程序在平面图中查找区域数

给定两个整数V和E ，它们表示平面图的顶点和边的数量。任务是找到该平面图的区域数。

平面图：平面图是指没有边彼此相交的图，或者可以在没有边相交的情况下在平面上绘制的图称为平面图。

区域：绘制没有边缘相交的平面图时，图的边缘和顶点会将平面划分为多个区域。

例子：

Input: V = 4, E = 5 
Output: R = 3 
 

Input: V = 3, E = 3 
Output: R = 2 
 

方法：欧拉发现平面图中的区域数量是顶点数量和图中边数的函数，即

下面是上述方法的实现：

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

Javascript

 
// 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
 

输出：

4