Check if a substring exists having only 2 distinct characters with frequency of one as twice the others

Given a string str[] of N lower case English alphabets, the task is to check if there exists a substring of the given string such that the substring is composed of only two characters and the frequency of 1^st character = 2 * frequency of 2^nd character.

Example:

Input: str[] = “aaaabbc”
Output: Yes
Explanation: The substring str[0… 5] = “aaaabb” of the given string is composed of only two characters ‘a’ and ‘b’ and frequency of ‘a’ = 2 * frequency of ‘b’, i.e, 4 = 2 * 2. Another example of a valid substring is str[4… 6] = “bbc”.

Input: str[] = “abcdefg”
Output: No

Naive Approach: The given problem can be solved by iterating over all the substrings of the given string and checking whether the string is made up of only two characters and the frequency of the 1^st character = 2 * frequency of the 2^nd character. 

Time Complexity: O(N³)
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized using a Greedy Technique. Upon observing carefully, it can be noticed that for any substring to be valid, there must exist a substring of size 3 of that string such that it is made up of only two characters and the frequency of the 1^st character = 2 * frequency of the 2^nd character. Hence, the given problem can be solved by iterating through the given string and for each substring of length 3, check if there exists a string of the form “xxy“, “xyx“, or “yxx“.

Below is the implementation of the above approach: 

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to check if there exist a
// substring such that it is made up of
// only two characters and freq of 1st
// char is equal to 2 * freq of 2nd char
bool isPossible(string str)
{
    // Loop to iterate over the string
    for (int i = 0; i + 2 < str.size(); i++) {

        // If the string is of
        // the form "xxy"
        if (str[i] == str[i + 1]
            && str[i] != str[i + 2]) {
            return true;
        }

        // If the string is of
        // the form "xyx"
        if (str[i] == str[i + 2]
            && str[i] != str[i + 1]) {
            return true;
        }

        // If the string is of
        // the form "yxx"
        if (str[i + 1] == str[i + 2]
            && str[i] != str[i + 1]) {
            return true;
        }
    }

    // If no valid substring exist
    return false;
}

// Driver Code
int main()
{
    string str = "aaaabbc";

    if (isPossible(str))
        cout << "Yes";
    else
        cout << "No";

    return 0;
}

Java

// Java program for the above approach
import java.io.*;
public class GFG {

    // Function to check if there exist a
    // substring such that it is made up of
    // only two characters and freq of 1st
    // char is equal to 2 * freq of 2nd char
    public static boolean isPossible(String str)
    {

        // Loop to iterate over the string
        for (int i = 0; i + 2 < str.length(); i++) {

            // If the string is of
            // the form "xxy"
            if (str.charAt(i) == str.charAt(i + 1)
                    && str.charAt(i) != str.charAt(i + 2)) {
                return true;
            }

            // If the string is of
            // the form "xyx"
            if (str.charAt(i) == str.charAt(i + 2)
                    && str.charAt(i) != str.charAt(i + 1)) {
                return true;
            }

            // If the string is of
            // the form "yxx"
            if (str.charAt(i + 1) == str.charAt(i + 2)
                    && str.charAt(i) != str.charAt(i + 1)) {
                return true;
            }
        }

        // If no valid substring exist
        return false;
    }

    // Driver Code
    public static void main(String args[]) {
        String str = "aaaabbc";

        if (isPossible(str))
            System.out.println("Yes");
        else
            System.out.println("No");

    }
}

// This code is contributed by saurabh_jaiswal.

Python3

# Python3 program for the above approach

# Function to check if there exist a
# substring such that it is made up of
# only two characters and freq of 1st
# char is equal to 2 * freq of 2nd char
def isPossible(str):

    # Loop to iterate over the string
    for i in range(0, len(str) - 2):

        # If the string is of
        # the form "xxy"
        if (str[i] == str[i + 1] and
            str[i] != str[i + 2]):
            return True

        # If the string is of
        # the form "xyx"
        if (str[i] == str[i + 2] and
            str[i] != str[i + 1]):
            return True

        # If the string is of
        # the form "yxx"
        if (str[i + 1] == str[i + 2] and
            str[i] != str[i + 1]):
            return True

    # If no valid substring exist
    return False

# Driver Code
if __name__ == "__main__":

    str = "aaaabbc"

    if (isPossible(str)):
        print("Yes")
    else:
        print("No")

# This code is contributed by rakeshsahni

C#

// C# program for the above approach
using System;
class GFG
{

    // Function to check if there exist a
    // substring such that it is made up of
    // only two characters and freq of 1st
    // char is equal to 2 * freq of 2nd char
    public static bool isPossible(String str)
    {

        // Loop to iterate over the string
        for (int i = 0; i + 2 < str.Length; i++)
        {

            // If the string is of
            // the form "xxy"
            if (str[i] == str[i + 1]
                    && str[i] != str[i + 2])
            {
                return true;
            }

            // If the string is of
            // the form "xyx"
            if (str[i] == str[i + 2]
                    && str[i] != str[i + 1])
            {
                return true;
            }

            // If the string is of
            // the form "yxx"
            if (str[i + 1] == str[i + 2]
                    && str[i] != str[i + 1])
            {
                return true;
            }
        }

        // If no valid substring exist
        return false;
    }

    // Driver Code
    public static void Main()
    {
        String str = "aaaabbc";

        if (isPossible(str))
            Console.Write("Yes");
        else
            Console.Write("No");

    }
}

// This code is contributed by saurabh_jaiswal.

Javascript

<script>

// JavaScript Program to implement
// the above approach

// Function to check if there exist a
// substring such that it is made up of
// only two characters and freq of 1st
// char is equal to 2 * freq of 2nd char
function isPossible( str)
{

    // Loop to iterate over the string
    for (let i = 0; i + 2 < str.length; i++) {

        // If the string is of
        // the form "xxy"
        if (str[i] == str[i + 1]
            && str[i] != str[i + 2]) {
            return true;
        }

        // If the string is of
        // the form "xyx"
        if (str[i] == str[i + 2]
            && str[i] != str[i + 1]) {
            return true;
        }

        // If the string is of
        // the form "yxx"
        if (str[i + 1] == str[i + 2]
            && str[i] != str[i + 1]) {
            return true;
        }
    }

    // If no valid substring exist
    return false;
}

// Driver Code
    let str = "aaaabbc";
    if (isPossible(str))
        document.write("Yes");
    else
        document.write("No");

    // This code is contributed by Potta Lokesh
    </script>

Output

Yes

Time Complexity: O(N)
Auxiliary Space: O(1)