A1147 Heaps（30分）PAT 甲级(Advanced Level) Practice（C++）满分题解【最大最小堆】

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

题意分析：

参考了柳神的题解

注意在层序遍历中，如果根节点的标号为i，则它的两个儿子的标号分别为2i和2i+1

反过来由两个儿子来索引父亲节点，如果儿子的标号为i，则他们的父节点就为i/2

代码如下：

#include
using namespace std;
int m, n;
vector<int> vec;
void postOrder(int root)
{
	if (root > n)return;
	postOrder(root * 2);
	postOrder(root * 2 + 1);
	cout << vec[root];
	if (root != 1)cout << " ";
    else cout << endl;
}
int main()
{
	cin >> m >> n;
	vec.resize(n + 1);
	while (m--) {
		bool minHeap = true, maxHeap = true;
		for (int i = 1; i <= n; i++)
			cin >> vec[i];
		for (int i = 2; i <= n; i++) {
			if (vec[i] > vec[i / 2]) {
				maxHeap = false;
			}
			if (vec[i] < vec[i / 2]) {
				minHeap = false;
			}
		}
		if (maxHeap)cout << "Max Heap" << endl;
		else if (minHeap)cout << "Min Heap" << endl;
		else cout << "Not Heap" << endl;
		postOrder(1);
	}
}

运行结果如下：