Check if incoming edges in a vertex of directed graph is equal to vertex itself or not - GeeksforGeeks

09 Sep, 2021
Given a directed Graph G(V, E) with V vertices and E edges, the task is to check that for all vertices of the given graph, the incoming edges in a vertex is equal to the vertex itself or not.
Examples: 
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.  
Approach: The idea is to traverse adjacency list for every vertex, and increment the count of edges of every vertex that has an incoming edge from i. Repeat the steps for every vertex and then check the in degrees for all the vertices equal to vertex value or not.
Below is the implementation of the above approach: 
C++
Java
Python3
C#
Javascript
// C++ implementation to check if the// incoming edges in a vertex of directed// graph is equal to the vertex itself or not #include <bits/stdc++.h>using namespace std; // A utility function to// add an edge in an// directed graphvoid add_edge(vector<int> adj[],              int x, int y){    adj[x].push_back(y);} // Function to check that given graph// in-degree value equal to vertex valuebool Indegree(vector<int> adj[], int v){    // Create array indeg    // initialized 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 codeint main(){     int v = 4;     // To store adjacency list of graph    vector<int> 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 implementation to check if the// incoming edges in a vertex of directed// graph is equal to the vertex itself or notimport java.util.*; class GFG{ // A utility function to// add an edge in an// directed graphstatic void add_edge(Vector<Integer> adj[],                     int x, int y){    adj[x].add(y);} // Function to check that given graph// in-degree value equal to vertex valuestatic boolean Indegree(Vector<Integer> adj[],                        int v){         // Create array indeg    // initialized 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 codepublic static void main(String[] args){     int v = 4;     // To store adjacency list of graph    @SuppressWarnings("unchecked")    Vector<Integer> []adj = new Vector[v];    for(int i = 0; i < adj.length; i++)        adj[i] = new Vector<Integer>();             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 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 graphdef add_edge(adj, x, y):         adj[x] = adj[x] + [y] # Function to check that given graph# in-degree value equal to vertex valuedef Indegree(adj, v):     # Create array indeg    # initialized 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 codeif __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# implementation to check if the// incoming edges in a vertex of directed// graph is equal to the vertex itself or notusing System;using System.Collections.Generic; class GFG{ // A utility function to// add an edge in an// directed graphstatic void add_edge(List<int> []adj,                     int x, int y){    adj[x].Add(y);} // Function to check that given graph// in-degree value equal to vertex valuestatic bool Indegree(List<int> []adj,                          int v){         // Create array indeg    // initialized 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 codepublic static void Main(String[] args){     int v = 4;     // To store adjacency list of graph    List<int> []adj = new List<int>[v];    for(int i = 0; i < adj.Length; i++)        adj[i] = new List<int>();             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
<script>  // 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 graphfunction add_edge(adj, x, y){    adj[x].push(y);} // Function to check that given graph// in-degree value equal to vertex valuefunction Indegree(adj, v){    // Create array indeg    // initialized 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 codevar v = 4; // To store adjacency list of graphvar 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"); </script>
Yes
 
Time Complexity: O(V + E) Auxiliary Space Complexity: O(V) 
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