PAT甲级 1115 Counting Nodes in a BST （30 分）bst

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

题目大意: 构建出bst，然后输出最高层数和次高层数的结点数以及结点数之和。这个可以通过一次先序遍历访问对应层数的结点，并配合map来记录层数的结点数，即可轻松解决。 

#include <iostream>
#include <queue>
#include <map>
using namespace std;

struct btnode{
	int v;
	btnode *left,*right;
};
int n,max_level = -1;
vector<int> vec;
map<int,int> mp;


void insert(btnode *&node,int value){
	if(node == nullptr)
	{
		node = new btnode();
		node->v = value;
		node->left = node->right = nullptr;
		return ;
	}
	if(node->v >= value)
	{
		insert(node->left,value);
	}else
		insert(node->right,value);
}

void createBST(btnode *&node){
	for(int i=0;i<n;i++){
		insert(node,vec[i]);
	}
}

void pre(btnode *node,int level){
	if(node == nullptr)
		return;
	if(level > max_level)
		max_level = level;
	mp[level]++;
	pre(node->left,level+1);
	pre(node->right,level+1);
}

int main(){
	cin>>n;
	vec.resize(n);
	for(int i=0;i<n;i++){
		cin>>vec[i];
	}
	btnode *root = nullptr;
	createBST(root);
	pre(root,1);
	int a = mp[max_level],b = mp[max_level-1];
	cout<<a<<" + "<<b<<" = "<<a+b<<endl;
	
	return 0;
}