PAT_A1147#Heaps

Source:

PAT A1147 Heaps (30 分)

Description:

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 (≤100), the number of trees to be tested; and N (1 < N ≤ 1,000), the number of keys in each tree, respectively. Then M lines follow, each contains N distinct integer keys (all in the range of int), which gives the level order traversal sequence of a complete binary tree.

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

Keys:

• 堆（Heap）
• 二叉树的遍历

Attention:

• 有点水了哈0,0；

Code:

 1 /*
 2 Data: 2019-05-19 20:12:32
 3 Problem: PAT_A1147#Heaps
 4 AC: 19:20
 5 
 6 题目大意：
 7 判断给定的完全二叉树是否是堆
 8 输入：
 9 第一行给出测试数M(<=100)和结点数N[1,1e3]
10 接下来M行，逐层给出完全二叉树的各个键值
11 输出：
12 大根堆，小根堆，非堆；
13 接下来输出二叉树的后序遍历
14 */
15 
16 #include<cstdio>
17 const int M=1e3+10;
18 int heap[M]={0},n,Max,Min;
19 
20 void IsHeap(int root)
21 {
22     if(root>n)
23         return;
24     if(root!=1)
25     {
26         if(heap[root] > heap[root/2])
27             Max=0;
28         if(heap[root] < heap[root/2])
29             Min=0;
30     }
31     IsHeap(root*2);
32     IsHeap(root*2+1);
33 }
34 
35 void PostOrder(int root)
36 {
37     if(root > n)
38         return;
39     PostOrder(root*2);
40     PostOrder(root*2+1);
41     printf("%d%c", heap[root],root==1?'\n':' ');
42 }
43 
44 int main()
45 {
46 #ifdef    ONLINE_JUDGE
47 #else
48     freopen("Test.txt", "r", stdin);
49 #endif
50 
51     int m;
52     scanf("%d%d", &m,&n);
53     while(m--)
54     {
55         Max=1;Min=1;
56         for(int i=1; i<=n; i++)
57             scanf("%d", &heap[i]);
58         IsHeap(1);
59         if(Max) printf("Max Heap\n");
60         else if(Min)    printf("Min Heap\n");
61         else    printf("Not Heap\n");
62         PostOrder(1);
63     }
64 
65     return 0;
66 }