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);
    }
    
    
}