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++ 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 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 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# 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 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 ?> |
<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> |
4
Time Complexity: O(1)
Auxiliary Space: O(1)