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, 7Input: 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 |
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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); } } } |
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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 |
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Output:
000 001 010 011 100 101 110 111
Time Complexity: 
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