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++
// 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
// 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
# 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#
// 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 |
Javascript
<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> |
Output:
Yes
Time Complexity: O(V + E)
Auxiliary Space Complexity: O(V)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
