Lecture 1-18-17

Graphs

• Care about form of storage because > constant factor
• Representations
  • Adjacency matrix
    • Nodes must be numbered
  • Adjacency lists

Time complexity

• Matrix: O(1)
• Adjacency list: O(n)
  • also can be considered “degree” of vertex
  • faster for finding Euler cycles
• Space:
  • Matrix: n^2
  • List: nlogm

Graph algorithms

• A^k[x, y] = number of paths from x to y of length k
• Shortest path (weighted, unweighted)
• Traveling salesman
• BFS
• DFS
  • Need to use adjacency lists

Homework