# 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 = 5Output:R = 3

Input:V = 3, E = 3Output: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

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