algorithm
- compare K&T to Wikipedia
- 

[From Wikipedia, https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm#Pseudocode]
 1  function Dijkstra(Graph, source):
 2     
 3      for each vertex v in Graph.Vertices:               <--- # iterations = N
 4          dist[v] ← INFINITY
 5          prev[v] ← UNDEFINED
 6          add v to Q
 7      dist[source] ← 0
 8     
 9      while Q is not empty:                              <--- # iterations?
10          u ← vertex in Q with min dist[u]
11          remove u from Q
12         
13          for each neighbor v of u still in Q:           <--- # iterations? 2*|E|
14              alt ← dist[u] + Graph.EdgeWeight(u, v)     <--- runtime of EdgeWeight?
15              if alt < dist[v]:
16                  dist[v] ← alt
17                  prev[v] ← u
18
19      return dist[], prev[]


What data structure is Q?
    operations needed: ?
        is given v in Q?
        change dist[v] while v is still in Q (line 16)
        extract minimum dist[u] from Q (line 10)
How are V, E, EdgeWeight stored?
    Adjacency list (makes line 13 faster)
What is its relationship to S in the K&T version?
What does prev[u] mean?
Runtime analysis of the nested loop--is it just (# iterations outer) * (# iterations inner)?


+ Minimum spanning trees
- What are they?
- What are they for?
- The problem
    In: ?
    Out: ?
    Brute force?