检查有向图顶点中的传入边是否等于顶点本身

给定一个有V个顶点和E 个边的有向图 G(V, E) ，任务是检查给定图的所有顶点，顶点中的传入边是否等于顶点本身。
例子：

Input: 
 

Output: Yes 
Explanation: 
For vertex 0 there are 0 incoming edges, for vertex 1 there is 1 incoming edge. Same for vertex 2 nd 3. 
 

方法：思想是遍历每个顶点的邻接表，并增加每个顶点的边数，该顶点的边数来自 i。对每个顶点重复这些步骤，然后检查所有顶点是否等于顶点值的度数。
下面是上述方法的实现：

C++

// C++ implementation to check if the
// incoming edges in a vertex of directed
// graph is equal to the vertex itself or not
 
#include 
using namespace std;
 
// A utility function to
// add an edge in an
// directed graph
void add_edge(vector adj[],
              int x, int y)
{
    adj[x].push_back(y);
}
 
// Function to check that given graph
// in-degree value equal to vertex value
bool Indegree(vector adj[], int v)
{
    // Create array indeg
    // intialized to zero
    int indeg[v] = { 0 };
 
    // Traversing across all
    // vertex to compute
    // in degree value
    for (int i = 0; i < v; i++) {
        for (int j = 0; j < adj[i].size(); j++) {
            indeg[adj[i][j]]++;
        }
    }
 
    // check in degree value
    // equal to vertex value
    for (int i = 0; i < v; i++) {
        if (i == indeg[i])
            continue;
        else
            return false;
    }
    return true;
}
 
// Driver code
int main()
{
 
    int v = 4;
 
    // To store adjacency list of graph
    vector adj[v];
    add_edge(adj, 0, 1);
    add_edge(adj, 1, 2);
    add_edge(adj, 0, 2);
    add_edge(adj, 0, 3);
    add_edge(adj, 1, 3);
    add_edge(adj, 2, 3);
 
    if (Indegree(adj, v))
        cout << "Yes";
 
    else
        cout << "No";
}

Java

// Java implementation to check if the
// incoming edges in a vertex of directed
// graph is equal to the vertex itself or not
import java.util.*;
 
class GFG{
 
// A utility function to
// add an edge in an
// directed graph
static void add_edge(Vector adj[],
                     int x, int y)
{
    adj[x].add(y);
}
 
// Function to check that given graph
// in-degree value equal to vertex value
static boolean Indegree(Vector adj[],
                        int v)
{
     
    // Create array indeg
    // intialized to zero
    int indeg[] = new int[v];
 
    // Traversing across all
    // vertex to compute
    // in degree value
    for(int i = 0; i < v; i++)
    {
        for(int j = 0; j < adj[i].size(); j++)
        {
            indeg[adj[i].get(j)]++;
        }
    }
 
    // Check in degree value
    // equal to vertex value
    for(int i = 0; i < v; i++)
    {
        if (i == indeg[i])
            continue;
        else
            return false;
    }
    return true;
}
 
// Driver code
public static void main(String[] args)
{
 
    int v = 4;
 
    // To store adjacency list of graph
    @SuppressWarnings("unchecked")
    Vector []adj = new Vector[v];
    for(int i = 0; i < adj.length; i++)
        adj[i] = new Vector();
         
    add_edge(adj, 0, 1);
    add_edge(adj, 1, 2);
    add_edge(adj, 0, 2);
    add_edge(adj, 0, 3);
    add_edge(adj, 1, 3);
    add_edge(adj, 2, 3);
 
    if (Indegree(adj, v))
        System.out.print("Yes");
    else
        System.out.print("No");
}
}
 
// This code is contributed by Amit Katiyar

Python3

# Python3 implementation to check if the
# incoming edges in a vertex of directed
# graph is equal to the vertex itself or not
 
# A utility function to
# add an edge in an
# directed graph
def add_edge(adj, x, y):
     
    adj[x] = adj[x] + [y]
 
# Function to check that given graph
# in-degree value equal to vertex value
def Indegree(adj, v):
 
    # Create array indeg
    # intialized to zero
    indeg = [0] * v
 
    # Traversing across all
    # vertex to compute
    # in degree value
    for i in range(v):
        for j in range(len(adj[i])):
            indeg[adj[i][j]] += 1
 
    # Check in degree value
    # equal to vertex value
    for i in range(v):
        if(i == indeg[i]):
            continue
        else:
            return False
 
    return True
 
# Driver code
if __name__ == '__main__':
 
    v = 4
 
    # To store adjacency list of graph
    adj = [[]] * 4
    add_edge(adj, 0, 1)
    add_edge(adj, 1, 2)
    add_edge(adj, 0, 2)
    add_edge(adj, 0, 3)
    add_edge(adj, 1, 3)
    add_edge(adj, 2, 3)
 
    if(Indegree(adj, v)):
        print("Yes")
    else:
        print("No")
 
# This code is contributed by Shivam Singh

C#

// C# implementation to check if the
// incoming edges in a vertex of directed
// graph is equal to the vertex itself or not
using System;
using System.Collections.Generic;
 
class GFG{
 
// A utility function to
// add an edge in an
// directed graph
static void add_edge(List []adj,
                     int x, int y)
{
    adj[x].Add(y);
}
 
// Function to check that given graph
// in-degree value equal to vertex value
static bool Indegree(List []adj,
                          int v)
{
     
    // Create array indeg
    // intialized to zero
    int []indeg = new int[v];
 
    // Traversing across all
    // vertex to compute
    // in degree value
    for(int i = 0; i < v; i++)
    {
        for(int j = 0; j < adj[i].Count; j++)
        {
            indeg[adj[i][j]]++;
        }
    }
 
    // Check in degree value
    // equal to vertex value
    for(int i = 0; i < v; i++)
    {
        if (i == indeg[i])
            continue;
        else
            return false;
    }
    return true;
}
 
// Driver code
public static void Main(String[] args)
{
 
    int v = 4;
 
    // To store adjacency list of graph
    List []adj = new List[v];
    for(int i = 0; i < adj.Length; i++)
        adj[i] = new List();
         
    add_edge(adj, 0, 1);
    add_edge(adj, 1, 2);
    add_edge(adj, 0, 2);
    add_edge(adj, 0, 3);
    add_edge(adj, 1, 3);
    add_edge(adj, 2, 3);
 
    if (Indegree(adj, v))
        Console.Write("Yes");
    else
        Console.Write("No");
}
}
 
// This code is contributed by Amit Katiyar

Javascript

 
 
// JavaScript implementation to check if the
// incoming edges in a vertex of directed
// graph is equal to the vertex itself or not
 
// A utility function to
// add an edge in an
// directed graph
function add_edge(adj, x, y)
{
    adj[x].push(y);
}
 
// Function to check that given graph
// in-degree value equal to vertex value
function Indegree(adj, v)
{
    // Create array indeg
    // intialized to zero
    var indeg = Array(v).fill(0);
 
    // Traversing across all
    // vertex to compute
    // in degree value
    for (var i = 0; i < v; i++) {
        for (var j = 0; j < adj[i].length; j++) {
            indeg[adj[i][j]]++;
        }
    }
 
    // check in degree value
    // equal to vertex value
    for (var i = 0; i < v; i++) {
        if (i == indeg[i])
            continue;
        else
            return false;
    }
    return true;
}
 
// Driver code
var v = 4;
 
// To store adjacency list of graph
var adj = Array.from(Array(v), ()=> new Array());
add_edge(adj, 0, 1);
add_edge(adj, 1, 2);
add_edge(adj, 0, 2);
add_edge(adj, 0, 3);
add_edge(adj, 1, 3);
add_edge(adj, 2, 3);
if (Indegree(adj, v))
    document.write( "Yes");
else
    document.write( "No");
 

输出：

Yes

时间复杂度： O(V + E)
辅助空间复杂度： O(V)

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