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Chapter 12: Problem 3

List the prefixes of the string \(P="\) aaabbaaa" that are also suffixes of \(P\)

Short Answer

Expert verified
a, aa, aaa, aaabbaaa

Step by step solution

01

Identify the prefixes

A prefix of a string is a substring that occurs at the beginning of the string. List all prefixes of the string 'aaabbaaa':1. a2. aa3. aaa4. aaab5. aaabb6. aaabba7. aaabbaa8. aaabbaaa
02

Identify the suffixes

A suffix of a string is a substring that occurs at the end of the string. List all suffixes of the string 'aaabbaaa':1. a2. aa3. aaa4. baaa5. bbaaa6. abbaaa7. aabbaaa8. aaabbaaa
03

Find common elements

Compare the prefixes and suffixes lists to find common elements, which are the prefixes that are also suffixes:1. a2. aa3. aaa4. aaabbaaa

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Prefix
A prefix is a substring that starts from the beginning of a string and includes any number of initial characters of that string. For example, in the string \( P = \text{aaabbaaa} \), the prefixes are as follows:
a
aa
aaa
aaab
aaabb
aaabba
aaabbaa
aaabbaaa.
Notice that each prefix gradually increases in length by one character starting from the first character of the string.
Suffix
A suffix is a substring that starts from the end of a string and includes any number of trailing characters. For instance, in the string \( P = \text{aaabbaaa} \), the suffixes are:
a
aa
aaa
baaa
bbaaa
abbaaa
aabbaaa
aaabbaaa.
As you can see, each suffix begins from the end and increases in length by adding one character from the left side.
Substring
A substring can be any consecutive sequence of characters within a string. Unlike prefixes and suffixes, it does not need to be anchored to the start or end. For example, in the string \( P = \text{aaabbaaa} \), \text{a}, \text{aa}, \text{aabb}, and \text{abbaa} are all substrings. To form a substring, you simply select any portion of the string maintaining the original sequence of characters.
Comparison of Strings
Comparing strings involves checking their characters either entirely or partially. When dealing with prefixes and suffixes, we compare segments of the string to identify common parts. For the string \( P = \text{aaabbaaa} \), we listed its prefixes and suffixes, then looked for overlaps.
Common elements between prefixes and suffixes are:
a
aa
aaa
aaabbaaa.
These common elements are valuable in different algorithms, such as string matching and searching operations.

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Most popular questions from this chapter

Compute a table representing the last function used in the BM pattern matching algorithm for the pattern string "the quick brown fox jumped over a lazy cat" assuming the following alphabet (which starts with the space character): \\[ \Sigma=\left\\{_{\boldsymbol{u}}, \mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}, \mathrm{g}, \mathrm{h}, \mathrm{i}, \mathrm{j}, \mathrm{k}, \mathrm{l}, \mathrm{m}, \mathrm{n}, \mathrm{o}, \mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{s}, \mathrm{t}, \mathrm{u}, \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{y}, \mathrm{z}\right\\} \\]

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What is the best way to multiply a chain of matrices with dimensions that are \(10 \times 5,5 \times 2,2 \times 20,20 \times 12,12 \times 4,\) and \(4 \times 60 ?\) Show your work.

What is the longest prefix of the string "cgtacgttcgtacg" that is also a suffix of this string?
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