1043 Is It a Binary Search Tree (25)（25 point(s)）

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本文介绍了一种算法，用于判断给定的整数序列是否为二叉搜索树的前序遍历序列或其镜像的前序遍历序列。通过分析输入序列的增减特性，并采用递归方法输出相应的后序遍历结果。

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1043 Is It a Binary Search Tree (25)（25 point(s)）

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.

If we swap the left and right subtrees of every node, then the resulting tree is called the Mirror Image of a BST.

Now given a sequence of integer keys, you are supposed to tell if it is the preorder traversal sequence of a BST or the mirror image of a BST.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=1000). Then N integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, first print in a line "YES" if the sequence is the preorder traversal sequence of a BST or the mirror image of a BST, or "NO" if not. Then if the answer is "YES", print in the next line the postorder traversal sequence of that tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.

Sample Input 1:

7
8 6 5 7 10 8 11

Sample Output 1:

YES
5 7 6 8 11 10 8

Sample Input 2:

7
8 10 11 8 6 7 5

Sample Output 2:

YES
11 8 10 7 5 6 8

Sample Input 3:

7
8 6 8 5 10 9 11

Sample Output 3:

NO

方法就是要么先增后减要么先减后增。输出用递归。

code

#include <iostream>
#include <vector>
using namespace std;
vector<int> vint;
void print(int l, int r);
bool isdeal(int l, int r);
int f;
bool ff = 1;
int main() {
	int n, x;
	cin >> n;
	for (int i = 0; i < n; ++i) {
		cin >> x;
		vint.push_back(x);
	}
	if (vint.size() > 1) {
		f = vint[1] < vint[0] ? 1 : 0;
		if (isdeal(0, vint.size() - 1)) {
			cout << "YES" << endl;
			print(0, vint.size() - 1);
		}
		else cout << "NO" << endl;
	}
	else {
		cout << "YES"<<endl;
		if (vint.size() == 1) {
			cout << vint[0];
		}
	}
	system("pause");
	return 0;
}
bool isdeal(int l, int r) {
	if (l >= r) return 1;
	int i;
	for (i = l+1; i <= r; ++i) {
		if (f) {
			if (vint[i] >= vint[l]) break;
		}
		else {
			if (vint[i] < vint[l]) break;
		}
	}
	for (int j = i; j <= r; ++j) {
		if (f) {
			if (vint[j] < vint[l]) return 0;
		}
		else {
			if (vint[j] >= vint[l]) return 0;
		}
	}
	if (i > r) return 1;
	if (isdeal(l+1, i - 1) && isdeal(i, r)) return 1;
	else return 0;
}
void print(int l, int r) {
	if (l > r) return;
	else if (l == r) {
		if (ff) ff = 0;
		else cout << ' ';
		cout << vint[l] ;
		return;
	}
	int i;
	for (i = l+1; i <= r; ++i) {
		if (f) {
			if (vint[i] >= vint[l]) break;
		}
		else {
			if (vint[i] < vint[l]) break;
		}
	}
	print(l + 1, i - 1);
	print(i, r);
	if (ff) ff = 0;
	else cout << ' ';
	cout << vint[l];
}