 # How Many Substrings in a String of Length n?

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).

1. 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.

## Sources

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