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# Count of substrings having the most frequent character in the string as first character

Given a string S consisting of lowercase alphabets of size N, the task is to count all substrings which contain the most frequent character in the string as the first character.

Note: If more than one character has a maximum frequency, consider the lexicographically smallest among them.

Examples:

Input: S = “abcab”
Output: 7
Explanation:
There are two characters a and b occurring maximum times i.e., 2 times.
Selecting the lexicographically smaller character i.e. ‘a’.
Substrings starts with ‘a’ are: “a”, “ab”, “abc”, “abca”, “abcab”, “a”, “ab”.
Therefore the count is 7.

Input: S= “cccc”
Output: 10

Approach: The idea is to first find the character that occurs the maximum number of times and then count the substring starting with that character in the string. Follow the steps below to solve the problem:

• Initialize the count as 0 that will store the total count of strings.
• Find the maximum occurring character in the string S. Let that character be ch.
• Traverse the string using the variable i and if the character at ith index is the same as ch, increment the count by (N – i).
• After the above steps, print the value of count as the result.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include``using` `namespace` `std;` `// Function to find all substrings``// whose first character occurs``// maximum number of times``int` `substringCount(string s)``{``    ` `    ``// Stores frequency of characters``    ``vector<``int``> freq(26, 0);` `    ``// Stores character that appears``    ``// maximum number of times``    ``char` `max_char = ``'#'``;` `    ``// Stores max frequency of character``    ``int` `maxfreq = INT_MIN;` `    ``// Updates frequency of characters``    ``for``(``int` `i = 0; i < s.size(); i++)``    ``{``        ``freq[s[i] - ``'a'``]++;` `        ``// Update maxfreq``        ``if` `(maxfreq < freq[s[i] - ``'a'``])``            ``maxfreq = freq[s[i] - ``'a'``];``    ``}` `    ``// Character that occurs``    ``// maximum number of times``    ``for``(``int` `i = 0; i < 26; i++)``    ``{``        ` `        ``// Update the maximum frequency``        ``// character``        ``if` `(maxfreq == freq[i])``        ``{``            ``max_char = (``char``)(i + ``'a'``);``            ``break``;``        ``}``    ``}` `    ``// Stores all count of substrings``    ``int` `ans = 0;` `    ``// Traverse over string``    ``for``(``int` `i = 0; i < s.size(); i++)``    ``{``        ` `        ``// Get the current character``        ``char` `ch = s[i];``        ` `        ``// Update count of substrings``        ``if` `(max_char == ch)``        ``{``            ``ans += (s.size() - i);``        ``}``    ``}``    ` `    ``// Return the count of all``    ``// valid substrings``    ``return` `ans;``}` `// Driver Code``int` `main()``{``    ``string S = ``"abcab"``;` `    ``// Function Call``    ``cout << (substringCount(S));``}` `// This code is contributed by mohit kumar 29`

## Java

 `// Java program for the above approach``import` `java.util.*;` `class` `GFG {` `    ``// Function to find all substrings``    ``// whose first character occurs``    ``// maximum number of times``    ``static` `int` `substringCount(String s)``    ``{` `        ``// Stores frequency of characters``        ``int``[] freq = ``new` `int``[``26``];` `        ``// Stores character that appears``        ``// maximum number of times``        ``char` `max_char = ``'#'``;` `        ``// Stores max frequency of character``        ``int` `maxfreq = Integer.MIN_VALUE;` `        ``// Updates frequency of characters``        ``for` `(``int` `i = ``0``;``             ``i < s.length(); i++) {``            ``freq[s.charAt(i) - ``'a'``]++;` `            ``// Update maxfreq``            ``if` `(maxfreq``                ``< freq[s.charAt(i) - ``'a'``])``                ``maxfreq``                    ``= freq[s.charAt(i) - ``'a'``];``        ``}` `        ``// Character that occurs``        ``// maximum number of times``        ``for` `(``int` `i = ``0``; i < ``26``; i++) {` `            ``// Update the maximum frequency``            ``// character``            ``if` `(maxfreq == freq[i]) {``                ``max_char = (``char``)(i + ``'a'``);``                ``break``;``            ``}``        ``}` `        ``// Stores all count of substrings``        ``int` `ans = ``0``;` `        ``// Traverse over string``        ``for` `(``int` `i = ``0``;``             ``i < s.length(); i++) {` `            ``// Get the current character``            ``char` `ch = s.charAt(i);` `            ``// Update count of substrings``            ``if` `(max_char == ch) {``                ``ans += (s.length() - i);``            ``}``        ``}` `        ``// Return the count of all``        ``// valid substrings``        ``return` `ans;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{` `        ``String S = ``"abcab"``;` `        ``// Function Call``        ``System.out.println(substringCount(S));``    ``}``}`

## Python3

 `# Python3 program for the above approach``import` `sys` `# Function to find all substrings``# whose first character occurs``# maximum number of times``def` `substringCount(s):``    ` `    ``# Stores frequency of characters``    ``freq ``=` `[``0` `for` `i ``in` `range``(``26``)]` `    ``# Stores character that appears``    ``# maximum number of times``    ``max_char ``=` `'#'` `    ``# Stores max frequency of character``    ``maxfreq ``=` `-``sys.maxsize ``-` `1` `    ``# Updates frequency of characters``    ``for` `i ``in` `range``(``len``(s)):``        ``freq[``ord``(s[i]) ``-` `ord``(``'a'``)] ``+``=` `1` `        ``# Update maxfreq``        ``if` `(maxfreq < freq[``ord``(s[i]) ``-` `ord``(``'a'``)]):``            ``maxfreq ``=` `freq[``ord``(s[i]) ``-` `ord``(``'a'``)]` `    ``# Character that occurs``    ``# maximum number of times``    ``for` `i ``in` `range``(``26``):``        ` `        ``# Update the maximum frequency``        ``# character``        ``if` `(maxfreq ``=``=` `freq[i]):``            ``max_char ``=` `chr``(i ``+` `ord``(``'a'``))``            ``break` `    ``# Stores all count of substrings``    ``ans ``=` `0` `    ``# Traverse over string``    ``for` `i ``in` `range``(``len``(s)):``        ` `        ``# Get the current character``        ``ch ``=` `s[i]``        ` `        ``# Update count of substrings``        ``if` `(max_char ``=``=` `ch):``            ``ans ``+``=` `(``len``(s) ``-` `i)``    ` `    ``# Return the count of all``    ``# valid substrings``    ``return` `ans` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``S ``=` `"abcab"``    ` `    ``# Function Call``    ``print``(substringCount(S))` `# This code is contributed by ipg2016107`

## C#

 `// C# program for the above approach``using` `System;`` ` `class` `GFG{``    ` `// Function to find all substrings``// whose first character occurs``// maximum number of times``static` `int` `substringCount(``string` `s)``{``    ` `    ``// Stores frequency of characters``    ``int``[] freq = ``new` `int``;``    ` `    ``// Stores character that appears``    ``// maximum number of times``    ``char` `max_char = ``'#'``;` `    ``// Stores max frequency of character``    ``int` `maxfreq = Int32.MinValue;` `    ``// Updates frequency of characters``    ``for``(``int` `i = 0; i < s.Length; i++)``    ``{``        ``freq[s[i] - ``'a'``]++;` `        ``// Update maxfreq``        ``if` `(maxfreq < freq[s[i] - ``'a'``])``            ``maxfreq = freq[s[i] - ``'a'``];``    ``}` `    ``// Character that occurs``    ``// maximum number of times``    ``for``(``int` `i = 0; i < 26; i++)``    ``{``        ` `        ``// Update the maximum frequency``        ``// character``        ``if` `(maxfreq == freq[i])``        ``{``            ``max_char = (``char``)(i + ``'a'``);``            ``break``;``        ``}``    ``}` `    ``// Stores all count of substrings``    ``int` `ans = 0;` `    ``// Traverse over string``    ``for``(``int` `i = 0; i < s.Length; i++)``    ``{``        ` `        ``// Get the current character``        ``char` `ch = s[i];` `        ``// Update count of substrings``        ``if` `(max_char == ch)``        ``{``            ``ans += (s.Length - i);``        ``}``    ``}` `    ``// Return the count of all``    ``// valid substrings``    ``return` `ans;``}` `// Driver Code``public` `static` `void` `Main()``{``    ``string` `S = ``"abcab"``;` `    ``// Function Call``    ``Console.WriteLine(substringCount(S));``}``}` `// This code is contributed by susmitakundugoaldanga`

## Javascript

 ``

Output:

`7`

Time Complexity: O(N), as we are using a loop to traverse the string.
Auxiliary Space: O(1), as we are using freq array of size 26 which is constant.