Diameter of N-Ary Tree LeetCode Solution

Difficulty Level Medium
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Problem Statement :

The Diameter of N-Ary Tree LeetCode Solution – Given a root of an N-ary tree, you need to compute the length of the diameter of the tree.

The diameter of an N-ary tree is the length of the longest path between any two nodes in the tree. This path may or may not pass through the root.

(Nary-Tree input serialization is represented in their level order traversal, each group of children is separated by the null value.)

 

Example :

Example 1

Diameter of N-Ary Tree LeetCode Solution

Input: root = [1,null,3,2,4,null,5,6]
Output: 3
Explanation: Diameter is shown in red color.

Example 2

Diameter of N-Ary Tree LeetCode Solution

Input: root = [1,null,2,null,3,4,null,5,null,6]
Output: 4

Example 3

Diameter of N-Ary Tree LeetCode Solution

Input: root = [1,null,2,3,4,5,null,null,6,7,null,8,null,9,10,null,null,11,null,12,null,13,null,null,14]
Output: 7

Intuition :

  • We are asked to calculate the diameter of an N-ary tree, which is defined as the longest path between any two nodes in the tree.
  • Consider a node with n children, then there are nC2 or n Choose 2 paths passing through this node.
  • The longest path will be given by maxheight1 + maxheight2 +2 where maxheight1 and maxheight2 are the two maximum heights between N children.
  • Length of the longest path passing through a node = 1st Max Height among N children + 2nd Max Height among N children + 2
  • With the above intuition, to find the diameter of the tree, we need to iterate over all the nodes and select the two children with the maximum height.
  • To iterate over all the nodes, we can use  Depth-First Search.

Algorithm :

  • Initialize a global variable diameter, and for each node update the variable, computing the length of the longest path passing through the node.
  • Define a function height(node root) {} that will return the max height.
  • In the height function, Iterate over all children and pick the best two children’s height i.e. maxheight1 and maxheight2.
  • Now, update the diameter global variable with the longest path passing through this node.
  •  At last return maxheight1 in the height function.
  • After the execution of the height function, return the diameter global variable, in the main function diameter(Node root){}.

Code

Diameter of N-Ary Tree Leetcode Java Solution:

/*
// Definition for a Node.
class Node {
    public int val;
    public List<Node> children;

    
    public Node() {
        children = new ArrayList<Node>();
    }
    
    public Node(int _val) {
        val = _val;
        children = new ArrayList<Node>();
    }
    
    public Node(int _val,ArrayList<Node> _children) {
        val = _val;
        children = _children;
    }
};
*/

class Solution {
    protected int diameter=0;
    public int diameter(Node root) {
        height(root);
       return this.diameter;
    }
    // Return  the maxheight in N-arry tree
    public int height(Node root){
         int maxheight1=0;
        int maxheight2=0;
        for(Node child:root.children){
            int height=height(child)+1;
            if(height>maxheight1){
                maxheight2=maxheight1;
                maxheight1=height;
            }
            else if(height>maxheight2){
                maxheight2=height;
            }
        }
        this.diameter=Math.max(maxheight1+maxheight2,this.diameter);
        return maxheight1;
    }
    
}

Diameter of N-Ary Tree Leetcode C++ Solution:

/*
// Definition for a Node.
class Node {
public:
    int val;
    vector<Node*> children;

    Node() {}

    Node(int _val) {
        val = _val;
    }

    Node(int _val, vector<Node*> _children) {
        val = _val;
        children = _children;
    }
};
*/

class Solution {
     int maxDiameter=0;
public:
    int diameter(Node* root) {
         height(root);
       return this->maxDiameter;
    }
    int height(Node* root){
         int maxheight1=0;
        int maxheight2=0;
        for(auto child:root->children){
            int rootHeight=height(child)+1;
            if(rootHeight>maxheight1){
                maxheight2=maxheight1;
                maxheight1=rootHeight;
            }
            else if(rootHeight>maxheight2){
                maxheight2=rootHeight;
            }
        }
        this->maxDiameter=max(maxheight1+maxheight2,this->maxDiameter);
        return maxheight1;
    }
};

Complexity Analysis For  Diameter of N-Ary Tree :

Time Complexity

O(N), since we are iterating each node in the tree once and only once via recursion.

.Space Complexity 

O(N), as recursion stack 0(N) is used.

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