# Level with maximum number of nodes using DFS in a N-ary tree

Given a N-ary tree, the task is to print the level with the maximum number of nodes.

Examples:

```Input : For example, consider the following tree
1               - Level 1
/     \
2       3           - Level 2
/   \       \
4     5       6        - Level 3
/  \     /
7    8   9         - Level 4

Output : Level-3 and Level-4
```

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

Approach:

• Insert all the connecting nodes to a 2-D vector tree.
• Run a DFS on the tree such that height[node] = 1 + height[parent]
• Once DFS traversal is completed, increase the count[] array by 1, for every node’s level.
• Iterate from first level to last level, and find the level with the maximum number of nodes.
• Re-traverse from first to last level, and print all the levels which have the same number of maximum nodes.

Below is the implementation of the above approach.

## C++

 `// C++ program to print the level ` `// with maximum number of nodes ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function for DFS in a tree ` `void` `dfs(``int` `node, ``int` `parent, ``int` `height[], ``int` `vis[], ` `         ``vector<``int``> tree[]) ` `{ ` `    ``// calculate the level of every node ` `    ``height[node] = 1 + height[parent]; ` ` `  `    ``// mark every node as visited ` `    ``vis[node] = 1; ` ` `  `    ``// iterate in the subtree ` `    ``for` `(``auto` `it : tree[node]) { ` ` `  `        ``// if the node is not visited ` `        ``if` `(!vis[it]) { ` ` `  `            ``// call the dfs function ` `            ``dfs(it, node, height, vis, tree); ` `        ``} ` `    ``} ` `} ` ` `  `// Function to insert edges ` `void` `insertEdges(``int` `x, ``int` `y, vector<``int``> tree[]) ` `{ ` `    ``tree[x].push_back(y); ` `    ``tree[y].push_back(x); ` `} ` ` `  `// Function to print all levels ` `void` `printLevelswithMaximumNodes(``int` `N, ``int` `vis[], ``int` `height[]) ` `{ ` `    ``int` `mark[N + 1]; ` `    ``memset``(mark, 0, ``sizeof` `mark); ` ` `  `    ``int` `maxLevel = 0; ` `    ``for` `(``int` `i = 1; i <= N; i++) { ` ` `  `        ``// count number of nodes ` `        ``// in every level ` `        ``if` `(vis[i]) ` `            ``mark[height[i]]++; ` ` `  `        ``// find the maximum height of tree ` `        ``maxLevel = max(height[i], maxLevel); ` `    ``} ` ` `  `    ``int` `maxi = 0; ` ` `  `    ``for` `(``int` `i = 1; i <= maxLevel; i++) { ` `        ``maxi = max(mark[i], maxi); ` `    ``} ` ` `  `    ``// print even number of nodes ` `    ``cout << ``"The levels with maximum number of nodes are: "``; ` `    ``for` `(``int` `i = 1; i <= maxLevel; i++) { ` `        ``if` `(mark[i] == maxi) ` `            ``cout << i << ``" "``; ` `    ``} ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``// Construct the tree ` ` `  `    ``/* 1  ` `     ``/  \  ` `    ``2    3  ` `    ``/ \   \  ` `   ``4   5   6  ` `      ``/ \  /  ` `     ``7   8 9  */` ` `  `    ``const` `int` `N = 9; ` ` `  `    ``vector<``int``> tree[N + 1]; ` ` `  `    ``insertEdges(1, 2, tree); ` `    ``insertEdges(1, 3, tree); ` `    ``insertEdges(2, 4, tree); ` `    ``insertEdges(2, 5, tree); ` `    ``insertEdges(5, 7, tree); ` `    ``insertEdges(5, 8, tree); ` `    ``insertEdges(3, 6, tree); ` `    ``insertEdges(6, 9, tree); ` ` `  `    ``int` `height[N + 1]; ` `    ``int` `vis[N + 1] = { 0 }; ` ` `  `    ``height = 0; ` ` `  `    ``// call the dfs function ` `    ``dfs(1, 0, height, vis, tree); ` ` `  `    ``// Function to print ` `    ``printLevelswithMaximumNodes(N, vis, height); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to print the level  ` `// with maximum number of nodes  ` `import` `java.util.*; ` ` `  `class` `GFG ` `{  ` `    ``static` `int` `N = ``9``; ` ` `  `// Function for DFS in a tree  ` `static` `void` `dfs(``int` `node, ``int` `parent, ``int` `height[], ``int` `vis[],  ` `        ``Vector tree[])  ` `{  ` `    ``// calculate the level of every node  ` `    ``height[node] = ``1` `+ height[parent];  ` ` `  `    ``// mark every node as visited  ` `    ``vis[node] = ``1``;  ` ` `  `    ``// iterate in the subtree  ` `    ``for` `(``int` `it : tree[node])  ` `    ``{  ` ` `  `        ``// if the node is not visited  ` `        ``if` `(vis[it] != ``1``)  ` `        ``{  ` ` `  `            ``// call the dfs function  ` `            ``dfs(it, node, height, vis, tree);  ` `        ``}  ` `    ``}  ` `}  ` ` `  `// Function to insert edges  ` `static` `void` `insertEdges(``int` `x, ``int` `y, Vector tree[])  ` `{  ` `    ``tree[x].add(y);  ` `    ``tree[y].add(x);  ` `}  ` ` `  `// Function to print all levels  ` `static` `void` `printLevelswithMaximumNodes(``int` `N, ``int` `vis[], ``int` `height[])  ` `{  ` `    ``int` `[]mark = ``new` `int``[N + ``1``];  ` ` `  `    ``int` `maxLevel = ``0``;  ` `    ``for` `(``int` `i = ``1``; i <= N; i++) {  ` ` `  `        ``// count number of nodes  ` `        ``// in every level  ` `        ``if` `(vis[i] == ``1``)  ` `            ``mark[height[i]]++;  ` ` `  `        ``// find the maximum height of tree  ` `        ``maxLevel = Math.max(height[i], maxLevel);  ` `    ``}  ` ` `  `    ``int` `maxi = ``0``;  ` ` `  `    ``for` `(``int` `i = ``1``; i <= maxLevel; i++)  ` `    ``{  ` `        ``maxi = Math.max(mark[i], maxi);  ` `    ``}  ` ` `  `    ``// print even number of nodes  ` `    ``System.out.print(``"The levels with maximum number of nodes are: "``);  ` `    ``for` `(``int` `i = ``1``; i <= maxLevel; i++) ` `    ``{  ` `        ``if` `(mark[i] == maxi)  ` `            ``System.out.print(i+ ``" "``);  ` `    ``}  ` `}  ` ` `  `// Driver Code  ` `public` `static` `void` `main(String[] args)  ` `{  ` `    ``// Conthe tree  ` ` `  `    ``/* 1  ` `    ``/ \  ` `    ``2 3  ` `    ``/ \ \  ` `4 5 6  ` `    ``/ \ /  ` `    ``7 8 9 */` ` `  `     `  ` `  `    ``Vector []tree = ``new` `Vector[N + ``1``];  ` `    ``for``(``int` `i= ``0``; i < N + ``1``; i++) ` `        ``tree[i] = ``new` `Vector(); ` `    ``insertEdges(``1``, ``2``, tree);  ` `    ``insertEdges(``1``, ``3``, tree);  ` `    ``insertEdges(``2``, ``4``, tree);  ` `    ``insertEdges(``2``, ``5``, tree);  ` `    ``insertEdges(``5``, ``7``, tree);  ` `    ``insertEdges(``5``, ``8``, tree);  ` `    ``insertEdges(``3``, ``6``, tree);  ` `    ``insertEdges(``6``, ``9``, tree);  ` ` `  `    ``int` `height[] = ``new` `int``[N + ``1``];  ` `    ``int` `vis[] = ``new` `int``[N + ``1``];  ` ` `  `    ``height[``0``] = ``0``;  ` ` `  `    ``// call the dfs function  ` `    ``dfs(``1``, ``0``, height, vis, tree);  ` ` `  `    ``// Function to print  ` `    ``printLevelswithMaximumNodes(N, vis, height);  ` ` `  `}  ` `}  ` ` `  `// This code is contributed by 29AjayKumar `

## Python3

 `# Python3 program to print the level  ` `# with the maximum number of nodes  ` ` `  `# Function for DFS in a tree  ` `def` `dfs(node, parent, height, vis, tree):  ` ` `  `    ``# calculate the level of every node  ` `    ``height[node] ``=` `1` `+` `height[parent]  ` ` `  `    ``# mark every node as visited  ` `    ``vis[node] ``=` `1` ` `  `    ``# iterate in the subtree  ` `    ``for` `it ``in` `tree[node]:  ` ` `  `        ``# if the node is not visited  ` `        ``if` `vis[it] ``=``=` `0``:  ` ` `  `            ``# call the dfs function  ` `            ``dfs(it, node, height, vis, tree)  ` `         `  `# Function to insert edges  ` `def` `insertEdges(x, y, tree):  ` ` `  `    ``tree[x].append(y)  ` `    ``tree[y].append(x)  ` ` `  `# Function to print all levels  ` `def` `printLevelswithMaximumNodes(N, vis, height):  ` ` `  `    ``mark ``=` `[``0``] ``*` `(N ``+` `1``)  ` ` `  `    ``maxLevel ``=` `0` `    ``for` `i ``in` `range` `(``1``, N ``+` `1``):  ` ` `  `        ``# count number of nodes  ` `        ``# in every level  ` `        ``if` `vis[i] ``=``=` `1``:  ` `            ``mark[height[i]] ``+``=` `1` ` `  `        ``# find the maximum height of tree  ` `        ``maxLevel ``=` `max``(height[i], maxLevel)  ` `     `  `    ``maxi ``=` `0` ` `  `    ``for` `i ``in` `range``(``1``, maxLevel ``+` `1``):  ` `        ``maxi ``=` `max``(mark[i], maxi)  ` `     `  `    ``# print even number of nodes  ` `    ``print``(``"The levels with maximum number"``,  ` `                ``"of nodes are:"``, end ``=` `" "``)  ` `    ``for` `i ``in` `range``(``1``, maxLevel ``+` `1``):  ` `        ``if` `mark[i] ``=``=` `maxi:  ` `            ``print``(i, end ``=` `" "``)  ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` `     `  `    ``# Construct the tree  ` `    ``N ``=` `9` ` `  `    ``# Create an empty 2-D list ` `    ``tree ``=` `[[] ``for` `i ``in` `range``(N ``+` `1``)] ` ` `  `    ``insertEdges(``1``, ``2``, tree)  ` `    ``insertEdges(``1``, ``3``, tree)  ` `    ``insertEdges(``2``, ``4``, tree)  ` `    ``insertEdges(``2``, ``5``, tree)  ` `    ``insertEdges(``5``, ``7``, tree)  ` `    ``insertEdges(``5``, ``8``, tree)  ` `    ``insertEdges(``3``, ``6``, tree)  ` `    ``insertEdges(``6``, ``9``, tree)  ` ` `  `    ``height ``=` `[``None``] ``*` `(N ``+` `1``)  ` `    ``vis ``=` `[``0``] ``*` `(N ``+` `1``)  ` ` `  `    ``height[``0``] ``=` `0` ` `  `    ``# call the dfs function  ` `    ``dfs(``1``, ``0``, height, vis, tree)  ` ` `  `    ``# Function to print  ` `    ``printLevelswithMaximumNodes(N, vis, height)  ` `     `  `# This code is contributed  ` `# by Rituraj Jain `

## C#

 `// C# program to print the level  ` `// with maximum number of nodes  ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `public` `class` `GFG ` `{  ` `    ``static` `int` `N = 9; ` `  `  `// Function for DFS in a tree  ` `static` `void` `dfs(``int` `node, ``int` `parent, ``int` `[]height, ``int` `[]vis,  ` `        ``List<``int``> []tree)  ` `{  ` `    ``// calculate the level of every node  ` `    ``height[node] = 1 + height[parent];  ` `  `  `    ``// mark every node as visited  ` `    ``vis[node] = 1;  ` `  `  `    ``// iterate in the subtree  ` `    ``foreach` `(``int` `it ``in` `tree[node])  ` `    ``{  ` `  `  `        ``// if the node is not visited  ` `        ``if` `(vis[it] != 1)  ` `        ``{  ` `  `  `            ``// call the dfs function  ` `            ``dfs(it, node, height, vis, tree);  ` `        ``}  ` `    ``}  ` `}  ` `  `  `// Function to insert edges  ` `static` `void` `insertEdges(``int` `x, ``int` `y, List<``int``> []tree)  ` `{  ` `    ``tree[x].Add(y);  ` `    ``tree[y].Add(x);  ` `}  ` `  `  `// Function to print all levels  ` `static` `void` `printLevelswithMaximumNodes(``int` `N, ``int` `[]vis, ``int` `[]height)  ` `{  ` `    ``int` `[]mark = ``new` `int``[N + 1];  ` `  `  `    ``int` `maxLevel = 0;  ` `    ``for` `(``int` `i = 1; i <= N; i++) {  ` `  `  `        ``// count number of nodes  ` `        ``// in every level  ` `        ``if` `(vis[i] == 1)  ` `            ``mark[height[i]]++;  ` `  `  `        ``// find the maximum height of tree  ` `        ``maxLevel = Math.Max(height[i], maxLevel);  ` `    ``}  ` `  `  `    ``int` `maxi = 0;  ` `  `  `    ``for` `(``int` `i = 1; i <= maxLevel; i++)  ` `    ``{  ` `        ``maxi = Math.Max(mark[i], maxi);  ` `    ``}  ` `  `  `    ``// print even number of nodes  ` `    ``Console.Write(``"The levels with maximum number of nodes are: "``);  ` `    ``for` `(``int` `i = 1; i <= maxLevel; i++) ` `    ``{  ` `        ``if` `(mark[i] == maxi)  ` `            ``Console.Write(i+ ``" "``);  ` `    ``}  ` `}  ` `  `  `// Driver Code  ` `public` `static` `void` `Main(String[] args)  ` `{  ` `    ``// Conthe tree  ` `  `  `    ``/* 1  ` `    ``/ \  ` `    ``2 3  ` `    ``/ \ \  ` `4 5 6  ` `    ``/ \ /  ` `    ``7 8 9 */` `  `  `      `  `  `  `    ``List<``int``> []tree = ``new` `List<``int``>[N + 1];  ` `    ``for``(``int` `i= 0; i < N + 1; i++) ` `        ``tree[i] = ``new` `List<``int``>(); ` `    ``insertEdges(1, 2, tree);  ` `    ``insertEdges(1, 3, tree);  ` `    ``insertEdges(2, 4, tree);  ` `    ``insertEdges(2, 5, tree);  ` `    ``insertEdges(5, 7, tree);  ` `    ``insertEdges(5, 8, tree);  ` `    ``insertEdges(3, 6, tree);  ` `    ``insertEdges(6, 9, tree);  ` `  `  `    ``int` `[]height = ``new` `int``[N + 1];  ` `    ``int` `[]vis = ``new` `int``[N + 1];  ` `  `  `    ``height = 0;  ` `  `  `    ``// call the dfs function  ` `    ``dfs(1, 0, height, vis, tree);  ` `  `  `    ``// Function to print  ` `    ``printLevelswithMaximumNodes(N, vis, height);  ` `  `  `}  ` `}  ` `  `  ` `  `// This code contributed by Rajput-Ji `

Output:

```The levels with maximum number of nodes are: 3 4
```

Time Complexity: O(N)
Auxiliary Space: O(N) My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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