1147 Heaps

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

#include 
using namespace std;
int m, n, cnt, flag;
int a[1010], post[1010];
 
void postorder(int x) {
	if (x > n) {
		return;
	}
	postorder(2 * x);
	postorder(2 * x + 1);
	post[cnt++] = a[x];
}
 
int main() {
	cin >> m >> n;
	while (m--) {
		cnt = 0;
		flag = 0;
		for (int i = 1; i <= n; i++) {
			cin >> a[i];
		}
		postorder(1);
		for (int i = 1; i <= n; i++) {
			if (2 * i <= n && flag != 3) {
				if (a[i] < a[i * 2] && flag != 2) {
					flag = 1;
				} else if (a[i] > a[i * 2] && flag != 1) {
					flag = 2;
				} else {
					flag = 3;
				}
			}
			if (2 * i + 1 <= n && flag != 3) {
				if (a[i] < a[i * 2 + 1] && flag != 2) {
					flag = 1;
				} else if (a[i] > a[i * 2 + 1] && flag != 1) {
					flag = 2;
				} else {
					flag = 3;
				}
			}
		}
		if (flag == 1) {
			cout << "Min Heap" << endl;
		} else if (flag == 2) {
			cout << "Max Heap" << endl;
		} else if (flag == 3) {
			cout << "Not Heap" << endl;
		}
		for (int i = 0; i < cnt; i++) {
			cout << post[i];
			if (i != cnt - 1) {
				cout << ' ';
			}
		}
		if (m) {
			cout << endl;
		}
	}
	return 0;
}