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Count the number of vowels occurring in all the substrings of given string

  • Difficulty Level : Medium
  • Last Updated : 21 May, 2021

Given a string of length N of lowercase characters containing 0 or more vowels, the task is to find the count of vowels that occurred in all the substrings of the given string.
Examples: 
 

Input: str = “abc” 
Output: 3
The given string “abc” contains only one vowel = ‘a’ 
Substrings of “abc” are = {“a”, “b”, “c”, “ab”, “bc, “abc”} 
Hence, the sum of occurrences of the vowel in these strings = 3.(‘a’ occurred 3 times)
Input: str = “daceh” 
Output: 16

 

Naive Approach: Given a string of length N, the number of substrings that can be formed=N(N+1)/2. A simple solution is for each substring, we count the occurrences of the vowels and add them to get the result. The time complexity of this approach is O(N3) which is not suitable for large values of N.
Efficient Approach: The idea is to use a prefix sum array-based technique where we store the occurrences of each character in all the substrings concatenated. 
 



  • For the first character, 
     

no. of occurrences = no. of substrings starting with the first character = N.

  • For each of the following characters, we store the 
     

no. of substrings starting with that character + the number of substrings formed by the previous characters containing this character the number of substrings formed by the previous characters only.

Below is the implementation of the above approach:
 

C++




// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Returns the total sum of
// occurrences of all vowels
int vowel_calc(string s)
{
    int n = s.length();
    vector<int> arr;
 
    for (int i = 0; i < n; i++) {
 
        if (i == 0)
            // No. of occurrences of 0th character
            // in all the substrings
            arr.push_back(n);
 
        else
            // No. of occurrences of the ith character
            // in all the substrings
            arr.push_back((n - i) + arr[i - 1] - i);
    }
 
    int sum = 0;
    for (int i = 0; i < n; i++)
 
        // Check if ith character is a vowel
        if (s[i] == 'a' || s[i] == 'e' || s[i] == 'i'
            || s[i] == 'o' || s[i] == 'u')
            sum += arr[i];
 
    // Return the total sum
    // of occurrences of vowels
    return sum;
}
 
// Driver code
int main()
{
    string s = "daceh";
    cout << vowel_calc(s) << endl;
 
    return 0;
}

Java




// Java implementation of the above approach
 
import java.io.*;
import java.util.*;
 
public class Gfg {
 
    // Returns the total sum of
    // occurrences of all vowels
    static int vowel_calc(String s)
    {
        int n = s.length();
        int arr[] = new int[n];
 
        for (int i = 0; i < n; i++) {
 
            if (i == 0)
                // No. of occurrences of 0th character
                // in all the substrings
                arr[i] = n;
 
            else
                // No. of occurrences of ith character
                // in all the substrings
                arr[i] = (n - i) + arr[i - 1] - i;
        }
 
        int sum = 0;
        for (int i = 0; i < n; i++) {
            char ch = s.charAt(i);
            // Check if ith character is a vowel
            if (ch == 'a' || ch == 'e' || ch == 'i'
                || ch == 'o' || ch == 'u')
                sum += arr[i];
        }
 
        // Return the total sum
        // of occurrences of vowels
        return sum;
    }
 
    // Driver Code
    public static void main(String args[])
    {
        String s = "daceh";
        System.out.println(vowel_calc(s));
    }
}

Python3




# Python 3 implementation of
# a more efficient approach.
# return sum of all occurrences of all vowels
def sumVowel(string):
    n = len(string)
    sum = 0
    string = string.lower()
 
    # iterate through every character in the string
    for i in range(0, n):
        s = string[i]
 
        # checks if the character is a vowel or not
        if (s=="a" or s == "e" or s == "i" or s == "o" or s == "u"):
 
            # uses below expression to calculate the count
                        # of all occurrences of character in substrings
                        # of the string
            sum += ((n - i) * (i + 1))           
 
    # return the total sum of occurrence
    return sum
 
#driver code
if __name__ == '__main__':
    #input string here
    string = "abhay"
    #print returned sum
    print(sumVowel(string))
 
# This code is contributed by
# Abhay Subramanian K

C#




// C# implementation of the above approach
  
 
using System;
  
public class Gfg {
  
    // Returns the total sum of
    // occurrences of all vowels
    static int vowel_calc(string s)
    {
        int n = s.Length;
        int[] arr = new int[n];
  
        for (int i = 0; i < n; i++) {
  
            if (i == 0)
                // No. of occurrences of 0th character
                // in all the substrings
                arr[i] = n;
  
            else
                // No. of occurrences of ith character
                // in all the substrings
                arr[i] = (n - i) + arr[i - 1] - i;
        }
  
        int sum = 0;
        for (int i = 0; i < n; i++) {
            char ch = s[i];
            // Check if ith character is a vowel
            if (ch == 'a' || ch == 'e' || ch == 'i'
                || ch == 'o' || ch == 'u')
                sum += arr[i];
        }
  
        // Return the total sum
        // of occurrences of vowels
        return sum;
    }
  
    // Driver Code
    public static void Main()
    {
        string s = "daceh";
        Console.Write(vowel_calc(s));
    }
}

PHP




<?php
// PHP implementation of the above approach
 
// Returns the total sum of
// occurrences of all vowels
function vowel_calc($s)
{
    $n = strlen($s);
    $arr = array();
 
    for ($i = 0; $i < $n; $i++)
    {
        if ($i == 0)
         
            // No. of occurrences of 0th character
            // in all the substrings
            $arr[$i] = $n;
 
        else
         
            // No. of occurrences of ith character
            // in all the substrings
            $arr[$i] = ($n - $i) + $arr[$i - 1] - $i;
        }
 
    $sum = 0;
    for ($i = 0; $i < $n; $i++)
    {
         
        // Check if ith character is a vowel
        if ($s[$i] == 'a' || $s[$i] == 'e' ||
            $s[$i] == 'i' || $s[$i] == 'o' ||
            $s[$i] == 'u')
            $sum += $arr[$i];
        }
 
        // Return the total sum
        // of occurrences of vowels
        return $sum;
    }
 
// Driver Code
$s = "daceh";
echo(vowel_calc($s));
 
// This code is contributed by Shivi_Aggarwal
?>

Javascript




<script>
 
// Javascript implementation of the above approach
 
// Returns the total sum of
// occurrences of all vowels
function vowel_calc(s)
{
    var n = s.length;
    var arr = [];
 
    for (var i = 0; i < n; i++) {
 
        if (i == 0)
            // No. of occurrences of 0th character
            // in all the substrings
            arr.push(n);
 
        else
            // No. of occurrences of the ith character
            // in all the substrings
            arr.push((n - i) + arr[i - 1] - i);
    }
 
    var sum = 0;
    for (var i = 0; i < n; i++)
 
        // Check if ith character is a vowel
        if (s[i] == 'a' || s[i] == 'e' || s[i] == 'i'
            || s[i] == 'o' || s[i] == 'u')
            sum += arr[i];
 
    // Return the total sum
    // of occurrences of vowels
    return sum;
}
 
// Driver code
var s = "daceh";
document.write( vowel_calc(s));
 
// This code is contributed by importantly.
</script>
Output: 
16

 

Time Complexity: O(N)
 




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