A substring is a sequence of characters that form a part of a larger string. For example, the string “abc” includes the substring “ab”, “bc”, and “abc” itself. If you’re given a string of length n, it’s useful to know how many substrings it contains.
In order to find the number of substrings in a string of length n, you can follow the steps below:
Count the number of single-character substrings in the string. These are substrings of length one, such as “a”, “b”, “c” from the example string “abc”. The number of single-character substrings is equal to the length of the string, so for a string of length n, you’ll have n single-character substrings.
Count the number of double-character substrings in the string. These are substrings of length two, such as “ab”, “bc” from the example string “abc”. To find the number, multiply the number of single-characters substrings by the total number of characters in the string minus one (n-1). This is because the first character in the double-character substring is fixed, but the second character is free to be any of the other n-1 character in the string. Therefore, the total number of double-character substrings is n*(n-1).
Count the number of triple-character substrings. These are substrings of length three, such as “abc” from the example string “abc”. To find the number, multiply the number of double-character substrings by the number of characters in the string minus two (n-2). This is because the first two characters in the triple-character substring are fixed, but the third character is free to be any of the other n-2 character in the string. Therefore, the total number of triple-character substrings is n*(n-1)*(n-2).
- Add the number of single-character, double-character, and triple-character substrings together. This total is the total number of substrings in a string of length n; n+(n*(n-1))+(n*(n-1)*(n-2)).
FAQ
What is a substring?
A substring is a sequence of characters that form a part of a larger string. For example, the string “abc” includes the substrings “ab”, “bc”, and “abc” itself.
How can I find the number of substrings in a string of length n?
To find the number of substrings in a string of length n, you can count the number of single-character, double-character, and triple-character substrings. The total is the total number of substrings in a string of length n; n+(n*(n-1))+(n*(n-1)*(n-2)).
What is the maximum number of substrings in a string of length n?
The maximum number of substrings in a string of length n is n^2. This is because there are n^2 possible combinations of characters that can be contained in the string.
How can I find the number of unique substrings in a string of length n?
The number of unique substrings in a string of length n is equal to the number of substrings minus the number of duplicate substrings. Each substring must be counted individually in order to find the number of unique substrings.
Does the length of the substring matter?
Yes, the length of the substring does matter. Single-character substrings, double-character substrings, and triple-character substrings must all be counted individually in order to find the total number of substrings in a string of length n.