## 1099build a binary search tree (30 points)

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 integerN(≤100) which is the total number of nodes in the tree. The nextNlines 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 toN−1, and 0 is always the root. If one child is missing, then−1will represent the NULL child pointer. FinallyNdistinct 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`

### thinking

- For a binary tree, the middle order sequence is incremental, so the given sequence is sorted from small to large, then traversed according to the middle order, the ordered sequence is inserted into the binary sort tree, and finally traversed hierarchically.

### code

```
#include <cstdio>
#include <queue>
#include <algorithm>
using namespace std;
const int maxn = 110;
int data[maxn];
int n;
struct node
{
int data;
int lchild, rchild;
}Node[maxn];
int num;
void in_create(int root)
{
if (root == -1)
return;
in_create(Node[root].lchild);
Node[root].data = data[num ++];
in_create(Node[root].rchild);
}
void layer_order(int root)
{
queue<int> q;
q.push(root);
int num = 0;
while (!q.empty())
{
int now = q.front();
q.pop();
num ++;
printf("%d", Node[now].data);
if (num < n)
{
printf(" ");
}
if (Node[now].lchild != -1) q.push(Node[now].lchild);
if (Node[now].rchild != -1) q.push(Node[now].rchild);
}
}
int main()
{
//freopen("test.txt","r", stdin);
scanf("%d", &n);
int lchild, rchild;
for (int i = 0; i < n; i ++)
{
scanf("%d %d", &lchild, &rchild);
Node[i].lchild = lchild;
Node[i].rchild = rchild;
}
for (int i = 0; i < n; i ++)
{
scanf("%d", &data[i]);
}
sort(data, data + n);
in_create(0);
layer_order(0);
return 0;
}
```