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Generate all binary strings from given pattern

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  • Difficulty Level : Medium
  • Last Updated : 20 Oct, 2022
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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

Recommended Practice

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 do the same for all remaining characters. We print the string if we reach at its end. 

Algorithm:
Step 1: Initialize the string first with some wildcard characters in it.
Step 2: Check if index position is equals to the size of string, If it is return.
Step 3: If wildcard character is present at index location, replace it by 0 or 1 accordingly.
Step 4: Print the output

Below is the implementation of the above approach:

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: 

10000101
10001101
10100101
10101101
11000101
11001101
11100101
11101101

 

Time Complexity: O(2N), where N is the length of the given string and there are 2 possibilities.
Auxiliary Space: O(N2), as a copy of the string is created in every recursive call.

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;
}

Java




/*package whatever //do not write package name here */
import java.io.*;
import java.util.*;
 
class GFG {
    // Iterative Java program to generate all binary
// strings formed by replacing each wildcard
// character by 0 or 1
 
// Iterative function to generate all binary strings
// formed by replacing each wildcard character by 0
// or 1
static void print(String str)
{
    Queue<String> q = new LinkedList<>();
    q.add(str);
 
    while (!q.isEmpty())
    {
        str = q.remove();
 
        // find position of first occurrence of wildcard
        int index = str.indexOf('?');
 
        // If no matches were found,
        // find returns string::npos
        if(index != -1)
        {
            // replace '?' by '0' and add string into queue
            str = str.substring(0,index) + '0' + str.substring(index+1);
            q.add(str);
 
            // replace '?' by '1' and add string into queue
            str = str.substring(0,index) + '1' + str.substring(index+1);
            q.add(str);
        }
 
        else
            // If no wildcard characters are left,
            // print the string.
            System.out.println(str);
 
    }
}
     
// Driver Code
public static void main(String args[])
{
    String str = "1??0?101";
    print(str);
 
}
}
 
// This code is contributed by shinjanpatra

Python3




# Iterative Python program to generate all binary
# strings formed by replacing each wildcard
# character by 0 or 1
  
# Iterative function to generate all binary strings
# formed by replacing each wildcard character by 0
# or 1
def Print(Str):
    q = []
    q.append(Str)
    while(len(q) > 0):
        Str = q[0]
         
        # find position of first occurrence of wildcard
        try:
            index = Str.index('?')
        except ValueError:
            index = -1
             
        # If no matches were found,
        # find returns -1
        if(index != -1):
            
            # replace '?' by '0' and push string into queue
            s1=Str.replace('?','0',1)
            q.append(s1)
             
            # replace '?' by '1' and push string into queue
            s2=Str.replace('?','1',1)
            q.append(s2)
        else:
            # If no wildcard characters are left,
            # print the string.
            print(Str)
        q.pop(0)
             
# Driver code
Str = "1??0?101"
Print(Str)
 
# This code is contributed by Pushpesh Raj

C#




// C# program to implement the approach
using System;
using System.Collections.Generic;
 
public class GFG
{
 
  // Iterative C# program to generate all binary
  // strings formed by replacing each wildcard
  // character by 0 or 1
 
  // Iterative function to generate all binary strings
  // formed by replacing each wildcard character by 0
  // or 1
  static void print(string Str)
  {
 
    var q = new List<string>();
    q.Add(Str);
    while (q.Count > 0) {
      Str = q[0];
 
      // find position of first occurrence of wildcard
      int index = Str.IndexOf('?');
 
      // If no matches were found,
      // find returns -1
      if (index != -1) {
 
        // replace '?' by '0' and push string into
        // queue
        Str = Str.Substring(0, index) + '0'
          + Str.Substring(index + 1);
        q.Add(Str);
 
        // replace '?' by '1' and push string into
        // queue
        Str = Str.Substring(0, index) + '1'
          + Str.Substring(index + 1);
        q.Add(Str);
      }
 
      else {
 
        // If no wildcard characters are left,
        // print the string.
        Console.WriteLine(Str);
      }
 
      q.RemoveAt(0);
    }
  }
 
  // Driver Code
  public static void Main(string[] args)
  {
    string str = "1??0?101";
     
    // Function call
    print(str);
  }
}
 
// This code is contributed by phasing17

Javascript




<script>
 
// Iterative JavaScript program to generate all binary
// strings formed by replacing each wildcard
// character by 0 or 1
 
// Iterative function to generate all binary strings
// formed by replacing each wildcard character by 0
// or 1
function Print(Str){
 
    let q = []
    q.push(Str)
 
    while (q.length > 0){
        let Str = q[0]
 
        // find position of first occurrence of wildcard
        let index = Str.indexOf('?')
     
        // If no matches were found,
        // find returns -1
        if(index != -1)
        {
         
            // replace '?' by '0' and push string into queue
            Str = Str.replace(Str[index] , '0')
            q.push(Str)
 
            // replace '?' by '1' and push string into queue
            Str = Str.replace(Str[index] , '1')
            q.push(Str)
        }
 
        else
        {
         
            // If no wildcard characters are left,
            // print the string.
            document.write(Str,"</br>")
        }
 
        q.shift()
    }
}
 
// Driver code to test above function
let Str = "1??0?101"
Print(Str)
 
// This code is contributed by shinjanpatra
 
</script>

Output: 

10000101
10001101
10100101
10101101
11000101
11001101
11100101
11101101

 

Time Complexity: O(N*2N),  where N is the size of the string.
Auxiliary Space: O(2N)

Method 3 (Using str and Recursion) 
 

C++




// C++ program to implement the approach
#include <bits/stdc++.h>
 
using namespace std;
 
/* 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 */
 
vector<string> res;
 
void genBin(string s)
{
    auto pos = s.find('?');
    if (pos != string::npos) {
        // copying s to s1
        string s1 = s;
        // replacing first occurrence of ?
        // with 0
        s1.replace(pos, 1, "0");
        // copying s to s2
        string s2 = s;
        // replacing first occurrence of ?
        // with 1
        s2.replace(pos, 1, "1");
        genBin(s1);
        genBin(s2);
    }
    else {
        res.push_back(s);
    }
}
 
// Driver code
int main()
{
    genBin("1??0?101");
    for (string x : res) {
        cout << x << " ";
    }
}
 
// This code is contributed by phasing17

Java




import java.io.*;
import java.util.*;
 
class GFG
{
 
  // 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
  static ArrayList<String>res = new ArrayList<String>();
  static void genBin(String s) {
    if (s.indexOf('?') != -1) {
      String s1 = s.replaceFirst("\\?", "0"); // only replace once
      String s2 = s.replaceFirst("\\?", "1"); // only replace once
      genBin(s1);
      genBin(s2);
    }
    else res.add(s);
  }
 
  public static void main(String[] args) {
    genBin("1??0?101");
    System.out.println(res);
  }
}

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

C#




// C# code to implement the approach
 
using System;
using System.Collections.Generic;
 
class GFG {
 
    // 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
    static List<string> res = new List<string>();
    static void genBin(string s)
    {
        int ind = s.IndexOf("?");
        if (ind != -1) {
            string s1 = s.Remove(ind, 1).Insert(
                ind, "0"); // only replace once
            string s2 = s.Remove(ind, 1).Insert(
                ind, "1"); // only replace once
            genBin(s1);
            genBin(s2);
        }
        else
            res.Add(s);
    }
     
   
      // Driver code
    public static void Main(string[] args)
    {
        genBin("1??0?101");
        foreach(var ele in res) Console.Write(ele + " ");
    }
}
 
 
// This code is contributed by phasing17

Javascript




<script>
/* 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 */
  
let res = []
function genBin(s){
  if(s.includes('?')){
    let s1 = s.replace(/\?/,'0') //only replace once
    let s2 = s.replace(/\?/,'1') //only replace once
    genBin(s1)
    genBin(s2)
  }else{
    res.push(s)
  }
}
  
// Driver code
genBin("1??0?101")
document.write(res)
  
// This code is contributed by
// Santanu Panda
</script>

Output: 

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

 

Time Complexity: O(N*2N),  where N is the size of the string.
Auxiliary Space: O(2N)

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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