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
已知N个数,插入二叉搜索树后,进行输出最后两层一共有多少个节点。
#include <iostream> using namespace std; struct node { int val, level; node *left = NULL, *right = NULL; node(int val):val(val){} }; node *root = NULL; int max_level = 0, a = 0, b = 0; /** 插入节点 */ node* Insert(node *n, int val) { if(n == NULL) return new node(val); else if(n->val < val) n->right = Insert(n->right, val); else n->left = Insert(n->left, val); return n; } /** 标注层级 */ void dfs(node *n, int level) { if(n != NULL) { n->level = level; max_level = max(max_level, level); dfs(n->left, level + 1); dfs(n->right, level + 1); } } /** 计算最后两层 */ void dfs_count(node *n) { if(n != NULL) { if(n->level == max_level) a++; if(n->level == max_level - 1) b++; dfs_count(n->left); dfs_count(n->right); } } int main() { int N, tmp; scanf("%d", &N); for(int i = 0; i < N; i++){ scanf("%d", &tmp); root = Insert(root, tmp); } dfs(root, 0); dfs_count(root); printf("%d + %d = %d", a, b, a + b); system("pause"); return 0; }