1155 Heap Paths

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 (1int), 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.

Sample Input 1:

8
98 72 86 60 65 12 23 50

Sample Output 1:

98 86 23
98 86 12
98 72 65
98 72 60 50
Max Heap

Sample Input 2:

8
8 38 25 58 52 82 70 60

Sample Output 2:

8 25 70
8 25 82
8 38 52
8 38 58 60
Min Heap

Sample Input 3:

8
10 28 15 12 34 9 8 56

Sample Output 3:

10 15 8
10 15 9
10 28 34
10 28 12 56
Not Heap

#include 
using namespace std;
int n, flag;
int a[1010], t[1010];

void dfs(int i, int c) {
	if (2 * i + 1 >= n) {
		t[c] = a[i];
		for (int i = 0; i <= c; i++) {
			cout << t[i];
			if (i != c) {
				cout << ' ';
			}
		}
		cout << endl;
		return;
	}
	t[c] = a[i];
	if (2 * i + 2 < n) {
		if (a[i] > a[2 * i + 2] && flag != 3 && flag != 2) {
			flag = 1;
		} else if (a[i] > a[2 * i + 2] && flag == 2) {
			flag = 3;
		} else if (a[i] < a[2 * i + 2] && flag != 3 && flag != 1) {
			flag = 2;
		} else if (a[i] < a[2 * i + 2] && flag == 1) {
			flag = 3;
		}
		dfs(2 * i + 2, c + 1);
	}
	if (2 * i + 1 < n) {
		if (a[i] > a[2 * i + 1] && flag != 3 && flag != 2) {
			flag = 1;
		} else if (a[i] > a[2 * i + 1] && flag == 2) {
			flag = 3;
		} else if (a[i] < a[2 * i + 1] && flag != 3 && flag != 1) {
			flag = 2;
		} else if (a[i] < a[2 * i + 1] && flag == 1) {
			flag = 3;
		}
		dfs(2 * i + 1, c + 1);
	}
}

int main() {
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}
	dfs(0, 0);
	if (flag == 1) {
		cout << "Max Heap";
	} else if (flag == 2) {
		cout << "Min Heap";
	} else {
		cout << "Not Heap";
	}
	return 0;
}