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

19 Mar, 2022
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: 3The 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++
Java
Python3
C#
PHP
Javascript
// C++ implementation of the above approach#include <bits/stdc++.h>using namespace std; // Returns the total sum of// occurrences of all vowelsint 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 codeint main(){    string s = "daceh";    cout << vowel_calc(s) << endl;     return 0;}
// 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));    }}
# Python 3 implementation of# a more efficient approach.# return sum of all occurrences of all vowelsdef 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 codeif __name__ == '__main__':    #input string here    string = "abhay"    #print returned sum    print(sumVowel(string)) # This code is contributed by# Abhay Subramanian K
// 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 implementation of the above approach // Returns the total sum of// occurrences of all vowelsfunction 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?>
<script> // Javascript implementation of the above approach // Returns the total sum of// occurrences of all vowelsfunction 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 codevar s = "daceh";document.write( vowel_calc(s)); // This code is contributed by importantly.</script>
16
 
Time Complexity: O(N)
Auxiliary Space: O(N) 
SouravAChowdhury_97
SURENDRA_GANGWAR
ukasp
Shivi_Aggarwal
AbhaySubramanian
nidhi_biet
importantly
rishavnitro
prefix-sum
substring
vowel-consonant
Competitive Programming
Hash
Strings
prefix-sum
Hash
Strings
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