# Program to find the number of region in Planar Graph

• Difficulty Level : Basic
• Last Updated : 07 Jun, 2022

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 ``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

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## Javascript

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Output:

`4`

Time Complexity: O(1)

Auxiliary Space: O(1)

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