Given a positive integer number N. The task is to generate all the binary strings of N bits. These binary strings should be in ascending order.
Examples:
Input: 2
Output:
0 0
0 1
1 0
1 1
Input: 3
Output:
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Approach: The idea is to try every permutation. For every position, there are 2 options, either ‘0’ or ‘1’. Backtracking is used in this approach to try every possibility/permutation.
Below is the implementation of the above approach:
C++
// C++ implementation of the above approach:#include <bits/stdc++.h>using namespace std;// Function to print the outputvoid printTheArray(int arr[], int n){ for (int i = 0; i < n; i++) { cout << arr[i] << " "; } cout << endl;}// Function to generate all binary stringsvoid generateAllBinaryStrings(int n, int arr[], int i){ if (i == n) { printTheArray(arr, n); return; } // First assign "0" at ith position // and try for all other permutations // for remaining positions arr[i] = 0; generateAllBinaryStrings(n, arr, i + 1); // And then assign "1" at ith position // and try for all other permutations // for remaining positions arr[i] = 1; generateAllBinaryStrings(n, arr, i + 1);}// Driver Codeint main(){ int n = 4; int arr[n]; // Print all binary strings generateAllBinaryStrings(n, arr, 0); return 0;} |
Java
// Java implementation of the above approach:import java.util.*;class GFG{// Function to print the outputstatic void printTheArray(int arr[], int n){ for (int i = 0; i < n; i++) { System.out.print(arr[i]+" "); } System.out.println();}// Function to generate all binary stringsstatic void generateAllBinaryStrings(int n, int arr[], int i){ if (i == n) { printTheArray(arr, n); return; } // First assign "0" at ith position // and try for all other permutations // for remaining positions arr[i] = 0; generateAllBinaryStrings(n, arr, i + 1); // And then assign "1" at ith position // and try for all other permutations // for remaining positions arr[i] = 1; generateAllBinaryStrings(n, arr, i + 1);}// Driver Codepublic static void main(String args[]){ int n = 4; int[] arr = new int[n]; // Print all binary strings generateAllBinaryStrings(n, arr, 0);}}// This code is contributed by// Surendra_Gangwar |
Python3
# Python3 implementation of the # above approach # Function to print the output def printTheArray(arr, n): for i in range(0, n): print(arr[i], end = " ") print()# Function to generate all binary strings def generateAllBinaryStrings(n, arr, i): if i == n: printTheArray(arr, n) return # First assign "0" at ith position # and try for all other permutations # for remaining positions arr[i] = 0 generateAllBinaryStrings(n, arr, i + 1) # And then assign "1" at ith position # and try for all other permutations # for remaining positions arr[i] = 1 generateAllBinaryStrings(n, arr, i + 1) # Driver Code if __name__ == "__main__": n = 4 arr = [None] * n # Print all binary strings generateAllBinaryStrings(n, arr, 0) # This code is contributed # by Rituraj Jain |
C#
// C# implementation of the above approach:using System;class GFG{// Function to print the outputstatic void printTheArray(int []arr, int n){ for (int i = 0; i < n; i++) { Console.Write(arr[i]+" "); } Console.WriteLine();}// Function to generate all binary stringsstatic void generateAllBinaryStrings(int n, int []arr, int i){ if (i == n) { printTheArray(arr, n); return; } // First assign "0" at ith position // and try for all other permutations // for remaining positions arr[i] = 0; generateAllBinaryStrings(n, arr, i + 1); // And then assign "1" at ith position // and try for all other permutations // for remaining positions arr[i] = 1; generateAllBinaryStrings(n, arr, i + 1);}// Driver Codepublic static void Main(String []args){ int n = 4; int[] arr = new int[n]; // Print all binary strings generateAllBinaryStrings(n, arr, 0);}}// This code has been contributed by 29AjayKumar |
Javascript
<script> // Javascript implementation of the above approach: // Function to print the output function printTheArray(arr, n) { for (let i = 0; i < n; i++) { document.write(arr[i]+" "); } document.write("</br>"); } // Function to generate all binary strings function generateAllBinaryStrings(n, arr, i) { if (i == n) { printTheArray(arr, n); return; } // First assign "0" at ith position // and try for all other permutations // for remaining positions arr[i] = 0; generateAllBinaryStrings(n, arr, i + 1); // And then assign "1" at ith position // and try for all other permutations // for remaining positions arr[i] = 1; generateAllBinaryStrings(n, arr, i + 1); } let n = 4; let arr = new Array(n); arr.fill(0); // Print all binary strings generateAllBinaryStrings(n, arr, 0);// This code is contributed by divyeshrabadiya07.</script> |
PHP
<?php// PHP implementation of the above approach// Function to print the outputfunction printTheArray($arr, $n){ for ($i = 0; $i < $n; $i++) { echo $arr[$i], " "; } echo "\n";}// Function to generate all binary stringsfunction generateAllBinaryStrings($n, $arr, $i){ if ($i == $n) { printTheArray($arr, $n); return; } // First assign "0" at ith position // and try for all other permutations // for remaining positions $arr[$i] = 0; generateAllBinaryStrings($n, $arr, $i + 1); // And then assign "1" at ith position // and try for all other permutations // for remaining positions $arr[$i] = 1; generateAllBinaryStrings($n, $arr, $i + 1);}// Driver Code$n = 4;$arr = array_fill(0, $n, 0);// Print all binary stringsgenerateAllBinaryStrings($n, $arr, 0);// This code is contributed by Ryuga ?> |
Output
0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1
Time complexity – O(2n)
Space complexity – O(n)
Approach 2: Bit Manipulation
Step-by-step Explanation:
- Generate all numbers from 0 to 2^n – 1.
- Convert each number to its binary representation using the bitset class from the C++ Standard Library.
- Extract the last n bits of the binary representation using the substr method.
C++
#include <iostream>#include <bitset>using namespace std;int main() { int n = 4; for (int i = 0; i < (1 << n); i++) { bitset<32> b(i); cout << b.to_string().substr(32-n) << endl; } return 0;} |
Java
public class Main { public static void main(String[] args) { int n = 4; // Loop over all possible combinations of n bits // using bit manipulation for (int i = 0; i < (1 << n); i++) { // Convert the integer 'i' to a binary string // representation of length 32 using the BitSet // class Note: Java's BitSet class does not have // a direct to_string() method like C++, so // we'll convert it to a binary string // representation using a custom method String binaryString = toBinaryString(i, n); System.out.println(binaryString); } } // Custom method to convert an integer 'num' to a binary // string representation of length 'length' static String toBinaryString(int num, int length) { StringBuilder sb = new StringBuilder(); // Loop to append the binary digits to the // StringBuilder for (int i = length - 1; i >= 0; i--) { // Use bitwise AND operation to extract the // binary digit at position 'i' int bit = (num & (1 << i)) >> i; // Append the binary digit to the StringBuilder sb.append(bit); } return sb.toString(); }} |
Python
def print_binary_combinations(n): # Loop through all numbers from 0 to 2^n - 1 for i in range(1 << n): # Convert the current number to a binary string of length n binary_str = format(i, '0' + str(n) + 'b') print(binary_str)# Example usagen = 4print_binary_combinations(n)#user_dtewbxkn77n |
C#
using System;class GFG { static void Main() { int n = 4; for (int i = 0; i < (1 << n); i++) { string binary = Convert.ToString(i, 2).PadLeft(n, '0'); Console.WriteLine(binary); } }} |
Output
0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
Time Complexity: O(n * 2^n)
Auxiliary Space: O(n)
Explanation:
The time complexity is O(n * 2^n) because we need to generate all 2^n binary strings and each binary string has a length of n. The auxiliary space complexity is O(n) because we need to store the binary representation of each number.
How is this approach different from another approach?
This approach is different from the recursive approach because it uses bit manipulation to generate all binary strings instead of recursion. The recursive approach has a time complexity of O(2^n) and an auxiliary space complexity of O(n), while this approach has a time complexity of O(n * 2^n) and an auxiliary space complexity of O(n).
Related Article: Generate all the binary number from 0 to n
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