PAT (Advanced Level) Practice 1099 Build A Binary Search Tree (30分) （二叉搜索树）

1.题目

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.题目分析

首先按照所给的左右节点静态建树，把data数据空下，我们知道二叉搜索树的中序遍历是从小到大的，所有用数组记录节点data再sort排序，然后在数中进行中序遍历为数中的data赋值，最后再进行层序遍历

 3.代码

#include<iostream>
#include<queue>
#include<algorithm>
using namespace std;
struct node
{
	int data;
	int left;
	int right;
}list[110],temp;
int n;
int nodelist[110];
void inorder(int head,int &amount)
{
	if(list[head].left!=-1)inorder(list[head].left,amount);
	list[head].data = nodelist[amount++];
	if (list[head].right != -1)inorder(list[head].right, amount);
}
bool space = false;
void level(int head)
{
	queue<node>out;
	out.push(list[head]);
	while (!out.empty())
	{
		temp = out.front(); out.pop();
		printf("%s%d", space == false ? "" : " ", temp.data); space = true;
		if (temp.left != -1)out.push(list[temp.left]);
		if (temp.right!= -1)out.push(list[temp.right]);
	}
}
int main()
{
	scanf("%d", &n);
	for (int i = 0; i < n; i++)
		scanf("%d %d", &list[i].left, &list[i].right);
	for (int i = 0; i < n; i++)
		scanf("%d", &nodelist[i]);
	sort(nodelist, nodelist + n);
	int amount = 0;
	inorder(0, amount);
	level(0);
}