PAT 1099 Build A Binary Search Tree [中序遍历建造二叉搜索树]

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根据给定的二叉树结构和整数序列构建唯一的二叉搜索树，并输出其层次遍历结果。题目描述了一种将节点和整数结合的方法，通过排序和中序遍历来实现。

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

-----------------------------------这是题目和解题的分割线-----------------------------------

给定一棵树的结构，再给定一堆数字，让填充成一棵二叉搜索树。

先排序，再中序遍历（二叉搜索树中序是递增的）改变树结点的data，最后层次遍历输出。这种读取方式用静态存储。

#include<cstdio>
#include<queue>
#include<algorithm>

using namespace std;

struct node
{
	int data;
	int left,right;
}tree[110];

int a[110],n,tmp[110],cnt = 0,num = 0;

//中序遍历替换data 
void inOrder(int index)
{
	if(tree[index].left!=-1) 
		inOrder(tree[index].left);
	tree[index].data = a[cnt++]; 
	if(tree[index].right!=-1)
		inOrder(tree[index].right);
}

//层次遍历输出 
void levelOrder(int index)
{
	queue<int> q;
	q.push(index);
	while(!q.empty())
	{
		int top = q.front();
		q.pop();
		printf("%d",tree[top].data);
		if(num!=n-1) printf(" ");//末尾无空格 
		num++;
		if(tree[top].left!=-1) q.push(tree[top].left);
		if(tree[top].right!=-1) q.push(tree[top].right);
	}
}

int main()
{
	int i,l,r;
	scanf("%d",&n);
	for(i=0;i<n;i++)
		scanf("%d%d",&tree[i].left,&tree[i].right);
	for(i=0;i<n;i++)
		scanf("%d",&a[i]);
	sort(a,a+n); 
	inOrder(0);
	levelOrder(0);
	return 0;
}