Number of ways to arrange a word such that all vowels occur together
Given a word containing vowels and consonants. The task is to find that in how many ways to word can be arranged so that the vowels always come together. Given that the length of the word <10.
Examples:
Input: str = "geek" Output: 6 Ways such that both 'e' comes together are 6 i.e. geek, gkee, kgee, eekg, eegk, keeg Input: str = "corporation" Output: 50400
Approach: Since word contains vowels and consonants together. All vowels are needed to remain together then we will take all vowels as a single letter.
As, in the word ‘geeksforgeeks’, we can treat the vowels “eeoee” as one letter.
Thus, we have gksfrgks (eeoee).
This has 9 (8 + 1) letters of which g, k, s each occurs 2 times and the rest are different.
The number of ways arranging these letters = 9!/(2!)x(2!)x(2!) = 45360 ways
Now, 5 vowels in which ‘e’ occurs 4 times and ‘o’ occurs 1 time, can be arranged in 5! /4! = 5 ways.
Required number of ways = (45360 x 5) = 226800
Below is the implementation of the above approach:
C++
// C++ program to calculate the no. of ways // to arrange the word having vowels together #include <bits/stdc++.h> #define ll long long int using namespace std; // Factorial of a number ll fact( int n) { ll f = 1; for ( int i = 2; i <= n; i++) f = f * i; return f; } // calculating ways for arranging consonants ll waysOfConsonants( int size1, int freq[]) { ll ans = fact(size1); for ( int i = 0; i < 26; i++) { // Ignore vowels if (i == 0 || i == 4 || i == 8 || i == 14 || i == 20) continue ; else ans = ans / fact(freq[i]); } return ans; } // calculating ways for arranging vowels ll waysOfVowels( int size2, int freq[]) { return fact(size2) / (fact(freq[0]) * fact(freq[4]) * fact(freq[8]) * fact(freq[14]) * fact(freq[20])); } // Function to count total no. of ways ll countWays(string str) { int freq[26] = { 0 }; for ( int i = 0; i < str.length(); i++) freq[str[i] - 'a' ]++; // Count vowels and consonant int vowel = 0, consonant = 0; for ( int i = 0; i < str.length(); i++) { if (str[i] != 'a' && str[i] != 'e' && str[i] != 'i' && str[i] != 'o' && str[i] != 'u' ) consonant++; else vowel++; } // total no. of ways return waysOfConsonants(consonant+1, freq) * waysOfVowels(vowel, freq); } // Driver code int main() { string str = "geeksforgeeks" ; cout << countWays(str) << endl; return 0; } |
Java
// Java program to calculate the no. of // ways to arrange the word having // vowels together import java.util.*; class GFG{ // Factorial of a number static int fact( int n) { int f = 1 ; for ( int i = 2 ; i <= n; i++) f = f * i; return f; } // Calculating ways for arranging consonants static int waysOfConsonants( int size1, int []freq) { int ans = fact(size1); for ( int i = 0 ; i < 26 ; i++) { // Ignore vowels if (i == 0 || i == 4 || i == 8 || i == 14 || i == 20 ) continue ; else ans = ans / fact(freq[i]); } return ans; } // Calculating ways for arranging vowels static int waysOfVowels( int size2, int [] freq) { return fact(size2) / (fact(freq[ 0 ]) * fact(freq[ 4 ]) * fact(freq[ 8 ]) * fact(freq[ 14 ]) * fact(freq[ 20 ])); } // Function to count total no. of ways static int countWays(String str) { int []freq = new int [ 200 ]; for ( int i = 0 ; i < 200 ; i++) freq[i] = 0 ; for ( int i = 0 ; i < str.length(); i++) freq[str.charAt(i) - 'a' ]++; // Count vowels and consonant int vowel = 0 , consonant = 0 ; for ( int i = 0 ; i < str.length(); i++) { if (str.charAt(i) != 'a' && str.charAt(i) != 'e' && str.charAt(i) != 'i' && str.charAt(i) != 'o' && str.charAt(i) != 'u' ) consonant++; else vowel++; } // Total no. of ways return waysOfConsonants(consonant + 1 , freq) * waysOfVowels(vowel, freq); } // Driver code public static void main(String []args) { String str = "geeksforgeeks" ; System.out.println(countWays(str)); } } // This code is contributed by rutvik_56 |
Python3
# Python3 program to calculate # the no. of ways to arrange # the word having vowels together # Factorial of a number def fact(n): f = 1 for i in range ( 2 , n + 1 ): f = f * i return f # calculating ways for # arranging consonants def waysOfConsonants(size1, freq): ans = fact(size1) for i in range ( 26 ): # Ignore vowels if (i = = 0 or i = = 4 or i = = 8 or i = = 14 or i = = 20 ): continue else : ans = ans / / fact(freq[i]) return ans # calculating ways for # arranging vowels def waysOfVowels(size2, freq): return (fact(size2) / / (fact(freq[ 0 ]) * fact(freq[ 4 ]) * fact(freq[ 8 ]) * fact(freq[ 14 ]) * fact(freq[ 20 ]))) # Function to count total no. of ways def countWays(str1): freq = [ 0 ] * 26 for i in range ( len (str1)): freq[ ord (str1[i]) - ord ( 'a' )] + = 1 # Count vowels and consonant vowel = 0 consonant = 0 for i in range ( len (str1)): if (str1[i] ! = 'a' and str1[i] ! = 'e' and str1[i] ! = 'i' and str1[i] ! = 'o' and str1[i] ! = 'u' ): consonant + = 1 else : vowel + = 1 # total no. of ways return (waysOfConsonants(consonant + 1 , freq) * waysOfVowels(vowel, freq)) # Driver code if __name__ = = "__main__" : str1 = "geeksforgeeks" print (countWays(str1)) # This code is contributed by Chitranayal |
C#
// C# program to calculate the no. of // ways to arrange the word having // vowels together using System.Collections.Generic; using System; class GFG{ // Factorial of a number static int fact( int n) { int f = 1; for ( int i = 2; i <= n; i++) f = f * i; return f; } // Calculating ways for arranging consonants static int waysOfConsonants( int size1, int []freq) { int ans = fact(size1); for ( int i = 0; i < 26; i++) { // Ignore vowels if (i == 0 || i == 4 || i == 8 || i == 14 || i == 20) continue ; else ans = ans / fact(freq[i]); } return ans; } // Calculating ways for arranging vowels static int waysOfVowels( int size2, int [] freq) { return fact(size2) / (fact(freq[0]) * fact(freq[4]) * fact(freq[8]) * fact(freq[14]) * fact(freq[20])); } // Function to count total no. of ways static int countWays( string str) { int []freq = new int [200]; for ( int i = 0; i < 200; i++) freq[i] = 0; for ( int i = 0; i < str.Length; i++) freq[str[i] - 'a' ]++; // Count vowels and consonant int vowel = 0, consonant = 0; for ( int i = 0; i < str.Length; i++) { if (str[i] != 'a' && str[i] != 'e' && str[i] != 'i' && str[i] != 'o' && str[i] != 'u' ) consonant++; else vowel++; } // Total no. of ways return waysOfConsonants(consonant + 1, freq) * waysOfVowels(vowel, freq); } // Driver code public static void Main() { string str = "geeksforgeeks" ; Console.WriteLine(countWays(str)); } } // This code is contributed by Stream_Cipher |
Javascript
<script> // Javascript program to calculate the no. of // ways to arrange the word having // vowels together // Factorial of a number function fact(n) { let f = 1; for (let i = 2; i <= n; i++) f = f * i; return f; } // Calculating ways for arranging consonants function waysOfConsonants(size1,freq) { let ans = fact(size1); for (let i = 0; i < 26; i++) { // Ignore vowels if (i == 0 || i == 4 || i == 8 || i == 14 || i == 20) continue ; else ans = Math.floor(ans / fact(freq[i])); } return ans; } // Calculating ways for arranging vowels function waysOfVowels(size2,freq) { return Math.floor(fact(size2) / (fact(freq[0]) * fact(freq[4]) * fact(freq[8]) * fact(freq[14]) * fact(freq[20]))); } // Function to count total no. of ways function countWays(str) { let freq = new Array(200); for (let i = 0; i < 200; i++) freq[i] = 0; for (let i = 0; i < str.length; i++) freq[str[i].charCodeAt(0) - 'a' .charCodeAt(0)]++; // Count vowels and consonant let vowel = 0, consonant = 0; for (let i = 0; i < str.length; i++) { if (str[i] != 'a' && str[i] != 'e' && str[i] != 'i' && str[i] != 'o' && str[i] != 'u' ) consonant++; else vowel++; } // Total no. of ways return waysOfConsonants(consonant + 1, freq) * waysOfVowels(vowel, freq); } // Driver code let str = "geeksforgeeks" ; document.write(countWays(str)); // This code is contributed by avanitrachhadiya2155 </script> |
226800
Further Optimizations: We can pre-compute required factorial values to avoid re-computations.