Data Modelling & AI Data Structure & Algorithm

Generate Binary Strings of length N using Branch and Bound

23 June 2025

0

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: $O(2^n)$

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Generate Binary Strings of length N using Branch and Bound

C++

Java

Python3

C#

Javascript

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