(pat)A1115. Counting Nodes in a BST

最新推荐文章于 2021-09-02 20:07:35 发布

原创最新推荐文章于 2021-09-02 20:07:35 发布 · 245 阅读

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本文介绍了一种算法，用于将一系列整数插入到二叉搜索树中，并统计生成树最低两层的节点数量。通过递归构建二叉搜索树并标记每个节点的深度，最终统计指定深度的节点总数。

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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
评价：：用静态链表和动态链表都可以做啦，记录每个节点的深度即可，但是我这个用的似乎静态链表的变种，我自己的风格。
代码：

#include<iostream>
#include<cstdio>
#include<vector>
#include<stack>
#include<algorithm>
#include<cstring> 
using namespace std;
int n;
struct node
{
    int data;
    int l,r;
}p[1005];
void insert(int root,int x)
{
    if(p[x].data<=p[root].data)
    {
        if(p[root].l==-1)
            p[root].l=x;
        else
            insert(p[root].l,x);
    }
    else
    {
        if(p[root].r==-1)
            p[root].r=x;
        else
            insert(p[root].r,x);
    }
}
int deep[1005];
int maxDeep=0;
void findD(int root)
{
    if(p[root].l!=-1)
    {
        deep[p[root].l]=deep[root]+1;
        maxDeep=max(maxDeep,deep[root]+1);
        findD(p[root].l);
    }
    if(p[root].r!=-1)
    {
        deep[p[root].r]=deep[root]+1;
        maxDeep=max(maxDeep,deep[root]+1);
        findD(p[root].r);
    }
}
int n1=0,n2=0;
void dfs(int root)
{
    if(root==-1)
    return;
    if(deep[root]==maxDeep)
        n1++;
    if(deep[root]==maxDeep-1)
        n2++;
    dfs(p[root].l);
    dfs(p[root].r);
}
int main()
{
    cin>>n;
    cin>>p[1].data;
    p[1].l=p[1].r=-1;
    for(int i=2;i<=n;i++)
    {
        cin>>p[i].data;
        p[i].l=p[i].r=-1;
        insert(1,i);
    }
    deep[1]=0;
    findD(1);
    dfs(1);
    printf("%d + %d = %d",n1,n2,n1+n2);
    return 0;
}