Generate all binary strings from given pattern

Difficulty Level : Medium
Last Updated : 09 Jun, 2021

Given a string containing of ‘0’, ‘1’ and ‘?’ wildcard characters, generate all binary strings that can be formed by replacing each wildcard character by ‘0’ or ‘1’.
Example :

Input str = "1??0?101"
Output: 
        10000101
        10001101
        10100101
        10101101
        11000101
        11001101
        11100101
        11101101

Method 1 (Using Recursion)
We pass index of next character to the recursive function. If the current character is a wildcard character ‘?’, we replace it with ‘0’ or ‘1’ and recurse for remaining characters. We print the string if we reach its end.
Below is recursive the implementation.

C++

// Recursive C++ program to generate all binary strings
// formed by replacing each wildcard character by 0 or 1
#include <iostream>
using namespace std;
 
// Recursive function to generate all binary strings
// formed by replacing each wildcard character by 0 or 1
void print(string str, int index)
{
    if (index == str.size())
    {
        cout << str << endl;
        return;
    }
 
    if (str[index] == '?')
    {
        // replace '?' by '0' and recurse
        str[index] = '0';
        print(str, index + 1);
 
        // replace '?' by '1' and recurse
        str[index] = '1';
        print(str, index + 1);
 
        // No need to backtrack as string is passed
        // by value to the function
    }
    else
        print(str, index + 1);
}
 
// Driver code to test above function
int main()
{
    string str = "1??0?101";
 
    print(str, 0);
 
    return 0;
}

Java

// Recursive Java program to generate all
// binary strings formed by replacing
// each wildcard character by 0 or 1
import java.util.*;
import java.lang.*;
import java.io.*;
 
class binStr
{  
    // Recursive function to generate all binary
    // strings formed by replacing each wildcard
    // character by 0 or 1
    public static void print(char str[], int index)
    {
        if (index == str.length)
        {
            System.out.println(str);
            return;
        }
 
        if (str[index] == '?')
        {
            // replace '?' by '0' and recurse
            str[index] = '0';
            print(str, index + 1);
             
            // replace '?' by '1' and recurse
            str[index] = '1';
            print(str, index + 1);
             
            // NOTE: Need to backtrack as string
            // is passed by reference to the
            // function
            str[index] = '?';
        }
        else
            print(str, index + 1);
    }
 
    // driver code
    public static void main (String[] args)
    {
        String input = "1??0?101";
        char[] str = input.toCharArray();
        print(str, 0);
    }
}
 
// This code is contributed by Chhavi

Python3

# Recursive Python program to generate all
# binary strings formed by replacing
# each wildcard character by 0 or 1
 
# Recursive function to generate all binary
# strings formed by replacing each wildcard
# character by 0 or 1
def _print(string, index):
    if index == len(string):
        print(''.join(string))
        return
 
    if string[index] == "?":
 
        # replace '?' by '0' and recurse
        string[index] = '0'
        _print(string, index + 1)
 
        # replace '?' by '1' and recurse
        string[index] = '1'
        _print(string, index + 1)
 
        # NOTE: Need to backtrack as string
        # is passed by reference to the
        # function
        string[index] = '?'
    else:
        _print(string, index + 1)
 
# Driver code
if __name__ == "__main__":
 
    string = "1??0?101"
    string = list(string)
    _print(string, 0)
 
    # This code is contributed by
    # sanjeev2552
 
# Note: function name _print is used because
# print is already a predefined function in Python

C#

// Recursive C# program to generate all
// binary strings formed by replacing
// each wildcard character by 0 or 1
using System;
 
class GFG
{
    // Recursive function to generate
    // all binary strings formed by
    // replacing each wildcard character
    // by 0 or 1
    public static void print(char []str,
                             int index)
    {
        if (index == str.Length)
        {
            Console.WriteLine(str);
            return;
        }
 
        if (str[index] == '?')
        {
            // replace '?' by
            // '0' and recurse
            str[index] = '0';
            print(str, index + 1);
             
            // replace '?' by
            // '1' and recurse
            str[index] = '1';
            print(str, index + 1);
             
            // NOTE: Need to backtrack
            // as string is passed by
            // reference to the function
            str[index] = '?';
        }
        else
            print(str, index + 1);
    }
 
    // Driver Code
    public static void Main ()
    {
        string input = "1??0?101";
        char []str = input.ToCharArray();
        print(str, 0);
    }
}
 
// This code is contributed by nitin mittal.

PHP

<?php
// Recursive PHP program to generate all binary strings
// formed by replacing each wildcard character by 0 or 1
 
// Recursive function to generate all binary strings
// formed by replacing each wildcard character by 0 or 1
function print1($str, $index)
{
    if ($index == strlen($str))
    {
        echo $str."\n";
        return;
    }
 
    if ($str[$index] == '?')
    {
        // replace '?' by '0' and recurse
        $str[$index] = '0';
        print1($str, $index + 1);
 
        // replace '?' by '1' and recurse
        $str[$index] = '1';
        print1($str, $index + 1);
 
        // No need to backtrack as string is passed
        // by value to the function
    }
    else
        print1($str, $index + 1);
}
 
// Driver code
 
    $str = "1??0?101";
 
    print1($str, 0);
 
     
// This code is contributed by chandan_jnu
?>

Javascript

<script>
 
      // Recursive JavaScript program to generate all
      // binary strings formed by replacing
      // each wildcard character by 0 or 1
       
      // Recursive function to generate
      // all binary strings formed by
      // replacing each wildcard character
      // by 0 or 1
      function print(str, index) {
        if (index === str.length) {
          document.write(str.join("") + "<br>");
          return;
        }
 
        if (str[index] === "?") {
          // replace '?' by
          // '0' and recurse
          str[index] = "0";
          print(str, index + 1);
 
          // replace '?' by
          // '1' and recurse
          str[index] = "1";
          print(str, index + 1);
 
          // NOTE: Need to backtrack
          // as string is passed by
          // reference to the function
          str[index] = "?";
        } else print(str, index + 1);
      }
 
      // Driver Code
 
      var input = "1??0?101";
      var str = input.split("");
      print(str, 0);
       
</script>

Output:

Method 2 (Using Queue)
We can also achieve this by using iteration. The idea is to use queue. We find position of first occurrence of wildcard character in the input string and replace it by ‘0’ , then ‘1’ and push both strings into the queue. Then we pop next string from the queue, and repeat the process till queue is empty. If no wildcard characters are left, we simply print the string.
Iterative C++ implementation using queue.

C++

// Iterative C++ program to generate all binary
// strings formed by replacing each wildcard
// character by 0 or 1
#include <iostream>
#include <queue>
using namespace std;
 
// Iterative function to generate all binary strings
// formed by replacing each wildcard character by 0
// or 1
void print(string str)
{
    queue<string> q;
    q.push(str);
 
    while (!q.empty())
    {
        string str = q.front();
 
        // find position of first occurrence of wildcard
        size_t index = str.find('?');
 
        // If no matches were found,
        // find returns string::npos
        if(index != string::npos)
        {
            // replace '?' by '0' and push string into queue
            str[index] = '0';
            q.push(str);
 
            // replace '?' by '1' and push string into queue
            str[index] = '1';
            q.push(str);
        }
 
        else
            // If no wildcard characters are left,
            // print the string.
            cout << str << endl;
 
        q.pop();
    }
}
 
// Driver code to test above function
int main()
{
    string str = "1??0?101";
 
    print(str);
 
    return 0;
}

Output:

Method 3 (Using str and Recursion)

Python3

#we store processed strings in all (array)
#we see if string as "?", if so, replace it with 0 and 1
#and send it back to recursive func until base case is reached
#which is no wildcard left
 
res = []
def genBin(s):
    if '?' in s:
        s1 = s.replace('?','0',1) #only replace once
        s2 = s.replace('?','1',1) #only replace once
        genBin(s1)
        genBin(s2)
    else: res.append(s)
 
# Driver code
genBin("1??0?101")
print(res)
 
# This code is contributed by
# divay pandey

Output:

['10000101', '10001101', '10100101', '10101101', '11000101', '11001101', '11100101', '11101101']

This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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