# Count the number of nodes at a given level in a tree using DFS

Given an integer l and a tree represented as an undirected graph rooted at vertex 0. The task is to print the number of nodes present at level l.

Examples:

Input: l = 2 Output: 4

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

We have already discussed the BFS approach, in this post we will solve it using DFS.

Approach: The idea is to traverse the graph in a DFS manner. Take two variables, count and curr_level. Whenever the curr_level = l increment the value of the count.

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Class to represent a graph ` `class` `Graph { ` ` `  `    ``// No. of vertices ` `    ``int` `V; ` ` `  `    ``// Pointer to an array containing ` `    ``// adjacency lists ` `    ``list<``int``>* adj; ` ` `  `    ``// A function used by NumOfNodes ` `    ``void` `DFS(vector<``bool``>& visited, ``int` `src, ``int``& curr_level, ` `             ``int` `level, ``int``& NumberOfNodes); ` ` `  `public``: ` `    ``// Constructor ` `    ``Graph(``int` `V); ` ` `  `    ``// Function to add an edge to graph ` `    ``void` `addEdge(``int` `src, ``int` `des); ` ` `  `    ``// Returns the no. of nodes ` `    ``int` `NumOfNodes(``int` `level); ` `}; ` ` `  `Graph::Graph(``int` `V) ` `{ ` `    ``this``->V = V; ` `    ``adj = ``new` `list<``int``>[V]; ` `} ` ` `  `void` `Graph::addEdge(``int` `src, ``int` `des) ` `{ ` `    ``adj[src].push_back(des); ` `    ``adj[des].push_back(src); ` `} ` ` `  `// DFS function to keep track of ` `// number of nodes ` `void` `Graph::DFS(vector<``bool``>& visited, ``int` `src, ``int``& curr_level, ` `                ``int` `level, ``int``& NumberOfNodes) ` `{ ` `    ``// Mark the current vertex as visited ` `    ``visited[src] = ``true``; ` ` `  `    ``// If current level is equal ` `    ``// to the given level, increment ` `    ``// the no. of nodes ` `    ``if` `(level == curr_level) { ` `        ``NumberOfNodes++; ` `    ``} ` `    ``else` `if` `(level < curr_level) ` `        ``return``; ` `    ``else` `{ ` `        ``list<``int``>::iterator i; ` ` `  `        ``// Recur for the vertices ` `        ``// adjacent to the current vertex ` `        ``for` `(i = adj[src].begin(); i != adj[src].end(); i++) { ` `            ``if` `(!visited[*i]) { ` `                ``curr_level++; ` `                ``DFS(visited, *i, curr_level, level, NumberOfNodes); ` `            ``} ` `        ``} ` `    ``} ` `    ``curr_level--; ` `} ` ` `  `// Function to return the number of nodes ` `int` `Graph::NumOfNodes(``int` `level) ` `{ ` `    ``// To keep track of current level ` `    ``int` `curr_level = 0; ` ` `  `    ``// For keeping track of visited ` `    ``// nodes in DFS ` `    ``vector<``bool``> visited(V, ``false``); ` ` `  `    ``// To store count of nodes at a ` `    ``// given level ` `    ``int` `NumberOfNodes = 0; ` ` `  `    ``DFS(visited, 0, curr_level, level, NumberOfNodes); ` ` `  `    ``return` `NumberOfNodes; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `V = 8; ` ` `  `    ``Graph g(8); ` `    ``g.addEdge(0, 1); ` `    ``g.addEdge(0, 4); ` `    ``g.addEdge(0, 7); ` `    ``g.addEdge(4, 6); ` `    ``g.addEdge(4, 5); ` `    ``g.addEdge(4, 2); ` `    ``g.addEdge(7, 3); ` ` `  `    ``int` `level = 2; ` ` `  `    ``cout << g.NumOfNodes(level); ` ` `  `    ``return` `0; ` `} `

Output:

```4
```

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