CS 470 Quiz 20 Name ________________________
a. You are given strings S = cbda and T = bcad. Trace the dynamic programming
algorithm to compute the length of the longest common subsequence for strings S and
T. Also reconstruct all possible optimum solutions; that is, find all common
subsequences of strings S and T that have this greatest length.
j=0 j=1 j=2 j=3 j=4
i=0 0 0 0 0 0
i=1 0 0 1 1 1
i=2 0 1 1 1 1
i=3 0 1 1 1 2
i=4 0 1 1 2 2
The 4 optimum solutions are: (i) cd, (ii) bd, (iii) ca, (iv) ba.
b. You are given strings S = cbda and T = bcad. Trace the dynamic programming
algorithm to compute the edit distance between strings S and T (that is, the smallest
number of insert, delete, and replace operations that can transform S into T). Also
reconstruct all possible optimum solutions; that is, find all shortest sequences of edit
operations that transform S into T.
j=0 j=1 j=2 j=3 j=4
i=0 0 1 2 3 4
i=1 1 1 1 2 3
i=2 2 1 2 2 3
i=3 3 2 2 3 2
i=4 4 3 3 2 3
The 2 optimum solutions are:
i. Insert b, [Keep c], Replace b by a, [Keep d], Delete a.
ii. Delete c, [Keep b], Replace d by c, [Keep a], Insert d.