PAT (Advanced Level)_1099 Build A Binary Search Tree (30分)(C++_dfs_bst)

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

Process

我的树真的贼菜，代码是参考柳神的。节点的中序遍历是从小到大的，所以只需要按照中序遍历来深度优先赋值就好了。

Code

#include
using namespace std;
int n, b[110], cnt;
struct node {
	int data, l, r, index, label;
	node() {}
	node(int a, int b, int c, int d, int e) :data(a), l(b), r(c), index(d), label(e) {}
}a[110];
bool cmp(node a, node b) {
	if (a.label != b.label)
		return a.label < b.label;
	else
		return a.index < b.index;
}
void dfs(int root, int index, int label)
{
	if (a[root].l == -1 && a[root].r == -1)
		a[root] = node(b[cnt++], -1, -1, index, label);
	else
	{
		if (a[root].l != -1)
			dfs(a[root].l, index * 2 + 1, label + 1);
		a[root] = node( b[cnt++], a[root].l, a[root].r, index, label );
		if (a[root].r != -1)
			dfs(a[root].r, index * 2 + 2, label + 1);
	}
}
int main()
{
	cin >> n;
	for (int i = 0; i < n; i++)
		cin >> a[i].l >> a[i].r;
	for (int i = 0; i < n; i++)
		cin >> b[i];
	sort(b, b + n);
	dfs(0, 0, 0);
	sort(a, a + n, cmp);
	for (int i = 0; i < n; i++)
	{
		if (i != 0)
			cout << " ";
		cout << a[i].data;
	}
	return 0;
}