[二叉查找树] 1115. Counting Nodes in a BST (30)

Posted 2020-09-01 熊猫

 

1115. Counting Nodes in a BST (30)

时间限制

400 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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 [-1000 1000] 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 <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;

const int maxn=10000;

struct Node
{
    int data;
    int layer;
    Node *lchild,*rchild;
};

void insert(Node * & root,int data)
{
    if(root==NULL)
    {
        root=new Node;
        root->lchild=NULL;
        root->rchild=NULL;
        root->data=data;
        return ;
    }
    if(root->data<data) insert(root->rchild,data);
    else insert(root->lchild,data);
}


int max_layer=0;
int layer[maxn]={0};

void layerOrder(Node * root)
{
    queue<Node *> q;
    root->layer=1;
    q.push(root);
    while(!q.empty())
    {
        Node * now=q.front();
        q.pop();
        if(now->layer>max_layer) max_layer=now->layer;
        layer[now->layer]+=1;
        if(now->lchild!=NULL)
        {
            now->lchild->layer=now->layer+1;
            q.push(now->lchild);
        }
        if(now->rchild!=NULL)
        {
            now->rchild->layer=now->layer+1;
            q.push(now->rchild);
        }
    }
}

int main()
{
    int n;
    cin>>n;
    Node * root=NULL;
    for(int i=0;i<n;i++)
    {
        int input;
        cin>>input;
        insert(root,input);
    }
    layerOrder(root);
    int a=layer[max_layer];
    int b=layer[max_layer-1];
    cout<<a<<" + "<<b<<" = "<<a+b<<endl;
    return 0;
}