PAT 1147 Heaps（30 分）

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of C. A common implementation of a heap is the binary heap, in which the tree is a complete binary tree. (Quoted from Wikipedia at https://en.wikipedia.org/wiki/Heap_(data_structure))

Your job is to tell if a given complete binary tree is a heap.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers: M (

Output Specification:

For each given tree, print in a line Max Heap if it is a max heap, or Min Heap for a min heap, or Not Heap if it is not a heap at all. Then in the next line print the tree's postorder traversal sequence. All the numbers are separated by a space, and there must no extra space at the beginning or the end of the line.

Sample Input:

3 8
98 72 86 60 65 12 23 50
8 38 25 58 52 82 70 60
10 28 15 12 34 9 8 56

Sample Output:

Max Heap
50 60 65 72 12 23 86 98
Min Heap
60 58 52 38 82 70 25 8
Not Heap
56 12 34 28 9 8 15 10

 1 #include<iostream>
 2 #include<vector>
 3 #include<algorithm>
 4 #include<stack>
 5 using namespace std;
 6 int n, m;
 7 bool isHeap1(vector<int>& v){//判断大堆顶
 8   int j = n/2;
 9   while(j>0){
10     if(v[j]>=v[j*2]){
11       if(j*2+1<=n && v[j]>=v[j*2+1] || j*2+1>n) j--;
12       else return false;
13     }
14     else return false;
15   }
16   return true;
17 }
18 
19 bool isHeap2(vector<int>& v){//判断小堆顶
20   int j=n/2;
21   while(j>0){
22     if(v[j]<=v[j*2]){
23       if(j*2+1<=n && v[j]<=v[j*2+1] || j*2+1>n) j--;
24       else return false;
25     }
26     else return false;
27   }
28   return true;
29 }
30 vector<int>  vis(1001, false), v(1001);
31 void postOrder(){//非递归后序遍历
32     stack<int> s;
33     vector<int> post;
34     int idx;
35     s.push(1);
36     while(s.size()){
37         idx = s.top();
38         if(idx*2<=n && !vis[idx*2]){
39             s.push(idx*2);
40             vis[idx*2] = true;
41         }else{
42             post.push_back(v[s.top()]);
43             s.pop();
44             if(s.size()){
45             idx = s.top()*2+1;
46             if(idx<=n && !vis[idx]){
47                 s.push(idx);
48                 vis[idx] = true;
49             }
50             }
51         }
52     }
53     for(int i=0; i<post.size(); i++){
54         if(i==0) printf("%d", post[i]);
55         else printf(" %d", post[i]);
56     }
57     printf("\n");
58 }
59 int main(){
60   int i, j;
61   scanf("%d %d", &m, &n);
62   for(i=0; i<m; i++){
63     for(j=1; j<=n; j++)scanf("%d", &v[j]);
64     bool flag;
65       fill(vis.begin(), vis.end(), false);
66     if(v[1]>=v[2] && v[1]>=v[3]){
67       flag = isHeap1(v);
68         if(flag) printf("Max Heap\n"); 
69         else printf("Not Heap\n"); 
70         postOrder();
71     }else {
72       flag = isHeap2(v);
73         if(flag) printf("Min Heap\n"); 
74         else printf("Not Heap\n"); 
75         postOrder();
76     }
77   }
78   return 0;
79 }