题目

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.

输入说明

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.

输出说明

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.

示例

输入

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

输出

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

Vocabulary

heap 堆

自己的想法

非常蠢的企图先把树建出来再挨个判断是大根堆还是小根堆，然后再将其转化为后序遍历输出。其实也有想过要不要直接根据二叉树的规律进行判断，因为对树相关的题目不够熟练所以打算先按自己的方法尝试一下，果然失败了。看了别人的答案之后才觉得自己的想法真是绕了太多的弯，且没能解决问题。

参考题解：

从后往前检查所有节点（除了根节点）和它的父节点的关系，判断是否破坏最大堆或者最小堆的性质，如果有不满足的情况将maxn或minn置为0，以此排除最大堆或者最小堆～

然后后序遍历，对于index结点分别遍历孩子index2和右孩子index2+1，遍历完左右子树后输出根结点～

参考代码

//https://www.liuchuo.net/archives/4667
#include <iostream>
using namespace std;
int a[1005], m, n;
void postOrder(int index) {
    if (index > n) return;
    postOrder(index * 2);
    postOrder(index * 2 + 1);
    printf("%d%s", a[index], index == 1 ? "\n" : " ");
}
int main() {
    scanf("%d %d", &m, &n);
    while (m--) {
        int minn = 1, maxn = 1;
        for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
        for (int i = 2; i <= n; i++) {
            if (a[i] > a[i / 2]) maxn = 0;
            if (a[i] < a[i / 2]) minn = 0;
        }
        if (maxn == 1) printf("Max Heap\n");
        else if (minn == 1) printf("Min Heap\n");
        else printf("Not Heap\n");
        postOrder(1);
    }
    return 0;
}