PAT甲1115 Counting Nodes in a BST【dfs】

1115 Counting Nodes in a BST （30 分）

A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

• The left subtree of a node contains only nodes with keys less than or equal to the node's key.
• The right subtree of a node contains only nodes with keys greater than the node's key.
• Both the left and right subtrees must also be binary search trees.

Insert a sequence of numbers into an initially empty binary search tree. Then you are supposed to count the total number of nodes in the lowest 2 levels of the resulting tree.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (≤1000) which is the size of the input sequence. Then given in the next line are the N integers in [−10001000] which are supposed to be inserted into an initially empty binary search tree.

Output Specification:

For each case, print in one line the numbers of nodes in the lowest 2 levels of the resulting tree in the format:

n1 + n2 = n

where n1 is the number of nodes in the lowest level, n2 is that of the level above, and n is the sum.

Sample Input:

9
25 30 42 16 20 20 35 -5 28

Sample Output:

2 + 4 = 6

题意：

给定n个数，建一棵二叉搜索树。问倒数第一层和倒数第二层分别有多少个节点。

思路：

先建树，然后dfs看每个节点的深度。

 #include <iostream>
 #include <set>
 #include <cmath>
 #include <stdio.h>
 #include <cstring>
 #include <algorithm>
 #include <vector>
 #include <queue>
 #include <map>
 #include <bits/stdc++.h>
 using namespace std;
 typedef long long LL;
 #define inf 0x7f7f7f7f

 const int maxn = ;
 int n, num[maxn], cnt[maxn], dep = -;
 struct node{
     int val;
     int left = -, right = -;
     int height;
 }tree[maxn];
 int tot;

 void add(node t, int rt)
 {
     if(t.val > tree[rt].val && tree[rt].right != -){
         add(t, tree[rt].right);
     }
     else if(t.val > tree[rt].val){
         tree[tot] = t;
         tree[rt].right = tot++;
     }
     else if(tree[rt].left != -){
         add(t, tree[rt].left);
     }
     else{
         tree[tot] = t;
         tree[rt].left = tot++;
     }
 }

 void dfs(int rt, int h)
 {
     tree[rt].height = h;
     cnt[h]++;
     dep = max(dep, h);
     if(tree[rt].left != -){
         dfs(tree[rt].left, h + );
     }
     if(tree[rt].right != -){
         dfs(tree[rt].right, h + );
     }
 }

 int main()
 {
     scanf("%d", &n);
     scanf("%d", &tree[tot++].val);
     for(int i = ; i < n; i++){
         node t;
         scanf("%d", &t.val);
         add(t, );
     }

     //printf("!\n");
     dfs(, );
     int n1 = cnt[dep], n2 = cnt[dep - ];
     printf("%d + %d = %d\n", n1, n2, n1 + n2);
     return ;
 }