Generate all the binary strings of N bits
Last Updated :
11 Jul, 2025
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 output
void printTheArray(int arr[], int n)
{
for (int i = 0; i < n; i++) {
cout << arr[i] << " ";
}
cout << endl;
}
// Function to generate all binary strings
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 Code
int 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 output
static 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 strings
static 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 Code
public 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
Python
# 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 output
static void printTheArray(int []arr, int n)
{
for (int i = 0; i < n; i++)
{
Console.Write(arr[i]+" ");
}
Console.WriteLine();
}
// Function to generate all binary strings
static 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 Code
public 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 output
function printTheArray($arr, $n)
{
for ($i = 0; $i < $n; $i++)
{
echo $arr[$i], " ";
}
echo "\n";
}
// 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);
}
// Driver Code
$n = 4;
$arr = array_fill(0, $n, 0);
// Print all binary strings
generateAllBinaryStrings($n, $arr, 0);
// This code is contributed by Ryuga
?>
Output0 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 usage
n = 4
print_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);
}
}
}
JavaScript
<script>
const n = 4;
for (let i = 0; i < (1 << n); i++) {
const binaryString = (i >>> 0).toString(2).padStart(n, '0');
console.log(binaryString);
}
</script>
Output0000
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
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Hereâs the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem