PAT 1147. Heaps (30) – 甲级

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 <= 1000), 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 trees 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

题目大意:给一个树的层序遍历,判断它是不是堆,是大顶堆还是小顶堆。输出这个树的后序遍历~
分析:30分大题,28行代码,一行代码一分……((⊙o⊙)嗯) // 我为什么这么机智可爱又伶俐?
首先根据v[0]和v[1]的大小比较判断可能是大顶还是小顶,分别赋值flag为1和-1,先根据层序遍历,从0~(n-1)/2【所有有孩子的结点】判断他们的孩子是不是满足flag的要求,如果有一个结点不满足,那就将flag=0表示这不是一个堆。根据flag输出是否是堆,大顶堆还是小顶堆,然后后序遍历,根据index分别遍历index*2+1和index*2+2,即他们的左右孩子,遍历完左右子树后输出根结点,即完成了后序遍历~

 

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