# Number of distinct permutation a String can have

We are given a string having only lowercase alphabets. The task is to find out total number of distinct permutation can be generated by that string.

Examples:

Input : aab Output : 3 Different permutations are "aab", "aba" and "baa". Input : ybghjhbuytb Output : 1663200

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A **simple solution** is to find all the distinct permutation and count them.

We can find the count **without finding all permutation**. Idea is to find all the characters that is getting repeated, i.e., frequency of all the character. Then, we divide the factorial of the length of string by multiplication of factorial of frequency of characters.

In second example, number of character is 11 and here **h** and **y** are repeated **2** times whereas **g** is repeated **3** times.

So, number of permutation is **11! / (2!2!3!) = 1663200**

Below is the implementation of above idea.

## C++

`// C++ program to find number of distinct` `// permutations of a string.` `#include<bits/stdc++.h>` `using` `namespace` `std;` `const` `int` `MAX_CHAR = 26;` `// Utility function to find factorial of n.` `int` `factorial(` `int` `n)` `{` ` ` `int` `fact = 1;` ` ` `for` `(` `int` `i = 2; i <= n; i++)` ` ` `fact = fact * i;` ` ` `return` `fact;` `}` `// Returns count of distinct permutations` `// of str.` `int` `countDistinctPermutations(string str)` `{` ` ` `int` `length = str.length();` ` ` `int` `freq[MAX_CHAR];` ` ` `memset` `(freq, 0, ` `sizeof` `(freq));` ` ` `// finding frequency of all the lower case` ` ` `// alphabet and storing them in array of` ` ` `// integer` ` ` `for` `(` `int` `i = 0; i < length; i++)` ` ` `if` `(str[i] >= ` `'a'` `)` ` ` `freq[str[i] - ` `'a'` `]++;` ` ` `// finding factorial of number of appearances` ` ` `// and multiplying them since they are` ` ` `// repeating alphabets` ` ` `int` `fact = 1;` ` ` `for` `(` `int` `i = 0; i < MAX_CHAR; i++)` ` ` `fact = fact * factorial(freq[i]);` ` ` `// finding factorial of size of string and` ` ` `// dividing it by factorial found after` ` ` `// multiplying` ` ` `return` `factorial(length) / fact;` `}` `// Driver code` `int` `main()` `{` ` ` `string str = ` `"fvvfhvgv"` `;` ` ` `printf` `(` `"%d"` `, countDistinctPermutations(str));` ` ` `return` `0;` `}` |

## Java

`// Java program to find number of distinct` `// permutations of a string.` `public` `class` `GFG {` ` ` ` ` `static` `final` `int` `MAX_CHAR = ` `26` `;` ` ` ` ` `// Utility function to find factorial of n.` ` ` `static` `int` `factorial(` `int` `n)` ` ` `{` ` ` `int` `fact = ` `1` `;` ` ` `for` `(` `int` `i = ` `2` `; i <= n; i++)` ` ` `fact = fact * i;` ` ` `return` `fact;` ` ` `}` ` ` ` ` `// Returns count of distinct permutations` ` ` `// of str.` ` ` `static` `int` `countDistinctPermutations(String str)` ` ` `{` ` ` `int` `length = str.length();` ` ` ` ` `int` `[] freq = ` `new` `int` `[MAX_CHAR];` ` ` ` ` `// finding frequency of all the lower case` ` ` `// alphabet and storing them in array of` ` ` `// integer` ` ` `for` `(` `int` `i = ` `0` `; i < length; i++)` ` ` `if` `(str.charAt(i) >= ` `'a'` `)` ` ` `freq[str.charAt(i) - ` `'a'` `]++;` ` ` ` ` `// finding factorial of number of appearances` ` ` `// and multiplying them since they are` ` ` `// repeating alphabets` ` ` `int` `fact = ` `1` `;` ` ` `for` `(` `int` `i = ` `0` `; i < MAX_CHAR; i++)` ` ` `fact = fact * factorial(freq[i]);` ` ` ` ` `// finding factorial of size of string and` ` ` `// dividing it by factorial found after` ` ` `// multiplying` ` ` `return` `factorial(length) / fact;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `String str = ` `"fvvfhvgv"` `;` ` ` `System.out.println(countDistinctPermutations(str));` ` ` `}` `}` `// This code is contributed by Sumit Ghosh` |

## Python

`# Python program to find number of distinct` `# permutations of a string.` `MAX_CHAR ` `=` `26` `# Utility function to find factorial of n.` `def` `factorial(n) :` ` ` ` ` `fact ` `=` `1` `;` ` ` `for` `i ` `in` `range` `(` `2` `, n ` `+` `1` `) :` ` ` `fact ` `=` `fact ` `*` `i;` ` ` `return` `fact` ` ` `# Returns count of distinct permutations` `# of str.` `def` `countDistinctPermutations(st) :` ` ` ` ` `length ` `=` `len` `(st)` ` ` `freq ` `=` `[` `0` `] ` `*` `MAX_CHAR` ` ` ` ` `# finding frequency of all the lower` ` ` `# case alphabet and storing them in` ` ` `# array of integer` ` ` `for` `i ` `in` `range` `(` `0` `, length) :` ` ` `if` `(st[i] >` `=` `'a'` `) :` ` ` `freq[(` `ord` `)(st[i]) ` `-` `97` `] ` `=` `freq[(` `ord` `)(st[i]) ` `-` `97` `] ` `+` `1` `;` ` ` ` ` `# finding factorial of number of` ` ` `# appearances and multiplying them` ` ` `# since they are repeating alphabets` ` ` `fact ` `=` `1` ` ` `for` `i ` `in` `range` `(` `0` `, MAX_CHAR) :` ` ` `fact ` `=` `fact ` `*` `factorial(freq[i])` ` ` ` ` `# finding factorial of size of string` ` ` `# and dividing it by factorial found` ` ` `# after multiplying` ` ` `return` `factorial(length) ` `/` `fact` `# Driver code` `st ` `=` `"fvvfhvgv"` `print` `(countDistinctPermutations(st))` `# This code is contributed by Nikita Tiwari.` |

## C#

`// C# program to find number of distinct` `// permutations of a string.` `using` `System;` `public` `class` `GFG {` ` ` ` ` `static` `int` `MAX_CHAR = 26;` ` ` ` ` `// Utility function to find factorial of n.` ` ` `static` `int` `factorial(` `int` `n)` ` ` `{` ` ` `int` `fact = 1;` ` ` `for` `(` `int` `i = 2; i <= n; i++)` ` ` `fact = fact * i;` ` ` ` ` `return` `fact;` ` ` `}` ` ` ` ` `// Returns count of distinct permutations` ` ` `// of str.` ` ` `static` `int` `countDistinctPermutations(String str)` ` ` `{` ` ` `int` `length = str.Length;` ` ` ` ` `int` `[] freq = ` `new` `int` `[MAX_CHAR];` ` ` ` ` `// finding frequency of all the lower case` ` ` `// alphabet and storing them in array of` ` ` `// integer` ` ` `for` `(` `int` `i = 0; i < length; i++)` ` ` `if` `(str[i] >= ` `'a'` `)` ` ` `freq[str[i] - ` `'a'` `]++;` ` ` ` ` `// finding factorial of number of appearances` ` ` `// and multiplying them since they are` ` ` `// repeating alphabets` ` ` `int` `fact = 1;` ` ` `for` `(` `int` `i = 0; i < MAX_CHAR; i++)` ` ` `fact = fact * factorial(freq[i]);` ` ` ` ` `// finding factorial of size of string and` ` ` `// dividing it by factorial found after` ` ` `// multiplying` ` ` `return` `factorial(length) / fact;` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main(String []args)` ` ` `{` ` ` `String str = ` `"fvvfhvgv"` `;` ` ` ` ` `Console.Write(countDistinctPermutations(str));` ` ` `}` `}` `// This code is contributed by parashar.` |

## Javascript

`<script>` ` ` `// Javascript program to find number of distinct` ` ` `// permutations of a string.` ` ` `let MAX_CHAR = 26;` ` ` `// Utility function to find factorial of n.` ` ` `function` `factorial(n)` ` ` `{` ` ` `let fact = 1;` ` ` `for` `(let i = 2; i <= n; i++)` ` ` `fact = fact * i;` ` ` `return` `fact;` ` ` `}` ` ` `// Returns count of distinct permutations` ` ` `// of str.` ` ` `function` `countDistinctPermutations(str)` ` ` `{` ` ` `let length = str.length;` ` ` `let freq = ` `new` `Array(MAX_CHAR);` ` ` `freq.fill(0);` ` ` `// finding frequency of all the lower case` ` ` `// alphabet and storing them in array of` ` ` `// integer` ` ` `for` `(let i = 0; i < length; i++)` ` ` `if` `(str[i].charCodeAt() >= ` `'a'` `.charCodeAt())` ` ` `freq[str[i].charCodeAt() - ` `'a'` `.charCodeAt()]++;` ` ` `// finding factorial of number of appearances` ` ` `// and multiplying them since they are` ` ` `// repeating alphabets` ` ` `let fact = 1;` ` ` `for` `(let i = 0; i < MAX_CHAR; i++)` ` ` `fact = fact * factorial(freq[i]);` ` ` `// finding factorial of size of string and` ` ` `// dividing it by factorial found after` ` ` `// multiplying` ` ` `return` `parseInt(factorial(length) / fact, 10);` ` ` `}` ` ` `let str = ` `"fvvfhvgv"` `;` ` ` `document.write(countDistinctPermutations(str));` ` ` ` ` `// This code is contributed by vaibhavrabadiya117.` `</script>` |

Output:

840

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