The order of a Tree

最新推荐文章于 2020-05-29 19:23:42 发布

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最新推荐文章于 2020-05-29 19:23:42 发布

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分类专栏：简单算法题文章标签： The order of a Tree 二叉排序树

本文链接：https://blog.youkuaiyun.com/ls158390/article/details/82707454

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本文探讨了二叉搜索树的构建过程，特别是如何通过给定的节点插入顺序生成具有相同结构但最小字典序的树。通过分析二叉排序树的性质，即左子树节点小于根节点而右子树节点大于根节点，文章提供了一个算法实例，演示了如何找到生成相同树形结构的最小字典序节点序列。

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Problem Description
As we know,the shape of a binary search tree is greatly related to the order of keys we insert. To be precisely:
1. insert a key k to a empty tree, then the tree become a tree with
only one node;
2. insert a key k to a nonempty tree, if k is less than the root ,insert
it to the left sub-tree;else insert k to the right sub-tree.
We call the order of keys we insert “the order of a tree”,your task is,given a oder of a tree, find the order of a tree with the least lexicographic order that generate the same tree.Two trees are the same if and only if they have the same shape.

Input
There are multiple test cases in an input file. The first line of each testcase is an integer n(n <= 100,000),represent the number of nodes.The second line has n intergers,k1 to kn,represent the order of a tree.To make if more simple, k1 to kn is a sequence of 1 to n.

Output
One line with n intergers, which are the order of a tree that generate the same tree with the least lexicographic.

Sample Input
4

1 3 4 2

Sample Output
1 3 2 4
分析

二叉排序树 保证左结点比上一结点小 右结点比上一结点大

代码总览：

#include <cstdio>
#include <iostream>
#include <cstring>
using namespace std;

typedef struct BiTreeNode
{
    int data;
    struct BiTreeNode *lchild,*rchild;
}*BiTree;

void add(BiTree &T,int val)
{
    if(T==NULL)
    {
        T=new BiTreeNode();
        T->data=val;
        T->lchild=T->rchild=NULL;
    }
    else if(T->data>val)
    add(T->lchild,val);
    else
    add(T->rchild,val);
}
void PreOrder(BiTree T,int flag)
{
    if(T==NULL)
    return;
    else{
    if(!flag)
    printf(" ");
    //cout<<T->data;
    printf("%d",T->data);
    PreOrder(T->lchild,0);
    PreOrder(T->rchild,0);
    }
}
int main()
{
    int n,v;
    BiTree T;
    while(scanf("%d",&n)!=EOF)
    {
     T=NULL;
     for(int i=0;i<n;i++)
     {
        scanf("%d",&v);
        add(T,v);
     }
      PreOrder(T,1);
     // printf("\n");   
    }
}