PAT1043 Is It a Binary Search Tree

Posted 2021-01-04 sgatbl

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

  1 #include<iostream>
  2 #include<stdlib.h>
  3 #include<vector>
  4 #include<stack>
  5 #include<algorithm>
  6 
  7 using namespace std;
  8 
  9 enum Tags{Left, Right};
 10 typedef struct node{
 11     int val;
 12     node *left, *right;
 13 }BSTNode;
 14 
 15 typedef struct stackElem{
 16     BSTNode *p;
 17     Tags flag;
 18 }StackElem;
 19 
 20 static const int MAX = 1000;
 21 int n, data[MAX];
 22 vector<int> pre, post;
 23 
 24 BSTNode *create(int e){
 25     BSTNode *t = (BSTNode*)malloc(sizeof(BSTNode));
 26     t->val = e;
 27     t->left = t->right = NULL;
 28     return t;
 29 }
 30 
 31 void Insert(BSTNode* &t, int e){
 32     if(t==NULL){
 33         t = create(e);
 34         return;
 35     }
 36     else if(t->val>e){
 37         Insert(t->left, e);
 38     }
 39     else{
 40         Insert(t->right, e);
 41     }
 42 }
 43 
 44 BSTNode *buildBSTree(){
 45     BSTNode *root = NULL;
 46     for(int i=0;i<n;i++){
 47         Insert(root, data[i]);
 48     }
 49     return root;
 50 }
 51 
 52 void PreOrder(BSTNode* &t){
 53     if(t!=NULL){
 54         pre.push_back(t->val);
 55         PreOrder(t->left);
 56         PreOrder(t->right);
 57     }
 58 }
 59 
 60 void PostOrder(BSTNode* &t){
 61     if(t!=NULL){
 62         PostOrder(t->left);
 63         PostOrder(t->right);
 64         post.push_back(t->val);
 65     }
 66 }
 67 
 68 void PostOrdered(BSTNode* &t){
 69     StackElem se;
 70     stack<StackElem> s;
 71     BSTNode *p;
 72     p = t;
 73     int num = 0;
 74     if(p==NULL){
 75         return;
 76     }
 77     while(p!=NULL||!s.empty()){
 78         while(p!=NULL){
 79             se.flag = Left;
 80             se.p = p;
 81             s.push(se);
 82             p = p->left;
 83         }
 84         se = s.top();
 85         s.pop();
 86         p = se.p;
 87         if(num==n-1){
 88             cout<<p->val;
 89             p = NULL;
 90         }
 91         else{
 92             if(se.flag==Left){
 93                 se.flag = Right;
 94                 s.push(se);
 95                 p = p->right;
 96             }
 97             else{
 98                 num++;
 99                 cout<<p->val<<" ";
100                 p = NULL;
101             }
102         }
103     }
104     cout<<endl;
105 }
106 
107 void mPostOrder(BSTNode* &t){
108     StackElem se;
109     stack<StackElem> s;
110     BSTNode *p;
111     p = t;
112     int num = 0;
113     if(p==NULL){
114         return;
115     }
116     while(p!=NULL||!s.empty()){
117         while(p!=NULL){
118             se.flag = Right;
119             se.p = p;
120             s.push(se);
121             p = p->right;
122         }
123         se = s.top();
124         s.pop();
125         p = se.p;
126         if(num==n-1){
127             cout<<p->val;
128             p = NULL;
129         }
130         else{
131             if(se.flag==Right){
132                 se.flag = Left;
133                 s.push(se);
134                 p = p->left;
135             }
136             else{
137                 num++;
138                 cout<<p->val<<" ";
139                 p = NULL;
140             }
141         }
142     }
143     cout<<endl;
144 }
145 
146 int main(){
147     cin>>n;
148     for(int i=0;i<n;i++){
149         cin>>data[i];
150     }
151     BSTNode *tree = buildBSTree();
152     PreOrder(tree);
153     PostOrder(tree);
154     reverse(post.begin(), post.end());
155     int pcnt = 0;
156     int mcnt = 0;
157     for(int i=0;i<n;i++){
158         if(pre[i]==data[i]){
159             pcnt++;
160         }
161         if(post[i]==data[i]){
162             mcnt++;
163         }
164     }
165     if(pcnt==n){
166         cout<<"YES"<<endl;
167         PostOrdered(tree);
168     }
169     else if(mcnt==n){
170         cout<<"YES"<<endl;
171         mPostOrder(tree);
172     }
173     else{
174         cout<<"NO"<<endl;
175     }
176     return 0;
177 }

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