求二叉树节点的最大距离

题目：如果我们把二叉树看成一个图，父子节点之间的连线看成是双向的。我们定义“距离”为两个节点之间边的条数。写一个程序，求一颗二叉树中相距最远的两个节点之间的距离。

解法：

 

C++代码如下：

#include<iostream>using namespace std;struct node   //structure of the node on the binary search tree{    int value;    node* left;    node* right;};struct binary_tree    //structure of the binary search tree{    node* root;};void insert(binary_tree& T,int value)   //insert node with value 'value' to the binary search tree T{    if(T.root==NULL)        //insert the first node of the binary search tree    {        T.root=(node*)malloc(sizeof(node));        T.root->value=value;        T.root->left=NULL;        T.root->right=NULL;    }    else    {        node* parent=T.root;   //parent indicate the parent of the being inserted value        while(true)        {            if(value>parent->value)            {                if(parent->right==NULL)                {                    parent->right=(node*)malloc(sizeof(node));                    parent->right->value=value;                    parent->right->left=NULL;                    parent->right->right=NULL;                    break;                }                else                {                {                    parent=parent->right;                }            }            else if(value<parent->value)            {                if(parent->left==NULL)                {                    parent->left=(node*)malloc(sizeof(node));                    parent->left->value=value;                    parent->left->left=NULL;                    parent->left->right=NULL;                    break;                }                else                {                    parent=parent->left;                }            }            else            {                cout<<"this value has already exist"<<endl;                break;            }        }    }}void delete_node(node* root)   //delete node binary search tree rooted by 'root'{    if(root==NULL)        return;    delete_node(root->left);  //recursively delete its left subtree    delete_node(root->right);  //recursively delete its right subtree    free(root);}//delete binary search tree Tvoid delete_binary_tree(binary_tree& T){    delete_node(T.root);}int calcu_depth(node* root,int& global_max)  //calculate the depth of the binary search tree rooted by 'root', and update the variable global_max the same time{    if(root==NULL)        return 0;    int local_max;    int left_depth,right_depth;    if(root->left==NULL&&root->right==NULL)        return 0;    else if(root->left==NULL)    {        right_depth=calcu_depth(root->right,global_max);        local_max=right_depth+1;        if(local_max>global_max)            global_max=local_max;        return right_depth+1;    }    else if(root->right==NULL)    {        left_depth=calcu_depth(root->left,global_max);        local_max=left_depth+1;        if(local_max>global_max)            global_max=local_max+1;        return left_depth+1;    }    else    {        left_depth=calcu_depth(root->left,global_max);        right_depth=calcu_depth(root->right,global_max);        local_max=left_depth+right_depth+2;        if(local_max>global_max)            global_max=local_max;        if(left_depth>right_depth)            return left_depth+1;        else            return right_depth+1;    }}int find_max_path(node* root)  //calculate the max length path between nodes on binary search tree root{    int global_max=0,max_depth=0;    max_depth=calcu_depth(root,global_max);    return global_max;}int main(int* argc,char* argv[]){    binary_tree B_T;    B_T.root=NULL;    int value;    while(cin>>value)    {        insert(B_T,value);    }    int max_path=find_max_path(B_T.root);    cout<<max_path<<endl;    delete_binary_tree(B_T);    return 0;}