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

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++

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// 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 graph
void 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 value
bool Indegree(vector<int> 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<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";
}

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Python3

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# 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

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Output:

Yes

Time Complexity: O(V + E)
Auxiliary Space Complexity: O(V)

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