# 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:

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;` `}`

 `# Python3 implementation of the approach` ` `  `# Class to represent a graph` `class` `Graph:` `    `  `    ``def` `__init__(``self``, V):` `        `  `        ``# No. of vertices` `        ``self``.V ``=` `V` `        `  `        ``# Pointer to an array containing` `        ``# adjacency lists` `        ``self``.adj ``=` `[[] ``for` `i ``in` `range``(``self``.V)]` `        `  `    ``def` `addEdge(``self``, src, des):` `        `  `        ``self``.adj[src].append(des)` `        ``self``.adj[des].append(src)` `        `  `    ``# DFS function to keep track of` `    ``# number of nodes` `    ``def` `DFS(``self``, visited, src, curr_level, ` `            ``level, 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 ``+``=` `1` `    `  `        ``elif` `(level < curr_level):` `            ``return` `        ``else``:` `            `  `            ``# Recur for the vertices` `            ``# adjacent to the current vertex` `            ``for` `i ``in` `self``.adj[src]:` `        `  `                ``if` `(``not` `visited[i]):` `                    ``curr_level ``+``=` `1` `                    ``curr_level, NumberOfNodes ``=` `self``.DFS(` `                        ``visited, i, curr_level, ` `                        ``level, NumberOfNodes)` `    `  `        ``curr_level ``-``=` `1` `        `  `        ``return` `curr_level, NumberOfNodes`   `    ``# Function to return the number of nodes` `    ``def` `NumOfNodes(``self``, level):`   `        ``# To keep track of current level` `        ``curr_level ``=` `0` ` `  `        ``# For keeping track of visited` `        ``# nodes in DFS` `        ``visited ``=` `[``False` `for` `i ``in` `range``(``self``.V)]` `    `  `        ``# To store count of nodes at a` `        ``# given level` `        ``NumberOfNodes ``=` `0` ` `  `        ``curr_level, NumberOfNodes ``=` `self``.DFS(` `            ``visited, ``0``, curr_level, ` `            ``level, NumberOfNodes)` ` `  `        ``return` `NumberOfNodes`   `# Driver code` `if` `__name__``=``=``'__main__'``:`   `    ``V ``=` `8` ` `  `    ``g ``=` `Graph(``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``)` ` `  `    ``level ``=` `2` ` `  `    ``print``(g.NumOfNodes(level))` ` `  `# This code is contributed by pratham76`

Output:
`4`

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