PAT A1147

1147 Heaps （30 分）
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
作者: CHEN, Yue
单位: 浙江大学
时间限制: 200 ms
内存限制: 64 MB
代码长度限制: 16 KB
此题和A1155题目类似，但用了两种不同的方法来判别是哪种堆：
1.通过各叶节点路径是否有序。（利用此是基于在题目的背景下催生的）
2.各顶点是否大于或小于子节点。（显然此方法简单一些）

#include<cstdio>
#include<algorithm>
#include<vector>
using namespace std;
int q, n;
int cnt = 0;
void postOR(int num, vector <int> arr) {
	if (num > n)
		return;
	postOR(2 * num, arr);
	postOR(2 * num + 1, arr);
	printf("%d", arr[num]);
	cnt++;
	if (cnt < n) {
		printf(" ");
	}
}
int main() {
	int flag1 = 0;
	int flag2 = 0;
	scanf("%d%d", &q, &n);
	for (int i = 0; i < q; i++) {
		vector<int> arr(n + 1);
		flag1 = 0;//标记量，显然若不是大顶堆或小顶堆，会使flag1及flag2同时为1！
		flag2 = 0;//标记量，显然若不是大顶堆或小顶堆，会使flag1及flag2同时为1！
		cnt = 0;
		for (int j = 1; j <= n; j++) {
			scanf("%d", &arr[j]);
		}
		for (int j = 2; j <= n; j++) {//判断是哪种类型的堆
			if (arr[j / 2] > arr[j]){
				flag1 = 1;
			}
			else {
				flag2 = 1;
			}
		}
		if (flag1 && flag2) {
			printf("Not Heap\n");
		}
		else if(flag1){
			printf("Max Heap\n");
		}
		else if (flag2) {
			printf("Min Heap\n");
		}
		postOR(1, arr);
		printf("\n");
	}
	return 0;
}