A1099 Build A Binary Search Tree(30 point(s))

得到树结构，匹配中序数据，得层序

1. 原文

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 the node’s key.
• The right subtree of a node contains only nodes with keys greater than or equal to the node’s key.
• Both the left and right subtrees must also be binary search trees.

Given the structure of a binary tree and a sequence of distinct integer keys, there is only one way to fill these keys into the tree so that the resulting tree satisfies the definition of a BST. You are supposed to output the level order traversal sequence of that tree. The sample is illustrated by Figure 1 and 2.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (≤100) which is the total number of nodes in the tree. The next N lines each contains the left and the right children of a node in the format left_index right_index, provided that the nodes are numbered from 0 to N−1, and 0 is always the root. If one child is missing, then −1 will represent the NULL child pointer. Finally N distinct integer keys are given in the last line.

output Specification:

For each test case, print in one line the level order traversal sequence of that tree. All the numbers must be separated by a space, with no extra space at the end of the line.

Sample Input:

9
1 6
2 3
-1 -1
-1 4
5 -1
-1 -1
7 -1
-1 8
-1 -1
73 45 11 58 82 25 67 38 42

Sample output:

58 25 82 11 38 67 45 73 42

2. 解析

已知树结构，根据中序遍历次序，插入数据

inorder(v[root].lchild);
v[root].data=in[t++];
inorder(v[root].rchild);

再BFS 得层序

3. AC代码

#include<cstdio>
#include<queue>
#include<algorithm>
using namespace std;
struct node{
	int data;
	int lchild,rchild;
}v[110];
int in[110]={};
int t=0;
void inorder(int root){
	if (root==-1)
	{
		return;
	}
	inorder(v[root].lchild);
	v[root].data=in[t++];
	inorder(v[root].rchild);
}
int key;
void levelorder(int root){
   queue<int> q;
   q.push(root);
   while(!q.empty()){
   	 int temp=q.front();
   	 if (key==0)
   	 {
   	 	printf("%d",v[temp].data);
   	 	key++;
   	 }else{
   	 	printf(" %d",v[temp].data);
   	 }
   	 q.pop();
   	 if (v[temp].lchild!=-1)
   	 {
   	 	q.push(v[temp].lchild);
   	 }
   	 if (v[temp].rchild!=-1)
   	 {
   	 	q.push(v[temp].rchild);
   	 }
   }

}
int main()
{
	int n;
	scanf("%d",&n);
	for (int i = 0; i < n; ++i)
	{
		scanf("%d%d",&v[i].lchild,&v[i].rchild);
	}
	for (int i = 0; i < n; ++i)
	{
		scanf("%d",&in[i]);
	}
	sort(in,in+n);
	inorder(0);
	levelorder(0);
	return 0;
}