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 (≤) which is the size of the input sequence. Then given in the next line are the N integers in [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
#include <iostream>
#include <queue>
#include <vector>
using namespace std;
struct Node
{
int v;
Node *l, *r;
Node(int a = -) :v(a), l(nullptr), r(nullptr) {}
};
Node* root = nullptr;
int n, level = -, a;
vector<int>res;
void creatTree(Node*& root, int x)
{
if (root == nullptr)
{
root = new Node(x);
return;
}
if (x <= root->v)
creatTree(root->l, x);
else
creatTree(root->r, x);
}
void BFS(Node* root)
{
queue<Node*>q;
q.push(root);
while (!q.empty())
{
int num = ;
queue<Node*>temp;
while (!q.empty())
{
Node* p = q.front();
q.pop();
num++;
if (p->l != nullptr)
temp.push(p->l);
if (p->r != nullptr)
temp.push(p->r);
}
q = temp;
res.push_back(num);
}
}
int main()
{ cin >> n;
while (n--)
{
cin >> a;
creatTree(root, a);
}
BFS(root);
cout << res[res.size() - ] << " + " << res[res.size() - ] << " = " << res[res.size() - ] + res[res.size() - ] << endl;
return ;
}