pat树之专题（30分）

（好好复习是王道）

1115. Counting Nodes in a BST (30)

分析：简单题——将bst树构造出来，然后给每个节点打上高度。最后求出树的高度。然后count树高的节点数加上树高节点数-1就ok了

 #include <iostream>
 #include <cstdio>

 #define MAXN 1003
 using namespace std;
 typedef struct Node{
     int key,hight;
     int left,right;
 }Node;

 Node node[MAXN];
 int solve_hight[MAXN];
 int main()
 {
     int n,index1,index2,max,a,b;
     scanf("%d",&n);

     scanf("%d",&node[].key);
     node[].left=node[].right=-;
     for(int i=;i<n;i++){
         scanf("%d",&node[i].key);
         node[i].left=node[i].right=-;
         int j=;
         while(){
             if(node[i].key>node[j].key)
                 if(node[j].right!=-)
                     j=node[j].right;
                 else
                     {
                         node[j].right=i;
                         break;
                     }
             else
                 if(node[j].left!=-)
                     j=node[j].left;
                 else
                     {
                         node[j].left=i;
                         break;
                     }
             }
         }
         index1=index2=;
         solve_hight[index2++]=;
         node[].hight=;
         while(index1!=index2){
             if(node[index1].left!=-){
                 solve_hight[index2++]=node[index1].left;
                 node[node[index1].left].hight=node[index1].hight+;
             }
             if(node[index1].right!=-){
                 solve_hight[index2++]=node[index1].right;
                 node[node[index1].right].hight=node[index1].hight+;
             }
             index1++;
         }

         a=b=max=;
         for(int i=;i<n;i++){
             if(node[i].left==-&&node[i].right==-&&node[i].hight>max)max=node[i].hight;
         }
         for(int i=;i<n;i++){
             if(max==node[i].hight)a++;
             if(max-==node[i].hight)b++;
         }
         printf("%d + %d = %d\n",a,b,a+b);

     return ;
 }

1099. Build A Binary Search Tree (30)

类似于上题的简单题，看来pat的题目是一年年变难，难度都被刷上去了。先构建树的框架，然后将所给序列中序遍历，最后层次遍历给出结果。每个人都要找到最适合自己，能最快写出的树的层次遍历的代码。

 #include <iostream>
 #include <cstdio>
 #include <algorithm>
 #define MAXN 105
 using namespace std;

 typedef struct Node{
     int left,right;
     Node(){
         left=right=-;
     }
 }Node;
 Node node[MAXN];
 int keynum[MAXN],ans[MAXN],mid[MAXN],count_num;
 void mid_travel(int index){
     if(node[index].left!=-)
         mid_travel(node[index].left);

     mid[count_num++]=index;
     if(node[index].right!=-)
         mid_travel(node[index].right);

 }
 int main()
 {
     int n,index1,index2;
     scanf("%d",&n);
     for(int i=;i<n;i++)
         scanf("%d%d",&node[i].left,&node[i].right);
     index1=index2=;
     ans[index2++]=;

     while(index1!=index2){
         if(node[ans[index1]].left!=-)
             ans[index2++]=node[ans[index1]].left;
         if(node[ans[index1]].right!=-)
             ans[index2++]=node[ans[index1]].right;
         index1++;
     }
     for(int i=;i<n;i++){
         scanf("%d",&keynum[i]);
     }
     //得到中序遍历序列
     sort(keynum,keynum+n);
     count_num=;
     mid_travel();
     bool flag=false;
     for(int i=;i<n;i++){
         for(int j=;j<n;j++)
             if(ans[i]==mid[j]){
                 if(!flag){
                     printf("%d",keynum[j]);
                     flag=true;
                 }else
                     printf(" %d",keynum[j]);
                 break;
             }
     }
     return ;
 }