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))

One thing for sure is that all the keys along any path from the root to a leaf in a max/min heap must be in non-increasing/non-decreasing order.

Your job is to check every path in a given complete binary tree, in order to tell if it is a heap or not.

## Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (1<N≤1,000), the number of keys in the tree. Then the next line 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, first print all the paths from the root to the leaves. Each path occupies a line, with all the numbers separated by a space, and no extra space at the beginning or the end of the line. The paths must be printed in the following order: for each node in the tree, all the paths in its right subtree must be printed before those in its left subtree.

Finally 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.

## 解答

#include<iostream>
#include<vector>
#include<set>

#define NOTHEAP 0
#define MAXHEAP 1
#define MINHEAP 2

using namespace std;

int keysNum;
vector<int> path, nodes;
set<int> flags;
void preOrderReverse(int id)
{
path.push_back(nodes[id]);
if (2 * id > keysNum) { // 叶子结点
bool sub[2] = { false, false };
printf("%d", path[0]);
for (int i = 1; i < path.size(); i++) {
printf(" %d", path[i]);
if (path[i] < path[i - 1]) sub[0] = true;
else if(path[i] > path[i - 1]) sub[1] = true;
}
if (sub[0] && sub[1]) flags.insert(NOTHEAP);
else if (sub[0]) flags.insert(MAXHEAP);
else if (sub[1]) flags.insert(MINHEAP);
printf("\n");
path.pop_back();
return;
}
// 有右孩子才访问左子树，否则会多输出一条路径
if (id * 2 + 1 <= keysNum) preOrderReverse(id * 2 + 1);
preOrderReverse(id * 2);
path.pop_back();
}
int main()
{
cin >> keysNum;
nodes.resize(keysNum + 1);
for (int i = 0; i < keysNum; i++) cin >> nodes[i + 1];
preOrderReverse(1);
if (flags.size() != 1 || *flags.begin() == NOTHEAP) printf("Not Heap");
else if (*flags.begin() == MINHEAP) printf("Min Heap");
else if (*flags.begin() == MAXHEAP) printf("Max Heap");
return 0;
}