Question

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

Short answer

a, aa, aaa, aaabbaaa

Step-by-step solution

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

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

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

Key concepts

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.