Program to find the number of region in Planar Graph

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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:

Time Complexity: O(1)

Auxiliary Space: O(1)

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