1115 Counting Nodes in a BST (30分)

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本文介绍了一种算法，用于在构建的二叉搜索树中计算最低两层的节点数量。通过递归插入元素并计算每个节点的深度，然后使用广度优先搜索策略在最低两层中计数节点，最后输出这些节点的数量。

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.

递归求出每个节点深度和根的深度，在bfs中计算相应深度的节点个数。

#include<iostream>
#include<queue>
using namespace std;
typedef struct node{
	int data, depth = 0;
	node* l,* r;
}*tree;
int lowest = 0, above = 0, maxDepth = 0;
void insertT(tree& t, int d) {
	if (t == NULL) {
		t = new node();
		t->data = d;
		t->r = t->l = NULL;
		return;
	}
	if (t->data < d)insertT(t->r, d);
	else
		insertT(t->l, d);
}
void getDepth(tree &t,int depth) {
	if (t == NULL) {
		return ;
	}
	maxDepth = (maxDepth > depth) ? maxDepth : depth;
	t->depth = depth;
	getDepth(t->l, depth + 1);
	getDepth(t->r, depth + 1);
}
void level(tree t) {
	queue<tree>q;
	q.push(t);
	while (!q.empty()) {
		auto temp = q.front();
		q.pop();
		if (temp->depth == maxDepth)lowest++;
		if (temp->depth == maxDepth-1)above++;
		if (temp->l != NULL)q.push(temp->l);
		if (temp->r != NULL)q.push(temp->r);
	}
}
int main() {
	int n;
	tree t=NULL;
	cin >> n;
	for (int i = 0; i < n; i++) {
		int d;
		cin >> d;
		insertT(t, d);
	}
	getDepth(t,1);
	level(t);
	cout << lowest << " + " << above << " = " << lowest + above << endl;
	return 0;
}