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题意：
按照给出的序列构建一棵BST，然后找出这颗BST最后两层的结点个数，进行输出。
思路：
构建的时候可以用while循环来进行插入，找到插入节点的父节点，如果插入的值大于父节点的值的话则root->right = new Node();而不能先进行root = root->right; 然后再root = new Node();如果这样做的话只是单纯的建立一个结点，并没有将父节点的指针指到该节点上。
层次遍历的时候，每一层结束的时候添加一个哨兵，用来表明该层已经查找完毕。用一个数组存储每一层的元素个数，最后在输出。
Code：
1 #include <bits/stdc++.h> 2 3 using namespace std; 4 5 typedef struct Node* node; 6 7 struct Node { 8 int val; 9 node left; 10 node right; 11 Node(int v) { 12 val = v; 13 left = NULL; 14 right = NULL; 15 } 16 }; 17 18 void levelTravelTree(node root) { 19 queue<node> que; 20 que.push(root); 21 que.push(NULL); 22 vector<int> v(1005); 23 int count = 0, index = 1; 24 while (!que.empty()) { 25 node q = que.front(); 26 que.pop(); 27 if (q == NULL) { 28 que.push(NULL); 29 v[index++] = count; 30 count = 0; 31 if (que.size() == 1) break; 32 } else { 33 if (q->left) que.push(q->left); 34 if (q->right) que.push(q->right); 35 count++; 36 } 37 } 38 cout << v[index - 1] << " + " << v[index - 2] << " = " 39 << v[index - 2] + v[index - 1] << endl; 40 } 41 42 int main() { 43 int n, v; 44 cin >> n; 45 node root = NULL; 46 for (int i = 0; i < n; ++i) { 47 cin >> v; 48 node temp = root; 49 while (temp != NULL) 50 if (v > temp->val && temp->right != NULL) 51 temp = temp->right; 52 else if (v <= temp->val && temp->left != NULL) 53 temp = temp->left; 54 else 55 break; 56 if (root == NULL) 57 root = new Node(v); 58 else if (v > temp->val) 59 temp->right = new Node(v); 60 else 61 temp->left = new Node(v); 62 } 63 64 levelTravelTree(root); 65 66 return 0; 67 }