1043 Is It a Binary Search Tree (25分)
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

思路：
根据题目数据先建立二叉搜索树；
进行判断：
1.是否是先序遍历结果。
2.是否是镜像的先序遍历结果。

#include<iostream>
#include<vector>
using namespace std;
struct node {int data;node* l;node* r;
};
vector<int>pre, mirror_pre, post;
void Insert(struct node*& root, int a)//&root，c++引用；
{if (root == nullptr){root = new node();root->data = a;return;}if (a < root->data)Insert(root->l, a);else Insert(root->r, a);return;
}
struct node* create_tree(vector<int>v)
{struct node* root = nullptr;for (int i = 0; i < v.size(); i++)//二叉搜索树建设{Insert(root, v[i]);}return root;
}
void preorder(struct node* root)//先序遍历，结果保存在pre数组中
{if (root){pre.push_back(root->data);preorder(root->l);preorder(root->r);}
}
void postorder(struct node* root)//后序遍历，结果保存在post数组
{if (root){postorder(root->l);postorder(root->r);post.push_back(root->data);}
}
void mirror_preorder(struct node* root)//镜像先序遍历，结果保存在mirror_pre数组中
{if (root){mirror_pre.push_back(root->data);mirror_preorder(root->r);mirror_preorder(root->l);}
}
void mirror_postorder(struct node* root)//镜像后序遍历，结果保存在post数组
{if (root){mirror_postorder(root->r);mirror_postorder(root->l);post.push_back(root->data);}
}
int main()
{int n;cin >> n;vector<int>v(n);//v存储给定的数组for (int i = 0; i < n; i++){cin >> v[i];}struct node* root = create_tree(v);//建树preorder(root);//先进行先序遍历，保存结果。mirror_preorder(root);//保存镜像先序遍历值if (v == pre)//如果先序遍历数组和题目给定的判别数组相同{postorder(root);//保存后续遍历数组cout << "YES" << endl;for (int i = 0; i < post.size(); i++){if (i != 0)cout << " ";cout << post[i];}}else if (v == mirror_pre)//如果镜像先序遍历数组和题目给定的判别数组相同{mirror_postorder(root);//保存镜像的后序遍历数组cout << "YES" << endl;for (int i = 0; i < post.size(); i++){if (i != 0)cout << " ";cout << post[i];}}elsecout << "NO";
}