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

Given a string of length N of lowercase characters containing 0 or more vowels, the task is to find the count of vowels 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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 occurences 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 the  
# above approach 
  
# Returns the total sum of  
# occurrences of all vowels 
def vowel_calc(s): 
    n = len(s) 
    arr = [] 
  
    for i in range(0, n, 1): 
        if (i == 0): 
              
            # No. of occurrences of 0th  
            # character in all the substrings 
            arr.append(n) 
  
        else: 
              
            # No. of occurrences of the ith  
            # character in all the substrings 
            arr.append((n - i) + arr[i - 1] - i) 
  
    sum = 0
    for i in range(0, n, 1): 
          
        # Check if ith character is a vowel 
        if (s[i] == 'a' or s[i] == 'e' or
            s[i] == 'i' or s[i] == 'o' or 
            s[i] == 'u'): 
            sum += arr[i] 
  
    # Return the total sum 
    # of occurrences of vowels 
    return sum
  
# Driver code 
if __name__ == '__main__': 
    s = "daceh"
    print(vowel_calc(s)) 
  
# This code is contributed by  
# Surendra_Gangwar 

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 occurences 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 occurences of vowels 
        return $sum; 
    } 
  
// Driver Code 
$s = "daceh"; 
echo(vowel_calc($s)); 
  
// This code is contributed by Shivi_Aggarwal 
?> 

Output:

Time Complexity: O(N)

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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