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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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PHP

Output:

4


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Improved By : AnkitRai01, jit_t, Code_Mech