Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

C-12.13
Describe an efficient algorithm to find the longest palindrome that is a suffix of
a string T of length n. Recall that apalindrome is a string that is equal to its
reversal. What is the running time of your method?
C-12.14
Given a sequence S = (x 0 , x 1 , x 2 ,…, x n−1 ) of numbers, describe an O(n 2 )-time
algorithm for finding a longest subsequence T = (x i 0,x i 1, x i 2,…x i k−1) of numbers,
such that i j < i j+1 and x ij > x ij+1 . That is, T is a longest decreasing subsequence of
S.
C-12.15
Define the edit distance between two strings X and Y of length n and m,
respectively, to be the number of edits that it takes to change X into Y. An edit
consists of a character insertion, a character deletion, or a character
replacement. For example, the strings "algorithm" and "rhythm" have
edit distance 6. Design an O(nm)-time algorithm for computing the edit distance
between X and Y.
C-12.16
Design a greedy algorithm for making change after someone buys some candy
costing x cents and the customer gives the clerk $1. Your algorithm should try
to minimize the number of coins returned.
a.
Show that your greedy algorithm returns the minimum number of coins if
the coins have denominations $0.25, $0.10, $0.05, and $0.01.
b.
Give a set of denominations for which your algorithm may not return the
minimum number of coins. Include an example where your algorithm fails.
C-12.17
Give an efficient algorithm for determining if a pattern P is a subsequence (not
substring) of a text T. What is the running time of your algorithm?
C-12.18
Let x and y be strings of length n and m respectively. Define B(i,j) to be the
length of the longest common substring of the suffix of length i in x and the
786