An Interesting Method to Generate Binary Numbers from 1 to n
Given a number n, write a function that generates and prints all binary numbers with decimal values from 1 to n.
Examples:
Input: n = 2 Output: 1, 10 Input: n = 5 Output: 1, 10, 11, 100, 101
Naive Method –
A simple method is to run a loop from 1 to n, call decimal to binary inside the loop.
Efficient Method –
Following is an interesting method that uses queue data structure to print binary numbers. Thanks to Vivek for suggesting this approach.
1) Create an empty queue of strings 2) Enqueue the first binary number "1" to queue. 3) Now run a loop for generating and printing n binary numbers. ......a) Dequeue and Print the front of queue. ......b) Append "0" at the end of front item and enqueue it. ......c) Append "1" at the end of front item and enqueue it.
Following is implementation of above algorithm.
C++
// C++ program to generate binary numbers from 1 to n#include <bits/stdc++.h>using namespace std;// This function uses queue data structure to print binary// numbersvoid generatePrintBinary(int n){ // Create an empty queue of strings queue<string> q; // Enqueue the first binary number q.push("1"); // This loops is like BFS of a tree with 1 as root // 0 as left child and 1 as right child and so on while (n--) { // print the front of queue string s1 = q.front(); q.pop(); cout << s1 << "\n"; string s2 = s1; // Store s1 before changing it // Append "0" to s1 and enqueue it q.push(s1.append("0")); // Append "1" to s2 and enqueue it. Note that s2 // contains the previous front q.push(s2.append("1")); }}// Driver program to test above functionint main(){ int n = 10; generatePrintBinary(n); return 0;} |
Java
// Java program to generate binary numbers from 1 to nimport java.util.LinkedList;import java.util.Queue;public class GenerateBNo { // This function uses queue data structure to print // binary numbers static void generatePrintBinary(int n) { // Create an empty queue of strings Queue<String> q = new LinkedList<String>(); // Enqueue the first binary number q.add("1"); // This loops is like BFS of a tree with 1 as root // 0 as left child and 1 as right child and so on while (n-- > 0) { // print the front of queue String s1 = q.peek(); q.remove(); System.out.println(s1); // Store s1 before changing it String s2 = s1; // Append "0" to s1 and enqueue it q.add(s1 + "0"); // Append "1" to s2 and enqueue it. Note that s2 // contains the previous front q.add(s2 + "1"); } } // Driver program to test above function public static void main(String[] args) { int n = 10; generatePrintBinary(n); }}// This code is contributed by Sumit Ghosh |
Python
# Python program to generate binary numbers from# 1 to n# This function uses queu data structure to print binary numbersdef generatePrintBinary(n): # Create an empty queue from Queue import Queue q = Queue() # Enqueu the first binary number q.put("1") # This loop is like BFS of a tree with 1 as root # 0 as left child and 1 as right child and so on while(n > 0): n -= 1 # Print the front of queue s1 = q.get() print s1 s2 = s1 # Store s1 before changing it # Append "0" to s1 and enqueue it q.put(s1+"0") # Append "1" to s2 and enqueue it. Note that s2 # contains the previous front q.put(s2+"1")# Driver program to test above functionn = 10generatePrintBinary(n)# This code is contributed by Nikhil Kumar Singh(nickzuck_007) |
C#
// C# program to generate binary// numbers from 1 to nusing System;using System.Collections.Generic;class GFG { // This function uses queue data // structure to print binary numbers public static void generatePrintBinary(int n) { // Create an empty queue of strings LinkedList<string> q = new LinkedList<string>(); // Enqueue the first binary number q.AddLast("1"); // This loops is like BFS of a tree // with 1 as root 0 as left child // and 1 as right child and so on while (n-- > 0) { // print the front of queue string s1 = q.First.Value; q.RemoveFirst(); Console.WriteLine(s1); // Store s1 before changing it string s2 = s1; // Append "0" to s1 and enqueue it q.AddLast(s1 + "0"); // Append "1" to s2 and enqueue it. // Note that s2 contains the previous front q.AddLast(s2 + "1"); } } // Driver Code public static void Main(string[] args) { int n = 10; generatePrintBinary(n); }}// This code is contributed by Shrikant13 |
Output
1 10 11 100 101 110 111 1000 1001 1010
Time Complexity: O(n)
This article is contributed by Abhishek. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
