HDU 3999 The order of a Tree （二叉搜索树+先序遍历）

刺骨的言语ヽ痛彻心扉 2024-02-17 21:20 37阅读 0赞

## The order of a Tree ##

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

题意：题意给出一个序列，构造一棵二叉搜索树，让你找一个序列，满足：能构成与给出的序列相同的二叉搜索树，同时，字典序最小。

分析：首先构造二叉搜索树，然后先序遍历输出即可。

AC代码：

#include<cstdio>
    #include<cstring>
    #include<cstdlib>
    using namespace std;
    typedef struct node{
    	int data;
    	node *lchild,*rchild; 
    }*Tree,tree;
    Tree root;
    int n;
    	
    void insert(Tree& root,int t){
    	if(root==NULL){
    		root=(Tree)malloc(sizeof(tree));
    		root->data=t;
    		root->lchild=NULL;
    		root->rchild=NULL;
    	}
    	else if(t<root->data){
    		insert(root->lchild,t);
    	}
    	else insert(root->rchild,t);
    }
    
    void preOder(Tree root,int& cnt){
      	if(root==NULL)return ; 
    	cnt++;   //用于控制输出格式 
      	if(cnt!=n)
      	printf("%d ",root->data);
      	else printf("%d\n",root->data);
      	preOder(root->lchild,cnt);
      	preOder(root->rchild,cnt);
    }
    
    int main(){
    	
    	while(scanf("%d",&n)==1){
    		int t;
    		for(int i=0;i<n;i++)
            {
            scanf("%d",&t);
    		insert(root,t);
    		}
    		
    		int cnt=0;
    		preOder(root,cnt);
    	}
    	return 0;
    }