PAT_A1147#Heaps
Source:
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, orMin Heap
for a min heap, orNot 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:
Attention:
- 有点水了哈0,0;
Code:
1 /* 2 Data: 2019-06-29 16:15:43 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N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 基本思路: 16 静态树存储BST,遍历判断是否为堆 17 */ 18 #include<cstdio> 19 #include<vector> 20 using namespace std; 21 const int M=1e3+10; 22 int bst[M],Min,Max,n,m; 23 vector<int> path; 24 25 void Travel(int root) 26 { 27 if(root > n) 28 return; 29 if(root!=1) 30 { 31 if(bst[root/2] > bst[root]) 32 Min=0; 33 if(bst[root/2] < bst[root]) 34 Max=0; 35 } 36 Travel(root*2); 37 Travel(root*2+1); 38 path.push_back(bst[root]); 39 } 40 41 int main() 42 { 43 #ifdef ONLINE_JUDGE 44 #else 45 freopen("Test.txt", "r", stdin); 46 #endif // ONLINE_JUDGE 47 48 scanf("%d%d", &m,&n); 49 while(m--) 50 { 51 for(int i=1; i<=n; i++) 52 scanf("%d", &bst[i]); 53 Min=1; 54 Max=1; 55 path.clear(); 56 Travel(1); 57 if(Max) printf("Max Heap\n"); 58 else if(Min) printf("Min Heap\n"); 59 else printf("Not Heap\n"); 60 for(int i=0; i<n; i++) 61 printf("%d%c", path[i],i==n-1?'\n':' '); 62 } 63 64 return 0; 65 }