面试题5：计算二叉树中最大节点到最小节点之间的距离

网易2016实习研发工程师编程题

有一棵二叉树，树上每个点标有权值，权值各不相同，请设计一个算法算出权值最大的叶节点到权值最小的叶节点的距离。二叉树每条边的距离为1，一个节点经过多少条边到达另一个节点为这两个节点之间的距离。

给定二叉树的根节点root，请返回所求距离。

#include <iostream>
#include <climits>
//struct ListNode {
//    int val;
//    ListNode* next;
//    ListNode() :
//            val(0), next(nullptr) {
//    }
//    ListNode(int x) :
//            val(x), next(nullptr) {
//    }
//};

struct TreeNode {
    int val;
    TreeNode* left;
    TreeNode* right;
    TreeNode() :
            val(0), left(nullptr), right(nullptr) {
    }
    TreeNode(int x) :
            val(x), left(nullptr), right(nullptr) {
    }
};

class Solution {
private:
    TreeNode* maxNode = new TreeNode(INT_MIN);
    TreeNode* minNode = new TreeNode(INT_MAX);
private:
    TreeNode* getLCANode(TreeNode* root, TreeNode* p, TreeNode* q) {
        if (root == nullptr || root == p || root == q) {
            return root;
        }
        TreeNode* left = getLCANode(root->left, p, q);
        TreeNode* right = getLCANode(root->right, p, q);
        if (left && right) {
            return root;
        }
        if (left == nullptr)
            return right;
        else // right == nullptr;
            return left;
    }

    void getMaxMinNode(TreeNode* root){
        if(root==nullptr) return;
        if(root->val > maxNode->val){
            maxNode = root;
        }
        if(root->val < minNode->val){
            minNode = root;
        }
        getMaxMinNode(root->left);
        getMaxMinNode(root->right);
    }

    //get distance between maxNode or minNode and LCAnode
    int getDis(TreeNode* LCANode,TreeNode* node){
        if(LCANode == nullptr) return -1;
        if(LCANode->val == node->val)
            return 0;
        int dis = getDis(LCANode->left,node);
        if(dis == -1){
            dis = getDis(LCANode->right,node);
        }
        if(dis != -1){
            return dis + 1;
        }
        return -1;
    }
public:
    int getMaxMinNodeDis(TreeNode* root){
        if(root == nullptr) return 0;
        getMaxMinNode(root);
        TreeNode* LCANode = getLCANode(root,maxNode,minNode);
        int a = getDis(LCANode,maxNode);
        int b = getDis(LCANode,minNode);
        return a+b;
    }
};