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

C++

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// CPP Program to generate
// Binary Strings using Branch and Bound
#include <bits/stdc++.h>
using namespace std;
  
// Creating a Node class
class Node
{
public:
    int *soln;
    int level;
    vector<Node *> child;
    Node *parent;
  
    Node(Node *parent, int level, int N)
    {
        this->parent = parent;
        this->level = level;
        this->soln = new int[N];
    }
};
  
// Utility function to generate binary strings of length n
void generate(Node *n, int &N, queue<Node *> &Q)
{
    // If list is full print combination
    if (n->level == N)
    {
        for (int i = 0; i < N; i++)
            cout << n->soln[i];
        cout << endl;
    }
    else
    {
        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.push_back(x);
            Q.push(x);
        }
    }
}
  
// Driver Code
int main()
{
    // Initiate Generation
    // Create a root Node
    int N = 3;
    Node *root;
    root = new Node(NULL, 0, N);
  
    // Queue that maintains the list of live Nodes
    queue<Node *> Q;
      
    // Instantiate the Queue
    Q.push(root);
  
    while (!Q.empty())
    {
        Node *E = Q.front();
        Q.pop();
        generate(E, N, Q);
    }
  
    return 0;
}
  
// This code is contributed by
// sanjeev2552

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Java














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// 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); 


        } 


    } 


} 



















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C#














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// 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 



















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Output:


000
001
010
011
100
101
110
111





Time Complexity: O(2^n)


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