Program to find the number of region in Planar Graph

Given two integers V and E which represent the number of Vertices and Edges of a Planar Graph. The Task is to find the number of regions of that planar graph.

Planar Graph: A planar graph is one in which no edges cross each other or a graph that can be drawn on a plane without edges crossing is called planar graph.

Region: When a planar graph is drawn without edges crossing, the edges and vertices of the graph divide the plane into regions.

Examples:

Input: V = 4, E = 5 
Output: R = 3 

Input: V = 3, E = 3 
Output: R = 2 

Approach: Euler found out the number of regions in a planar graph as a function of the number of vertices and number of edges in the graph i.e. 

Below is the implementation of the above approach: 

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function to return the number
// of regions in a Planar Graph
int Regions(int Vertices, int Edges)
{
    int R = Edges + 2 - Vertices;

    return R;
}

// Driver code
int main()
{
    int V = 5, E = 7;

    cout << Regions(V, E);

    return 0;
}

Java

// Java implementation of the approach
import java.io.*;

class GFG {

    // Function to return the number
    // of regions in a Planar Graph
    static int Regions(int Vertices, int Edges)
    {
        int R = Edges + 2 - Vertices;

        return R;
    }

    // Driver code
    public static void main(String[] args)
    {

        int V = 5, E = 7;
        System.out.println(Regions(V, E));
    }
}

// This code is contributed by akt_mit

Python3

# Python3 implementation of the approach

# Function to return the number
# of regions in a Planar Graph
def Regions(Vertices, Edges) :

    R = Edges + 2 - Vertices;

    return R;

# Driver code
if __name__ == "__main__" :

    V = 5; E = 7;

    print(Regions(V, E));

# This code is contributed
# by AnkitRai01

C#

// C# implementation of the approach
using System;

class GFG {

    // Function to return the number
    // of regions in a Planar Graph
    static int Regions(int Vertices, int Edges)
    {
        int R = Edges + 2 - Vertices;

        return R;
    }

    // Driver code
    static public void Main()
    {

        int V = 5, E = 7;
        Console.WriteLine(Regions(V, E));
    }
}

// This code is contributed by ajit

PHP

<?php
// PHP implementation of the approach

// Function to return the number
// of regions in a Planar Graph
function Regions($Vertices, $Edges)
{
    $R = $Edges + 2 - $Vertices;

    return $R;
}

// Driver code
$V = 5; $E = 7;
echo(Regions($V, $E));

// This code is contributed
// by Code_Mech
?>

Javascript

<script>

// Javascript implementation of the approach

// Function to return the number
// of regions in a Planar Graph
function Regions(Vertices, Edges)
{
    var R = Edges + 2 - Vertices;

    return R;
}

// Driver code
var V = 5, E = 7;

document.write( Regions(V, E));

// This code is contributed by itsok

</script>

Output:

4

Time Complexity: O(1)

Auxiliary Space: O(1)