FB面经Prepare: Find Longest Path in a Multi-Tree

给的多叉树, 找这颗树里面最长的路径长度 

解法就是在子树里面找最大的两个（或一个，如果只有一个子树的话）高度加起来。

对于每一个treenode, 维护它的最高的高度和第二高的高度，经过该点的最大路径就是：  最高高度+第二高高度，然后return 最高高度

 package fbPractise;

 import java.util.*;

 class TreeNode {
     int val;
     List<TreeNode> children;
     public TreeNode(int value) {
         this.val = value;
         this.children = new ArrayList<TreeNode>();
     }
 }

 public class LongestPathInTree {
     static int maxLen = 0;

     public static int findLongestPath(TreeNode node) {
         findMaxPath(node);
         return maxLen;
     }

     public static int findMaxPath(TreeNode node) {
         if (node == null) return 0;
         int heightest1 = 0;
         int heightest2 = 0;

         for (TreeNode child : node.children) {
             int childHeight = findMaxPath(child);

             if (childHeight > heightest1) {
                 heightest2 = heightest1;
                 heightest1 = childHeight;
             }
             else if (childHeight > heightest2) {
                 heightest2 = childHeight;
             }
         }
         maxLen = Math.max(maxLen, 1 + heightest1 + heightest2);
         return 1 + heightest1;
     }

     public static void main(String[] args) {
         TreeNode node1 = new TreeNode(1);
         TreeNode node2 = new TreeNode(2);
         TreeNode node3 = new TreeNode(3);
         TreeNode node4 = new TreeNode(4);
         TreeNode node5 = new TreeNode(5);
         TreeNode node6 = new TreeNode(6);
         node1.children.add(node2);
         node1.children.add(node3);
         node2.children.add(node4);
         node2.children.add(node5);
         node5.children.add(node6);

         int res = findLongestPath(node1);
         System.out.println(res);
     }

 }