# Sum of dependencies in a graph

• Difficulty Level : Basic
• Last Updated : 08 Jul, 2022

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.

Implementation:

## 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``;` `          ``@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

 `# 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#

 `// 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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