# 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

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 ` `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 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``; ` `          ``@SuppressWarnings``(``"unchecked"``) ` `        ``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 `

 `# Python3 program to find the sum  ` `# of dependencies ` ` `  `# To add an edge ` `def` `addEdge(adj, u, v): ` ` `  `    ``adj[u].append(v) ` ` `  `# Find the sum of all dependencies ` `def` `findSum(adj, V): ` `     `  `    ``sum` `=` `0` `     `  `    ``# Just find the size at each  ` `    ``# vector's index ` `    ``for` `u ``in` `range``(V): ` `        ``sum` `+``=` `len``(adj[u]) ` `         `  `    ``return` `sum` ` `  `# Driver code ` `if` `__name__``=``=``'__main__'``: ` ` `  `    ``V ``=` `4` `    ``adj ``=` `[[] ``for` `i ``in` `range``(V)] ` `     `  `    ``addEdge(adj, ``0``, ``2``) ` `    ``addEdge(adj, ``0``, ``3``) ` `    ``addEdge(adj, ``1``, ``3``) ` `    ``addEdge(adj, ``2``, ``3``) ` `     `  `    ``print``(``"Sum of dependencies is"``, ` `          ``findSum(adj, V)) ` `     `  `# This code is contributed by rutvik_56`

 `// C# program to find the sum of dependencies ` `using` `System; ` `using` `System.Collections; ` ` `  `class` `GFG{ ` `     `  `// To add an edge ` `static` `void` `addEdge(ArrayList []adj, ``int` `u, ` `                                     ``int` `v) ` `{ ` `    ``adj[u].Add(v); ` `} ` ` `  `// Find the sum of all dependencies ` `static` `int` `findSum(ArrayList []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].Count; ` `  `  `    ``return` `sum; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(``string``[] args)  ` `{ ` `    ``int` `V = 4; ` `       `  `    ``ArrayList []adj = ``new` `ArrayList[V]; ` `     `  `    ``for``(``int` `i = 0; i < V; i++) ` `    ``{ ` `        ``adj[i] = ``new` `ArrayList(); ` `    ``} ` `     `  `    ``addEdge(adj, 0, 2); ` `    ``addEdge(adj, 0, 3); ` `    ``addEdge(adj, 1, 3); ` `    ``addEdge(adj, 2, 3); ` `  `  `    ``Console.Write(``"Sum of dependencies is "` `+ ` `                  ``findSum(adj, V)); ` `} ` `} ` ` `  `// This code is contributed by pratham76`

Output:

`Sum of dependencies is 4`

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

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Improved By : rutvik_56, pratham76

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