计算无向图中的边数

给定一个邻接表表示无向图。编写一个函数来计算无向图中的边数。

预期时间复杂度：O(V)

例子：

输入：下图的邻接表表示。输出：9

想法基于握手引理。握手引理是关于无向图的。在每个有限无向图中，奇数度的顶点数总是偶数。握手引理是度数和公式的结果（有时也称为握手引理）

所以我们遍历所有的顶点，计算它们的邻接表大小的总和，最后返回 sum/2。下面实现上述想法

C++

// C++ program to count number of edge in
// undirected graph
#include
using namespace std;
  
// Adjacency list representation of graph
class Graph
{
    int V ;
    list < int > *adj;
public :
    Graph( int V )
    {
        this->V = V ;
        adj = new list[V];
    }
    void addEdge ( int u, int v ) ;
    int countEdges () ;
};
  
// add edge to graph
void Graph :: addEdge ( int u, int v )
{
    adj[u].push_back(v);
    adj[v].push_back(u);
}
  
// Returns count of edge in undirected graph
int Graph :: countEdges()
{
    int sum = 0;
  
    //traverse all vertex
    for (int i = 0 ; i < V ; i++)
  
        // add all edge that are linked to the
        // current vertex
        sum += adj[i].size();
  
  
    // The count of edge is always even because in
    // undirected graph every edge is connected
    // twice between two vertices
    return sum/2;
}
  
// driver program to check above function
int main()
{
    int V = 9 ;
    Graph g(V);
  
    // making above shown graph
    g.addEdge(0, 1 );
    g.addEdge(0, 7 );
    g.addEdge(1, 2 );
    g.addEdge(1, 7 );
    g.addEdge(2, 3 );
    g.addEdge(2, 8 );
    g.addEdge(2, 5 );
    g.addEdge(3, 4 );
    g.addEdge(3, 5 );
    g.addEdge(4, 5 );
    g.addEdge(5, 6 );
    g.addEdge(6, 7 );
    g.addEdge(6, 8 );
    g.addEdge(7, 8 );
  
    cout << g.countEdges() << endl;
  
    return 0;
}

Java

// Java program to count number of edge in 
// undirected graph
import java.io.*;
import java.util.*;
  
// Adjacency list representation of graph
class Graph 
{
    int V;
    Vector[] adj;
  
    //@SuppressWarnings("unchecked")
    Graph(int V)
    {
        this.V = V;
        this.adj = new Vector[V];
  
        for (int i = 0; i < V; i++)
            adj[i] = new Vector();
    }
  
    // add edge to graph
    void addEdge(int u, int v)
    {
        adj[u].add(v);
        adj[v].add(u);
    }
  
    // Returns count of edge in undirected graph
    int countEdges()
    {
        int sum = 0;
  
        // traverse all vertex
        for (int i = 0; i < V; i++)
  
            // add all edge that are linked to the
            // current vertex
            sum += adj[i].size();
  
        // The count of edge is always even because in
        // undirected graph every edge is connected
        // twice between two vertices
        return sum / 2;
    }
}
  
class GFG 
{
  
    // Driver Code
    public static void main(String[] args) throws IOException 
    {
        int V = 9;
        Graph g = new Graph(V);
  
        // making above shown graph
        g.addEdge(0, 1);
        g.addEdge(0, 7);
        g.addEdge(1, 2);
        g.addEdge(1, 7);
        g.addEdge(2, 3);
        g.addEdge(2, 8);
        g.addEdge(2, 5);
        g.addEdge(3, 4);
        g.addEdge(3, 5);
        g.addEdge(4, 5);
        g.addEdge(5, 6);
        g.addEdge(6, 7);
        g.addEdge(6, 8);
        g.addEdge(7, 8);
  
        System.out.println(g.countEdges());
    }
}
  
// This code is contributed by
// sanjeev2552

Python3

# Python3 program to count number of 
# edge in undirected graph 
  
# Adjacency list representation of graph 
class Graph:
    def __init__(self, V):
        self.V = V 
        self.adj = [[] for i in range(V)]
  
    # add edge to graph 
    def addEdge (self, u, v ):
        self.adj[u].append(v) 
        self.adj[v].append(u)
      
    # Returns count of edge in undirected graph 
    def countEdges(self):
        Sum = 0
      
        # traverse all vertex 
        for i in range(self.V):
      
            # add all edge that are linked 
            # to the current vertex 
            Sum += len(self.adj[i]) 
      
        # The count of edge is always even  
        # because in undirected graph every edge  
        # is connected twice between two vertices 
        return Sum // 2
  
# Driver Code
if __name__ == '__main__':
      
    V = 9
    g = Graph(V) 
  
    # making above shown graph 
    g.addEdge(0, 1 ) 
    g.addEdge(0, 7 ) 
    g.addEdge(1, 2 ) 
    g.addEdge(1, 7 ) 
    g.addEdge(2, 3 ) 
    g.addEdge(2, 8 ) 
    g.addEdge(2, 5 ) 
    g.addEdge(3, 4 ) 
    g.addEdge(3, 5 ) 
    g.addEdge(4, 5 ) 
    g.addEdge(5, 6 ) 
    g.addEdge(6, 7 ) 
    g.addEdge(6, 8 ) 
    g.addEdge(7, 8 ) 
  
    print(g.countEdges())
  
# This code is contributed by PranchalK

C#

// C# program to count number of edge in 
// undirected graph
using System;
using System.Collections.Generic;
  
// Adjacency list representation of graph
class Graph 
{
    public int V;
    public List[] adj;
    public Graph(int V)
    {
        this.V = V;
        this.adj = new List[V];
  
        for (int i = 0; i < V; i++)
            adj[i] = new List();
    }
  
    // add edge to graph
    public void addEdge(int u, int v)
    {
        adj[u].Add(v);
        adj[v].Add(u);
    }
  
    // Returns count of edge in undirected graph
    public int countEdges()
    {
        int sum = 0;
  
        // traverse all vertex
        for (int i = 0; i < V; i++)
  
            // add all edge that are linked to the
            // current vertex
            sum += adj[i].Count;
  
        // The count of edge is always even because in
        // undirected graph every edge is connected
        // twice between two vertices
        return sum / 2;
    }
}
  
class GFG 
{
  
    // Driver Code
    public static void Main(String[] args)
    {
        int V = 9;
        Graph g = new Graph(V);
  
        // making above shown graph
        g.addEdge(0, 1);
        g.addEdge(0, 7);
        g.addEdge(1, 2);
        g.addEdge(1, 7);
        g.addEdge(2, 3);
        g.addEdge(2, 8);
        g.addEdge(2, 5);
        g.addEdge(3, 4);
        g.addEdge(3, 5);
        g.addEdge(4, 5);
        g.addEdge(5, 6);
        g.addEdge(6, 7);
        g.addEdge(6, 8);
        g.addEdge(7, 8);
  
        Console.WriteLine(g.countEdges());
    }
}
  
// This code is contributed by PrinciRaj1992

输出：

时间复杂度： O(V)