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
题意:给出n个数,让你建立一棵二叉搜索树,然后输出这棵树的最后两层节点数。
思路:首先建立二叉搜索树,然后使用先序遍历统计每一层节点数,最后输出最后两层即可。
参考代码:
#include<cstdio>
#include<algorithm>
using namespace std;
const int maxn=1010;
int n,Count[maxn],maxL=0; //maxL标记最后一层
struct node{
int data;
node* lchild;
node* rchild;
node(int a):data(a),lchild(NULL),rchild(NULL){}
};
void insert(node*& root,int x){
if(root==NULL){
root=new node(x);
}else if(x<=root->data)
insert(root->lchild,x);
else
insert(root->rchild,x);
}
void DFS(node* root,int d){
if(root!=NULL){
Count[d]++;
maxL=max(maxL,d);
DFS(root->lchild,d+1);
DFS(root->rchild,d+1);
}
}
int main()
{
int t;
node* root=NULL; //记得初始化为空
scanf("%d",&n);
for(int i=0;i<n;i++){
scanf("%d",&t);
insert(root,t);
}
DFS(root,1);
printf("%d + %d = %d\n",Count[maxL],Count[maxL-1],Count[maxL]+Count[maxL-1]);
return 0;
}