pat 1043. Is It a Binary Search Tree (25)

1043. Is It a Binary Search Tree (25)

时间限制

400 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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

解：先判断输入的数值是否是前序遍历的结果或者是结果的镜像；如果是，进行后序遍历，即左-右-根。

代码：

#include<iostream>
#include<cstdlib>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<vector>
using namespace std;
struct Node  //结点结构
{
    int val;
    Node *left;
    Node *right;
};

bool Is_BST(int *val,int n,Node **r)   //判断前序遍历
{
    if(val==NULL||n<=0)
    {
        return false;
    }
    *r=new Node();
    Node *root=*r;
    root->val=val[0];
    root->left=NULL;
    root->right=NULL;
    int i,j;
    for(i=1;i<n;i++)
    {
        if(val[i]>=root->val)
            break;
    }
    for(j=i;j<n;j++)
    {
        if(val[j]<root->val)
            return false;
    }
    bool left=true;
    if(i>1)
        left=Is_BST(val+1,i-1,&root->left);
    bool right=true;
    if(i<n)
        right=Is_BST(val+i,n-i,&root->right);
    return left&&right;
}
bool Is_MirrorBST(int *val,int n,Node **r)  //判断镜像前序遍历
{
 if(val==NULL||n<=0)
    {
        return false;
    }
    *r=new Node();
    Node *root=*r;
    root->val=val[0];
    root->left=NULL;
    root->right=NULL;
    int i,j;
    for(i=1;i<n;i++)
    {
        if(val[i]<root->val)
            break;
    }
    for(j=i;j<n;j++)
    {
        if(val[j]>=root->val)
            return false;
    }
    bool left=true;
    if(i>1)
        left=Is_MirrorBST(val+1,i-1,&root->left);
    bool right=true;
    if(i<n)
        right=Is_MirrorBST(val+i,n-i,&root->right);
    return left&&right;
}
bool Judge(int *val,int n,Node **root)  //总判断
{
    if(Is_BST(val,n,root))
    {
        return true;
    }
    if(Is_MirrorBST(val,n,root))
    {
        return true;
    }
    return false;
}
void PostrOrder(Node *root,vector<int> *temp) //后序遍历
{
   if(root!=NULL)
   {
       if(root->left!=NULL)
       {
           PostrOrder(root->left,temp);
       }
       if(root->right!=NULL)
       {
           PostrOrder(root->right,temp);
       }
       (*temp).push_back(root->val);
   }
}

int main()
{
    int n;
    while(scanf("%d",&n)==1)
    {
        int *val=new int[n+1];
        for(int i=0;i<n;i++)  scanf("%d",&val[i]);
        Node *root=NULL;
        if(Judge(val,n,&root))
        {
            printf("YES
");
            vector<int> temp;
            PostrOrder(root,&temp);
            if(!temp.empty())
            {
                printf("%d",temp[0]);
                for(int i=1;i<temp.size();i++)
                {
                    printf(" %d",temp[i]);
                }
                printf("
");
            }
        }
        else
        {
            printf("NO
");
        }
    }
    return 0;
}