Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Vertex cover Problem
For an undirected graph, the vertex cover is a subset of the vertices, where for every edge (u, v) of the graph either u or v is in the set.
Using a binary tree, we can easily solve the vertex cover problem.
This problem can be divided into two sub-problems. When the root is part of the vertex cover. For this case, the root covers all children edges. We can simply find the size of vertex cover for left and right sub-tree, and add 1 for the root.
Input and Output
Input: A binary tree.Output: The vertex cover is 3.
Algorithm
vertexCover(root node)
In this problem, one binary tree will be formed, each node will hold the data and number of vertices covered by that node.
Input − The root of the binary tree.
Output − The number of vertices covered by root.
Begin if root is φ, then return 0 if root has no child, then return 0 if vCover(root) ≠ 0, then return vCover(root) withRoot := 1 + vertexCover(left(root)) + vertexCover(right(root)) withoutRoot := 0 if root has left child, then withoutRoot := withoutRoot + vertexCover(left(left(root))) + vertexCover(left(right(root))) if root has right child, then withoutRoot := withoutRoot + vertexCover(right(left(root))) + vertexCover(right(right(root))) return vCover(root) End
Example
#include <iostream>
#include <algorithm>
using namespace std;
struct node {
int data;
int vCover;
node *left, *right;
};
node *getNode(int data) {
node *newNode = new (node);
newNode->data = data;
newNode->vCover = 0; //set vertex cover to 0
newNode->left = NULL;
newNode->right = NULL;
return newNode; //newly created node
}
int vertexCover(node *root) {
if(root == NULL) //when tree is empty
return 0;
if(root->left == NULL && root->right == NULL) //when no other edge from root
return 0;
if(root->vCover != 0) //when vertex cover of this node is found, leave that node
return root->vCover;
int sizeWithRoot = 1 + vertexCover(root->left) + vertexCover(root->right);
int sizeWithOutRoot = 0;
if(root->left != NULL) //when root is not included and go for left child
sizeWithOutRoot += 1 + vertexCover(root->left->left) + vertexCover(root->left->right);
if(root->right != NULL) //when root is not included and go for right child
sizeWithOutRoot += 1 + vertexCover(root->right->left) + vertexCover(root->right->right);
root->vCover = (sizeWithRoot < sizeWithOutRoot)?sizeWithRoot:sizeWithOutRoot; //minimum vertex cover
return root->vCover;
}
int main() {
//create tree to check vertex cover
node *root = getNode(20);
root->left = getNode(8); root->right = getNode(22);
root->left->left = getNode(4); root->left->right = getNode(12);
root->left->right->left = getNode(10); root->left->right->right = getNode(14);
root->right->right = getNode(25);
cout << "Minimal vertex cover: " << vertexCover(root);
}Output
Minimal vertex cover: 3
Updated on: 17-Jun-2020
1K+ Views
Advertisements