1147.Heaps

题目描述

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

考点

1.最大堆、最小堆的判别；
2.后序遍历。

代码

#include 
#include 
using namespace std;
vector heap;
int n;
void postOrder(int key) {
    if (key > n) {
        return;
    }
    postOrder(key * 2);
    postOrder(key * 2 + 1);
    cout << heap[key] << (key == 1 ? "\n" : " ");
    
}
int main() {
    int m;
    cin >> m;
    cin >> n;
    heap.resize(n + 1);
    for (int i = 0; i < m; i++) {
        int min = 1, max = 1;
        for (int j = 1; j <= n; j++) {
            cin >> heap[j];
        }
        for (int k = 2; k <= n; k++) {
            if (heap[k / 2] > heap[k])min = 0;
            if (heap[k / 2] < heap[k])max = 0;
        }
        if (!max & !min) cout << "Not Heap" << endl;
        else {
            cout << (max == 1 ? "Max Heap" : "Min Heap") << endl;
        }
        postOrder(1);
    }
    return 0;
}