求二叉树的给定两个结点之间的距离

给定一颗二叉树，和两个给定的结点，求出这两个结点之间的距离

拿到题目时不要认为是求出二叉树的结点之间的最大距离，题目是求两个结点的之间的距离

题目有几种情况

• 两个结点分布在根节点的左子树或者右子树
• 一个结点分布在根节点的左子树，一个结点分布在根节点的右子树
• 这两个结点是兄弟结点
• 一个结点是另外结点的祖先结点

本题的解题思路是

利用层次遍历的方法，获取每个结点的高度，根节点左子树的高度用正数表示，根节点右子树的高度用负数表示

这样当两个结点分布在：一个结点分布在根节点的左子树，一个结点分布在根节点的右子树时，只需要两个结点的高度的差得绝对值即可

如果一个结点是另一个结点的祖先结点，只需要高度大的结点顺着祖先结点找到高度小得结点，如果到达相同的高度结点不相同说明是兄弟结点关系

#include <iostream>
#include <vector>
#include <queue>
#include <stack>
#include <string>
#include <algorithm>

using namespace std;

struct TreeNode{
    int val;
    TreeNode* left;
    TreeNode* right;
    TreeNode(int val_ = 0):val(val_),left(NULL),right(NULL){}
};

struct TreeHeightNode{
    int height;
    TreeNode* node;
    TreeHeightNode* parent;
    TreeHeightNode(TreeNode* node_ = NULL,int height_ = 0,TreeHeightNode* parent_ =NULL): node(node_), height(height_),parent(parent_){}
};

int getDistanceBetweenNode(TreeNode* root,TreeNode* a, TreeNode* b){
    if(root == NULL ) return -1;
    queue<TreeHeightNode *> que;
    que.push(new TreeHeightNode(root,0));
    bool flagA = false, flagB = false;
   // int heightA = 0, heightB = 0;
    TreeHeightNode* heightA =NULL, *heightB = NULL;
    while(!que.empty()){
        TreeHeightNode* tmp = que.front(); que.pop();
        TreeNode *node = tmp->node;
        if(node == a) {flagA = true;heightA = tmp;}
        if(node == b) {flagB = true;heightB = tmp;}
        if(flagA && flagB) break;
        if(node->left){
            if(node->val == 0) que.push(new TreeHeightNode(node->left,1,tmp));
            else if(node->val > 0) que.push(new TreeHeightNode(node->left,tmp->height+1,tmp));
            else if(node->val < 0) que.push(new TreeHeightNode(node->left,tmp->height-1,tmp));
        }
        if(node->right){
            if(node->val == 0) que.push(new TreeHeightNode(node->right,-1,tmp));
            else if(node->val > 0) que.push(new TreeHeightNode(node->right,tmp->height+1,tmp));
            else if(node->val < 0) que.push(new TreeHeightNode(node->right,tmp->height-1,tmp));
        }
    }

    if(!flagA || !flagB) return -1;
    else{
        int ha = heightA->height, hb =heightB->height;
       if(ha*hb <=0)  return ha-hb;
       else{
           if((ha >= hb && hb > 0) || (ha < hb && hb < 0)){
               int cnt = ha-hb;
               while(cnt-->0){
                   heightA=heightA->parent;
               }
               if(heightA == heightB) return ha-hb;
               else return ha-hb+2;
           }else{
               int cnt = hb - ha;
               while(cnt-- > 0){
                   heightB=heightB->parent;
               }
               if(heightB == heightA) return hb-ha;
               else return hb-ha+2;
           }
       }
    }
}

int main(){
    TreeNode *root = new TreeNode(1);
    TreeNode *left = new TreeNode(2);
    TreeNode *right = new TreeNode(3);
    root->left = left;
    root->right = right;
    TreeNode *left1 = new TreeNode(4);
    TreeNode *right1 = new TreeNode(5);
    left->left = left1;
    left->right = right1;
    TreeNode *left2 = new TreeNode(4);
    TreeNode *right2 = new TreeNode(5);
    left1->left = left2;
    left1->right = right2;
    cout<<getDistanceBetweenNode(root,left2,right)<<endl;
    return 0;
}

其实寻找两个结点的距离就是求两个结点的公共祖先结点，所以另一种方法是找到o最小其公共祖先结点

然后

求二叉树的给定两个结点之间的距离