Sum of dependencies in a graph

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++ 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;
}

Output:

Sum of dependencies is 4

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

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