CSE 5211
Fall 2007
Exam 2
Points: 50
Time: 115 min
1.
Organize the following nodes into an optimum cost Binary search tree using the
Dynamic programming algorithm: (a, 10), (b, 5), (c, 7), (d, 12), where the number in the
parenthesis corresponds to the frequency of the respective node. Show the full resulting
cost matrix, and calculations of only three elements in the matrix including the final
corner element.
[8]
What is the exact total number of steps in your computation (as it corresponds to the big
O of the algorithm)?
[2]
2a.
Hamiltonian path for a graph is a path via each node appearing once and only once in
the path. For a weighted graph one may find the total weight of the shortest Hamiltonian
path by using a Dynamic Programming algorithm. The following is the recurrence for
that purpose.
P(S, k) = min {P(S{k}, m) + w(m, k)  for all
m
∈
S {k} } when S >1,
and P(S, k) = w(1, k) when S = {k},
where P(S, k) means the minimum weight of a path from a special starting node (say, ‘
a
’)
to the node
k
, with
S
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '12
 Dmitra
 Algorithms, Dynamic Programming, Binary Search, C Programming, Computational complexity theory, Glossary of graph theory, dynamic programming algorithm, NPcomplete

Click to edit the document details