Generate Binary Strings of length N using Branch and Bound

The task is to generate a binary string of length N using branch and bound technique

Examples:

Input: N = 3
Output:
000
001
010
011
100
101
110
111
Explanation:
Numbers with 3 binary digits are
0, 1, 2, 3, 4, 5, 6, 7



Input: N = 2
Output:
00
01
10
11

Approach:

Generate Combinations using Branch and Bound :

  • It starts with an empty solution vector.
  • While Queue is not empty remove partial vector from queue.
  • If it is a final vector print the combination else,
  • For the next component of partial vector create k child vectors by fixing all possible states for the next component insert vectors into the queue.

Below is the implementation of the above approach

Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java Program to generate
// Binary Strings using Branch and Bound
  
import java.io.*;
import java.util.*;
  
// Creating a Node class
class Node {
  
    int soln[];
    int level;
    ArrayList<Node> child;
    Node parent;
  
    Node(Node parent, int level, int N)
    {
        this.parent = parent;
        this.level = level;
        this.soln = new int[N];
    }
}
  
class GFG {
  
    static int N;
  
    // Queue that maintains the list of live Nodes
    public static Queue<Node> Q;
  
    // Utility function to generate binary strings of length n
    public static void generate(Node n)
    {
        // If list is full print combination
        if (n.level == N) {
            for (int i = 0; i <= N - 1; i++) {
                System.out.print(n.soln[i]);
            }
            System.out.println();
        }
        else {
  
            // Create a new vector for new combination
            n.child = new ArrayList<Node>();
  
            int l = n.level;
  
            // iterate while length is not equal to n
            for (int i = 0; i <= 1; i++) {
                Node x = new Node(n, l + 1, N);
                for (int k = 0; k < l; k++) {
                    x.soln[k] = n.soln[k];
                }
                x.soln[l] = i;
                n.child.add(x);
                Q.add(x);
            }
        }
    }
  
    // Driver code
    public static void main(String args[])
    {
        // Initiate Generation
        // Create a root Node
        N = 3;
        Node root = new Node(null, 0, N);
  
        // Instantiate the Queue
        Q = new LinkedList<Node>();
        Q.add(root);
  
        while (Q.size() != 0) {
            Node E = Q.poll();
            generate(E);
        }
    }
}

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# Program to generate
// Binary Strings using Branch and Bound
using System;
using System.Collections.Generic;
  
// Creating a Node class
public class Node 
{
    public int []soln;
    public int level;
    public List<Node> child;
    public Node parent;
  
    public Node(Node parent, 
                int level, int N)
    {
        this.parent = parent;
        this.level = level;
        this.soln = new int[N];
    }
}
  
class GFG
{
    static int N;
  
    // Queue that maintains the list of live Nodes
    public static Queue<Node> Q;
  
    // Utility function to generate 
    // binary strings of length n
    public static void generate(Node n)
    {
        // If list is full print combination
        if (n.level == N)
        {
            for (int i = 0; i <= N - 1; i++)
            {
                Console.Write(n.soln[i]);
            }
            Console.WriteLine();
        }
        else
        {
  
            // Create a new vector for new combination
            n.child = new List<Node>();
  
            int l = n.level;
  
            // iterate while length is not equal to n
            for (int i = 0; i <= 1; i++) 
            {
                Node x = new Node(n, l + 1, N);
                for (int k = 0; k < l; k++) 
                {
                    x.soln[k] = n.soln[k];
                }
                x.soln[l] = i;
                n.child.Add(x);
                Q.Enqueue(x);
            }
        }
    }
  
    // Driver code
    public static void Main(String []args)
    {
        // Initiate Generation
        // Create a root Node
        N = 3;
        Node root = new Node(null, 0, N);
  
        // Instantiate the Queue
        Q = new Queue<Node>();
        Q.Enqueue(root);
  
        while (Q.Count != 0)
        {
            Node E = Q.Dequeue();
            generate(E);
        }
    }
}
  
// This code is contributed by Rajput-Ji

chevron_right


Output:

000
001
010
011
100
101
110
111

Time Complexity: O(2^n)



My Personal Notes arrow_drop_up


If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : Rajput-Ji