N-Ary 树的深度

给定一棵 N-Ary 树，求树的深度。 N-Ary 树是其中节点最多可以有N个子节点的树。
例子：
示例 1：

narry1

示例 2：

N-Ary 树可以像普通树一样被遍历。我们只需要考虑给定节点的所有子节点并在每个节点上递归调用该函数。

C++

// C++ program to find the height of
// an N-ary tree
#include 
using namespace std;
 
// Structure of a node of an n-ary tree
struct Node
{
   char key;
   vector child;
};
 
// Utility function to create a new tree node
Node *newNode(int key)
{
   Node *temp = new Node;
   temp->key = key;
   return temp;
}
 
// Function that will return the depth
// of the tree
int depthOfTree(struct Node *ptr)
{
    // Base case
    if (!ptr)
        return 0;
 
    // Check for all children and find
    // the maximum depth
    int maxdepth = 0;
    for (vector::iterator it = ptr->child.begin();
                              it != ptr->child.end(); it++)
        maxdepth = max(maxdepth, depthOfTree(*it));
 
    return maxdepth + 1 ;
}
 
// Driver program
int main()
{
   /*   Let us create below tree
   *             A
   *         / /  \  \
   *       B  F   D  E
   *      / \    |  /|\
   *     K  J    G  C H I
   *      /\            \
   *    N   M            L
   */
 
   Node *root = newNode('A');
   (root->child).push_back(newNode('B'));
   (root->child).push_back(newNode('F'));
   (root->child).push_back(newNode('D'));
   (root->child).push_back(newNode('E'));
   (root->child[0]->child).push_back(newNode('K'));
   (root->child[0]->child).push_back(newNode('J'));
   (root->child[2]->child).push_back(newNode('G'));
   (root->child[3]->child).push_back(newNode('C'));
   (root->child[3]->child).push_back(newNode('H'));
   (root->child[3]->child).push_back(newNode('I'));
   (root->child[0]->child[0]->child).push_back(newNode('N'));
   (root->child[0]->child[0]->child).push_back(newNode('M'));
   (root->child[3]->child[2]->child).push_back(newNode('L'));
 
   cout << depthOfTree(root) << endl;
 
   return 0;
}

Java

// Java program to find the height of
// an N-ary tree
import java.util.*;
 
class GFG
{
 
// Structure of a node of an n-ary tree
static class Node
{
    char key;
    Vector child;
};
 
// Utility function to create a new tree node
static Node newNode(int key)
{
    Node temp = new Node();
    temp.key = (char) key;
    temp.child = new Vector();
    return temp;
}
 
// Function that will return the depth
// of the tree
static int depthOfTree(Node ptr)
{
    // Base case
    if (ptr == null)
        return 0;
 
    // Check for all children and find
    // the maximum depth
    int maxdepth = 0;
    for (Node it : ptr.child)
        maxdepth = Math.max(maxdepth,
                            depthOfTree(it));
 
    return maxdepth + 1 ;
}
 
// Driver Code
public static void main(String[] args)
{
    /* Let us create below tree
    *             A
    *         / / \ \
    *     B F D E
    *     / \ | /|\
    *     K J G C H I
    *     /\         \
    * N M         L
    */
     
    Node root = newNode('A');
    (root.child).add(newNode('B'));
    (root.child).add(newNode('F'));
    (root.child).add(newNode('D'));
    (root.child).add(newNode('E'));
    (root.child.get(0).child).add(newNode('K'));
    (root.child.get(0).child).add(newNode('J'));
    (root.child.get(2).child).add(newNode('G'));
    (root.child.get(3).child).add(newNode('C'));
    (root.child.get(3).child).add(newNode('H'));
    (root.child.get(3).child).add(newNode('I'));
    (root.child.get(0).child.get(0).child).add(newNode('N'));
    (root.child.get(0).child.get(0).child).add(newNode('M'));
    (root.child.get(3).child.get(2).child).add(newNode('L'));
     
    System.out.print(depthOfTree(root) + "\n");
}
}
 
// This code is contributed by Rajput-Ji

C#

// C# program to find the height of
// an N-ary tree
using System;
using System.Collections.Generic;
 
class GFG
{
 
// Structure of a node of an n-ary tree
public class Node
{
    public char key;
    public List child;
};
 
// Utility function to create a new tree node
static Node newNode(int key)
{
    Node temp = new Node();
    temp.key = (char) key;
    temp.child = new List();
    return temp;
}
 
// Function that will return the depth
// of the tree
static int depthOfTree(Node ptr)
{
    // Base case
    if (ptr == null)
        return 0;
 
    // Check for all children and find
    // the maximum depth
    int maxdepth = 0;
    foreach (Node it in ptr.child)
        maxdepth = Math.Max(maxdepth,
                            depthOfTree(it));
 
    return maxdepth + 1 ;
}
 
// Driver Code
public static void Main(String[] args)
{
     
    /* Let us create below tree
    *             A
    *         / / \ \
    *     B F D E
    *     / \ | /|\
    *     K J G C H I
    *     /\         \
    * N M         L
    */
    Node root = newNode('A');
    (root.child).Add(newNode('B'));
    (root.child).Add(newNode('F'));
    (root.child).Add(newNode('D'));
    (root.child).Add(newNode('E'));
    (root.child[0].child).Add(newNode('K'));
    (root.child[0].child).Add(newNode('J'));
    (root.child[2].child).Add(newNode('G'));
    (root.child[3].child).Add(newNode('C'));
    (root.child[3].child).Add(newNode('H'));
    (root.child[3].child).Add(newNode('I'));
    (root.child[0].child[0].child).Add(newNode('N'));
    (root.child[0].child[0].child).Add(newNode('M'));
    (root.child[3].child[2].child).Add(newNode('L'));
     
    Console.Write(depthOfTree(root) + "\n");
}
}
 
// This code is contributed by Rajput-Ji

Javascript

输出：