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结尾无空行

Sample Output 1:

YES
5 7 6 8 11 10 8结尾无空行

Sample Input 2:

7
8 10 11 8 6 7 5结尾无空行

Sample Output 2:

YES
11 8 10 7 5 6 8结尾无空行

Sample Input 3:

7
8 6 8 5 10 9 11结尾无空行

Sample Output 3:

NO



结尾无空行

Code：

/*
分析：假设它是⼆叉搜索树，⼀开始isMirror为FALSE，根据⼆叉搜索树的性质将已知的前序转换为后
序，转换过程中，如果发现最后输出的后序数组⻓度不为n，那就设isMirror为true，然后清空后序数
组，重新再转换⼀次（根据镜⾯⼆叉搜索树的性质），如果依旧转换后数组⼤⼩不等于n，就输出no
否则输出yes
*/
#include <cstdio>
#include <vector>

using namespace std;
bool isMirror;
vector<int> pre, post;

void getpost(int root, int tail)
{
    if (root > tail)
        return;
    int i = root + 1, j = tail;
    if (!isMirror)
    {
        while (i <= tail && pre[root] > pre[i])
            i++;
        while (j > root && pre[root] <= pre[j])
            j--;
    } else
    {
        while (i <= tail && pre[root] <= pre[i])
            i++;
        while (j > root && pre[root] > pre[j])
            j--;
    }
    if (i - j != 1)
        return;
    getpost(root + 1, j);
    getpost(i, tail);
    post.push_back(pre[root]);
}

int main()
{
    int n;
    scanf("%d", 
    pre.resize(n);
    for (int i = 0; i < n; i++)
        scanf("%d", 
    getpost(0, n - 1);
    if (post.size() != n)
    {
        isMirror = true;
        post.clear();
        getpost(0, n - 1);
    }
    if (post.size() == n)
    {
        printf("YES\n%d", post[0]);
        for (int i = 1; i < n; i++)
            printf(" %d", post[i]);
    } else
    {
        printf("NO");
    }
    return 0;
}