Homework Assignments

Homework 1: Page 22 13, Page 67 1-6

Homework 3: Page 107 #1,5,7   Page 192#9   Plus the algorithm runs given in class.

Homework 4: Prove the following are true about Ackerman's function, where
Ackerman's function A(m,n) is defined by:

A(0,n)=n+1     A(m,0)=A(m-1,1)     A(m,n)=A(m-1,A(m,n-1))    if m>0 and n>0

       1. A(1,n)=n+2
       2. A(2,n)=2n+3
       3. A(3,n)=2ⁿ⁺³-3
       4. A(4,n)=2 raised to itself n+3 times - 3

Also find the shortest path from node A to all other nodes in the graph from the quiz
using Djikstra's algorithm. Show all steps.

Also find the shortest paths between all nodes in that graph using the All-Pairs
shortest path algorithm.

Homework 5: Compute the all-pairs shortest paths for the graph with the following adjacency matrix:

Edge/Edge	0	1	2	3
0	0	2	17	5
1	2	0	3	12
2	17	3	0	100
3	5	12	100	0

Find the optimal binary search tree for values 0,1,2,3,4 if they have probabilities (0.05,0.15,0.4,0.1,0.3), respectively.