# 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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

 ` `

Output:

```4
```

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Improved By : AnkitRai01, jit_t, Code_Mech