Generate Binary Strings of length N using Branch and Bound

0 0 5 minutes read

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++

// 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

Java

// 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);
        }
    }
}

Python3

from queue import Queue
 
# Creating a Node class
class Node:
    def __init__(self, parent, level, N):
        self.parent = parent
        self.level = level
        self.soln = [0]*N
        self.child = []
 
# Queue that maintains the list of live Nodes
Q = Queue()
 
# Utility function to generate binary strings of length n
def generate(n):
    # If list is full print combination
    if n.level == N:
        print(''.join(str(x) for x in n.soln))
    else:
        # Create a new list for new combination
        n.child = []
 
        l = n.level
 
        # iterate while length is not equal to n
        for i in range(2):
            x = Node(n, l + 1, N)
            x.soln[:l] = n.soln[:l]
            x.soln[l] = i
            n.child.append(x)
            Q.put(x)
 
# Driver code
if __name__ == '__main__':
    # Initiate Generation
    # Create a root Node
    N = 3
    root = Node(None, 0, N)
 
    # Instantiate the Queue
    Q.put(root)
 
    while not Q.empty():
        E = Q.get()
        generate(E)

C#

// 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

Javascript

// Javascript code for the above approach
 
// Creating a Node class
class Node {
  constructor(parent, level, N) {
    this.parent = parent;
    this.level = level;
    this.soln = new Array(N).fill(0);
    this.child = [];
  }
}
 
// Queue that maintains the list of live Nodes
const Q = [];
 
// Utility function to generate binary strings of length n
function generate(n, N) {
  // If list is full print combination
  if (n.level === N) {
    console.log(n.soln.join(""));
  } else {
    // Create a new list for new combination
    n.child = [];
 
    const l = n.level;
 
    // iterate while length is not equal to n
    for (let i = 0; i < 2; i++) {
      const x = new Node(n, l + 1, N);
      x.soln = n.soln.slice();
      x.soln[l] = i;
      n.child.push(x);
      Q.push(x);
    }
  }
}
 
// Driver code
(() => {
  // Initiate Generation
  // Create a root Node
  const N = 3;
  const root = new Node(null, 0, N);
 
  // Instantiate the Queue
  Q.push(root);
 
  while (Q.length > 0) {
    const E = Q.shift();
    generate(E, N);
  }
})();
 
 
// This code is contributed by sdeadityasharma

Output:

Time Complexity: $O(2^n)$

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!