Find Binary String of size at most 3N containing at least 2 given strings of size 2N as subsequences

Given three binary strings a, b, and c each having 2*N characters each, the task is to find a string having almost 3*N characters such that at least two of the given three strings occur as its one of the subsequence.

Examples:

Input: a = “00”, b = “11”, c = “01”
Output: “010”
Explanation: The strings “00” and “01” are subsequences of string “010” and is has not more than 3*N characters. Also, “001”, “011” can be the possible answers.

Input: a = “011001”, b = “111010”, c = “010001”
Output: “011001010″
Explanation: Here, all the three given strings occur as the subsequences of the output string.

Approach: The given problem can be solved using the following observations:

• It can be observed that according to the Pigeonhole Principle, there must exist a set of two strings such that the most frequent character in both the strings is the same and its frequency is >=N.
• Hence, for two such strings, a string of N most frequent characters can be created. The other remaining N characters of both the strings can be appended into the string respectively according to the order they occur. Therefore, the maximum size of the resultant string will be at most 3*N.

Therefore, after finding the set of strings with the same most frequent element, the rest can be solved using the two-pointer approach. Maintain two pointers, one for each string, and follow the below steps:

• Initially, i =0 and j = 0, where i represent the 1st string s1 and j represent the second string s2.
• If s1[i] is not equal to the most frequent character, print s1[i] and increment i.
• If s2[j] is not equal to the most frequent character, print s2[i] and increment j.
• If both s1[i] and s2[j] is representing the most frequent character, print s1[i] and increment both i and j.

Below is the implementation of the above approach:

C++

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

// Function to find most frequent
// character in the given string
char MostFrequent(string s)
{
    // Stores the frequency of
    // 0 and 1 respectively
    int arr[] = { 0, 0 };

    for (char ch : s) {
        arr[ch - '0']++;
    }

    // Stores most frequent character
    char result = arr[0] > arr[1] ? '0' : '1';

    // Return Answer
    return result;
}

// Function to find a Binary String of
// at most 3N characters having at least
// two of the given three strings of 2N
// characters as one of its subsequence
void findStr(string& a, string& b, string& c)
{
    // Stores most frequent char
    char freq;

    // Stores the respective string
    // with most frequent values
    string s1, s2;

    // Code to find the set of
    // two strings with same
    // most frequent characters
    if (MostFrequent(a) == MostFrequent(b)) {
        s1 = a;
        s2 = b;
        freq = MostFrequent(a);
    }
    else if (MostFrequent(a) == MostFrequent(c)) {
        s1 = a;
        s2 = c;
        freq = MostFrequent(a);
    }
    else {
        s1 = b;
        s2 = c;
        freq = MostFrequent(b);
    }

    // Pointer to iterate strings
    int i = 0, j = 0;

    // Traversal using the
    // two-pointer approach
    while (i < s1.size() && j < s2.size()) {

        // if current character
        // is not most frequent
        while (i < s1.size() && s1[i] != freq) {
            cout << s1[i++];
        }
        // if current character
        // is not most frequent
        while (j < s2.size() && s2[j] != freq) {
            cout << s2[j++];
        }

        // If end of string is reached
        if (i == s1.size() || j == s2.size())
            break;

        // If both string character
        // are same as most frequent
        if (s1[i] == s2[j]) {
            cout << s1[i];
            i++;
            j++;
        }
        else {
            cout << s1[i];
            i++;
        }
    }

    // Print leftover characters
    // of the string s1
    while (i < s1.size()) {
        cout << s1[i++];
    }

    // Print leftover characters
    // of the string s2
    while (j < s2.size()) {
        cout << s2[j++];
    }
}

// Driver Code
int main()
{
    string a, b, c;
    a = "00";
    b = "11";
    c = "01";

    findStr(a, b, c);
    return 0;
}

Java

// Java program for the above approach
class GFG
{
  // Function to find most frequent
  // character in the given String
  static char MostFrequent(String s)
  {
    // Stores the frequency of
    // 0 and 1 respectively
    int []arr = { 0, 0 };

    for(char ch : s.toCharArray()) {
      arr[ch - '0']++;
    }

    // Stores most frequent character
    char result = arr[0] > arr[1] ? '0' : '1';

    // Return Answer
    return result;
  }

  // Function to find a Binary String of
  // at most 3N characters having at least
  // two of the given three Strings of 2N
  // characters as one of its subsequence
  static void findStr(String a, String b, String c)
  {
    // Stores most frequent char
    char freq;

    // Stores the respective String
    // with most frequent values
    String s1 = "", s2 = "";

    // Code to find the set of
    // two Strings with same
    // most frequent characters
    if (MostFrequent(a) == MostFrequent(b)) {
      s1 = a;
      s2 = b;
      freq = MostFrequent(a);
    }
    else if (MostFrequent(a) == MostFrequent(c)) {
      s1 = a;
      s2 = c;
      freq = MostFrequent(a);
    }
    else {
      s1 = b;
      s2 = c;
      freq = MostFrequent(b);
    }

    // Pointer to iterate Strings
    int i = 0, j = 0;

    // Traversal using the
    // two-pointer approach
    while (i < s1.length()&& j < s2.length()) {

      // if current character
      // is not most frequent
      while (i < s1.length() && s1.charAt(i) != freq) {
        System.out.print(s1.charAt(i++));
      }
      // if current character
      // is not most frequent
      while (j < s2.length() && s2.charAt(j) != freq) {
        System.out.print(s2.charAt(j++));
      }

      // If end of String is reached
      if (i == s1.length()|| j == s2.length())
        break;

      // If both String character
      // are same as most frequent
      if (s1.charAt(i) == s2.charAt(j)) {
        System.out.print(s1.charAt(i));
        i++;
        j++;
      }
      else {
        System.out.print(s1.charAt(i));
        i++;
      }
    }

    // Print leftover characters
    // of the String s1
    while (i < s1.length()) {
      System.out.print(s1.charAt(i++));
    }

    // Print leftover characters
    // of the String s2
    while (j < s2.length()) {
      System.out.print(s2.charAt(j++));
    }
  }

  // Driver Code
  public static void main(String args[])
  {
    String a = "00";
    String b = "11";
    String c = "01";

    findStr(a, b, c);
  }
}

// This code is contributed Saurabh Jaiswal

C#

// C# program for the above approach
using System;
class GFG
{
  // Function to find most frequent
  // character in the given string
  static char MostFrequent(string s)
  {
    // Stores the frequency of
    // 0 and 1 respectively
    int []arr = { 0, 0 };

    foreach (char ch in s) {
      arr[ch - '0']++;
    }

    // Stores most frequent character
    char result = arr[0] > arr[1] ? '0' : '1';

    // Return Answer
    return result;
  }

  // Function to find a Binary String of
  // at most 3N characters having at least
  // two of the given three strings of 2N
  // characters as one of its subsequence
  static void findStr(string a, string b, string c)
  {
    // Stores most frequent char
    char freq;

    // Stores the respective string
    // with most frequent values
    string s1 = "", s2 = "";

    // Code to find the set of
    // two strings with same
    // most frequent characters
    if (MostFrequent(a) == MostFrequent(b)) {
      s1 = a;
      s2 = b;
      freq = MostFrequent(a);
    }
    else if (MostFrequent(a) == MostFrequent(c)) {
      s1 = a;
      s2 = c;
      freq = MostFrequent(a);
    }
    else {
      s1 = b;
      s2 = c;
      freq = MostFrequent(b);
    }

    // Pointer to iterate strings
    int i = 0, j = 0;

    // Traversal using the
    // two-pointer approach
    while (i < s1.Length && j < s2.Length) {

      // if current character
      // is not most frequent
      while (i < s1.Length && s1[i] != freq) {
        Console.Write(s1[i++]);
      }
      // if current character
      // is not most frequent
      while (j < s2.Length && s2[j] != freq) {
        Console.Write(s2[j++]);
      }

      // If end of string is reached
      if (i == s1.Length || j == s2.Length)
        break;

      // If both string character
      // are same as most frequent
      if (s1[i] == s2[j]) {
        Console.Write(s1[i]);
        i++;
        j++;
      }
      else {
        Console.Write(s1[i]);
        i++;
      }
    }

    // Print leftover characters
    // of the string s1
    while (i < s1.Length) {
      Console.Write(s1[i++]);
    }

    // Print leftover characters
    // of the string s2
    while (j < s2.Length) {
      Console.Write(s2[j++]);
    }
  }

  // Driver Code
  public static void Main()
  {
    string a = "00";
    string b = "11";
    string c = "01";

    findStr(a, b, c);
  }
}

// This code is contributed Samim Hossain Mondal.

Python3

# python3 program for the above approach

# Function to find most frequent
# character in the given string
def MostFrequent(s):

    # Stores the frequency of
    # 0 and 1 respectively
    arr = [0, 0]

    for ch in s:
        arr[ord(ch) - ord('0')] += 1

    # Stores most frequent character
    result = '0' if arr[0] > arr[1] else '1'

    # Return Answer
    return result

# Function to find a Binary String of
# at most 3N characters having at least
# two of the given three strings of 2N
# characters as one of its subsequence
def findStr(a, b, c):

    # Stores most frequent char
    freq = ''

    # Stores the respective string
    # with most frequent values
    s1, s2 = "", ""

    # Code to find the set of
    # two strings with same
    # most frequent characters
    if (MostFrequent(a) == MostFrequent(b)):
        s1 = a
        s2 = b
        freq = MostFrequent(a)

    elif (MostFrequent(a) == MostFrequent(c)):
        s1 = a
        s2 = c
        freq = MostFrequent(a)

    else:
        s1 = b
        s2 = c
        freq = MostFrequent(b)

    # Pointer to iterate strings
    i, j = 0, 0

    # Traversal using the
    # two-pointer approach
    while (i < len(s1) and j < len(s2)):

        # if current character
        # is not most frequent
        while (i < len(s1) and s1[i] != freq):
            print(s1[i], end="")
            i += 1

        # if current character
        # is not most frequent
        while (j < len(s2) and s2[j] != freq):
            print(s2[j], end="")
            j += 1

        # If end of string is reached
        if (i == len(s1) or j == len(s2)):
            break

        # If both string character
        # are same as most frequent
        if (s1[i] == s2[j]):
            print(s1[i], end="")
            i += 1
            j += 1

        else:
            print(s1[i], end="")
            i += 1

    # Print leftover characters
    # of the string s1
    while (i < len(s1)):
        print(s1[i], end="")
        i += 1

    # Print leftover characters
    # of the string s2
    while (j < len(s2)):
        print(s2[j], end="")
        j += 1

# Driver Code
if __name__ == "__main__":

    a = "00"
    b = "11"
    c = "01"

    findStr(a, b, c)

    # This code is contributed by rakeshsahni

Javascript

<script>
    // JavaScript code for the above approach

    // Function to find most frequent
    // character in the given string
    function MostFrequent(s)
    {

        // Stores the frequency of
        // 0 and 1 respectively
        let arr = new Array(2).fill(0)

        for (let i = 0; i < s.length; i++) {
            let ch = s[i];
            arr[ch.charCodeAt(0) - '0'.charCodeAt(0)]++;
        }

        // Stores most frequent character
        let result = arr[0] > arr[1] ? '0' : '1';

        // Return Answer
        return result;
    }

    // Function to find a Binary String of
    // at most 3N characters having at least
    // two of the given three strings of 2N
    // characters as one of its subsequence
    function findStr(a, b, c)
    {

        // Stores most frequent char
        let freq;

        // Stores the respective string
        // with most frequent values
        let s1, s2;

        // Code to find the set of
        // two strings with same
        // most frequent characters
        if (MostFrequent(a) == MostFrequent(b)) {
            s1 = a;
            s2 = b;
            freq = MostFrequent(a);
        }
        else if (MostFrequent(a) == MostFrequent(c)) {
            s1 = a;
            s2 = c;
            freq = MostFrequent(a);
        }
        else {
            s1 = b;
            s2 = c;
            freq = MostFrequent(b);
        }

        // Pointer to iterate strings
        let i = 0, j = 0;

        // Traversal using the
        // two-pointer approach
        while (i < s1.length && j < s2.length) {

            // if current character
            // is not most frequent
            while (i < s1.length && s1[i] != freq) {
                document.write(s1[i++]);
            }
            // if current character
            // is not most frequent
            while (j < s2.length && s2[j] != freq) {
                document.write(s2[j++]);
            }

            // If end of string is reached
            if (i == s1.length || j == s2.length)
                break;

            // If both string character
            // are same as most frequent
            if (s1[i] == s2[j]) {
                document.write(s1[i]);
                i++;
                j++;
            }
            else {
                document.write(s1[i]);
                i++;
            }
        }

        // Print leftover characters
        // of the string s1
        while (i < s1.length) {
            document.write(s1[i++]);
        }

        // Print leftover characters
        // of the string s2
        while (j < s2.length) {
            document.write(s2[j++]);
        }
    }

    // Driver Code
    let a, b, c;
    a = "00";
    b = "11";
    c = "01";

    findStr(a, b, c);

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

Output

011

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