PAT 甲级 A 1099 Build A Binary Search Tree

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

题意：

给出n个结点的子结点，和n个结点的权重（输入顺序和结点顺序不是一 一对应的，要找到那个权重是那个结点的），求这棵二叉查找树的层序遍历。

思路：

将给的权重从小到大排序就可以得到二叉查找树的中序遍历序列，根据中序遍历的规律，将第一小的值，第二小的值...第n小的值都放到对应的结点，使得该树的结点都有权重，然后再进行层次遍历就好了。
 

代码：
 

//属于二叉寻找树中小蝌蚪找妈妈类型 
#include<iostream>
#include<algorithm>
#include<queue>
using namespace std;
//给出的是编号和结点的关系，所以使用二叉查找树的静态写法比较方便; 
const int maxn=110;
int weight[maxn];
int index=0,n;
struct node{
	int data;
	int lchild,rchild; 
}Node[maxn];
void inorder(int root){
	if(root==-1)return ;//递归边界; 
	inorder(Node[root].lchild);//在左子树防止第一小，第二小...这样子像小蝌蚪找妈妈一样一个个按中序遍历的顺序找到各自的位置； 
	Node[root].data=weight[index++];
	inorder(Node[root].rchild);
}

int num=0;
void BFS(int root){//结点已经全部赋值，开始层序遍历; 
	queue<int > q;
	q.push(root);
	while(!q.empty()){
		int top=q.front();
		q.pop();
		printf("%d",Node[top].data);
		num++;
		if(num!=n)printf(" ");
		if(Node[top].lchild!=-1) q.push(Node[top].lchild);
		if(Node[top].rchild!=-1) q.push(Node[top].rchild);
	}
}

int main( ){
	scanf("%d",&n);
	for(int i=0;i<n;i++)scanf("%d %d",&Node[i].lchild,&Node[i].rchild);//建立二叉树； 
	for(int i=0;i<n;i++)scanf("%d",&weight[i]);
	sort(weight,weight+n);//得到中序遍历序列; 
	inorder(0); 
	BFS(0);
	return 0;
}