Sum of dependencies in a graph

1.2

Given a directed and connected graph with n nodes. If there is an edge from u to v then u depends on v. Our task was to find out the sum of dependencies for every node.

Example:
For the graph in diagram,
A depends on C and D i.e. 2
B depends on D i.e. 1
C depends on D i.e. 1
And D depends on none.
Hence answer -> 0 + 1 + 1 + 2 = 4

Asked in : Flipkart Interview

Idea is to check adjacency list and find how many edges are there from each vertex and return the total number of edges.

C++

// C++ program to find the sum of dependencies
#include <bits/stdc++.h>
using namespace std;

// To add an edge
void addEdge(vector <int> adj[], int u,int v)
{
    adj[u].push_back(v);
}

// find the sum of all dependencies
int findSum(vector<int> adj[], int V)
{
    int sum = 0;

    // just find the size at each vector's index
    for (int u = 0; u < V; u++)
        sum += adj[u].size();

    return sum;
}

// Driver code
int main()
{
    int V = 4;
    vector<int >adj[V];
    addEdge(adj, 0, 2);
    addEdge(adj, 0, 3);
    addEdge(adj, 1, 3);
    addEdge(adj, 2, 3);

    cout << "Sum of dependencies is "
         << findSum(adj, V);
    return 0;
}

Java

// Java program to find the sum of dependencies

import java.util.Vector;

class Test
{
	// To add an edge
	static void addEdge(Vector <Integer> adj[], int u,int v)
	{
	    adj[u].addElement((v));
	}
	
	// find the sum of all dependencies
	static int findSum(Vector<Integer> adj[], int V)
	{
	    int sum = 0;
	 
	    // just find the size at each vector's index
	    for (int u = 0; u < V; u++)
	        sum += adj[u].size();
	 
	    return sum;
	}
	
    // Driver method
    public static void main(String[] args) 
    {
    	int V = 4;
        Vector<Integer> adj[] = new Vector[V];
        
        for (int i = 0; i < adj.length; i++) {
			adj[i] = new Vector<>();
		}
        
        addEdge(adj, 0, 2);
        addEdge(adj, 0, 3);
        addEdge(adj, 1, 3);
        addEdge(adj, 2, 3);
     
        System.out.println("Sum of dependencies is " +
                            findSum(adj, V));
    }
}
// This code is contributed by Gaurav Miglani


Output:

Sum of dependencies is 4

Time complexity : O(V) where V is number of vertices in graph.

This article is contributed by Sahil Chhabra (akku). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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