Program to Calculate the Edge Cover of a Graph

Given the number of vertices N of a graph. The task is to determine the Edge cover.

Edge Cover: Minimum number of edge required to cover all vertex is known as Edge Cover.

Examples:

Input : N = 5
Output : 3

Input : N = 4
Output : 2

Example 1: For N = 5 vertices,

Edge Cover is: 3 (Choosing the edges marked in Red, all of the vertices will get covered)

Example 2: For N = 8 vertices,

Edge Cover is: 4 (Choosing the edges marked in Red, all of the vertices will get covered)

Formula:

Edge Cover = ceil (no. of vertices / 2)

Below is the implementation of the above approach:

C++

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// C++ program to find Edge Cover
#include <bits/stdc++.h>
using namespace std;
  
// Function that calculates Edge Cover
int edgeCover(int n)
{
    float result = 0;
  
    result = ceil(n / 2.0);
  
    return result;
}
  
// Driver Code
int main()
{
    int n = 5;
  
    cout << edgeCover(n);
  
    return 0;
}

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Java

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// Java program to find Edge Cover
import java.util.*;
import java.lang.*;
import java.io.*;
  
class GFG{
// Function that calculates Edge Cover
static int edgeCover(int n)
{
    int result = 0;
   
    result = (int)Math.ceil((double)n / 2.0);
   
    return result;
}
   
// Driver Code
public static void main(String args[])
{
    int n = 5;
   
    System.out.print(edgeCover(n));
}
  
}

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Python3

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# Python 3 implementation of the above approach.
  
import math
  
# Function that calculates Edge Cover 
def edgeCover(n):
      
    result = 0
      
    result = math.ceil(n / 2.0)
      
    return result
      
      
# Driver code      
if __name__ == "__main__"
    
    n =  5
    
    print(int(edgeCover(n)))
  
# this code is contributed by Naman_Garg

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C#

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// C# program to find Edge Cover
using System;
  
class GFG
{
// Function that calculates Edge Cover
static int edgeCover(int n)
{
    int result = 0;
  
    result = (int)Math.Ceiling((double)n / 2.0);
  
    return result;
}
  
// Driver Code
static public void Main ()
{
    int n = 5;
      
    Console.Write(edgeCover(n));
}
}
  
// This code is contributed by Raj

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PHP

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<?php
// PHP program to find Edge Cover
  
// Function that calculates
// Edge Cover
function edgeCover($n)
{
    $result = 0;
  
    $result = ceil($n / 2.0);
  
    return $result;
}
  
// Driver Code
$n = 5;
  
echo edgeCover($n);
  
// This code is contributed by Raj
?>

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Output:

3


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