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:输出一个二叉搜索树的最后两层结点个数a和b,以及他们的和c:“a + b = c”
思路:建立二叉搜索树,dfs
代码:
#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for(int i=a;i<n;i++)
#define drep(i,n,a) for(int i=n;i>=a;i--)
#define mem(a,n) memset(a,n,sizeof(a))
#define lowbit(i) ((i)&(-i))
typedef long long ll;
typedef unsigned long long ull;
const ll INF=0x3f3f3f3f;
const double eps = 1e-6;
const int N = 1e5+5;
struct Node{
int data;
Node *left, *right;
};
Node* build(Node* root,int x){
if(root==NULL){
root=new Node();
root->data=x;
root->left=root->right=NULL;
}else if(root->data>=x){
root->left=build(root->left,x);
}else if(root->data<x){
root->right=build(root->right,x);
}
return root;
}
int cnt[N],maxDepth=1;
void dfs(Node* root,int depth){
if(root==NULL){
maxDepth=max(maxDepth,depth);
return ;
}
cnt[depth]++;
dfs(root->left,depth+1);
dfs(root->right,depth+1);
}
int main(){
int n,x;
scanf("%d",&n);
Node *root=NULL;
for(int i=0;i<n;i++){
scanf("%d",&x);
root=build(root,x);
}
dfs(root,1);
printf("%d + %d = %d",cnt[maxDepth-1],cnt[maxDepth-2],cnt[maxDepth-1]+cnt[maxDepth-2]);
return 0;
}