# 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 C i.e. 1
D depends on C i.e. 1
And C depends on none.
Hence answer -> 0 + 1 + 1 + 2 = 4

## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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 ` `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 adj[], ``int` `u,``int` `v) ` `    ``{ ` `        ``adj[u].addElement((v)); ` `    ``} ` `     `  `    ``// find the sum of all dependencies ` `    ``static` `int` `findSum(Vector 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 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.

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