1099 Build A Binary Search Tree (30分)树的遍历

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
思路：二叉搜索树中序，元素从小到大排列。
1.中序一次记录中序序列的数组下标，对排序后的a数组填入res数组中。2.然后层序遍历一次记录层序遍历的数组下标。按数组下标输出相应元素。

#include <iostream>
#include <cstdio>
#include <map>
#include <vector>
#include <string>
#include <memory.h>
#include <set>
#include <list>
#include <stack>
#include <queue>
#include <unordered_map>
#include <iomanip>
#include <algorithm>
#include <cmath>
using namespace std;
struct node {
	int l, r, pos;
}s[110];
vector<int > v,lay;
void inorder(int index) {
	if (s[index].l != -1)
		inorder(s[index].l);
	v.push_back(s[index].pos);
	if (s[index].r != -1)
		inorder(s[index].r);
}
void layer(int index) {
	queue<int > q;
	q.push(index);
	while (!q.empty()) {
		int temp = q.front();
		q.pop();
		lay.push_back(temp);
		if (s[temp].l != -1)
			q.push(s[temp].l);
		if (s[temp].r != -1)
			q.push(s[temp].r);
	}
}

int main(){
	int n, a[110], res[110];
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> s[i].l >> s[i].r;
		s[i].pos = i;
	}
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}
	sort(a, a + n);
	inorder(0);
	for (int i = 0; i < v.size(); i++) {
		res[v[i]] = a[i];
	}
	layer(0);
	for (int i = 0; i < n; i++) {
		if (i != 0)
			cout << " ";
		cout << res[lay[i]];
	}
}