PAT甲级 1155 Heap Paths (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))

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 (1<N≤1,000), the number of keys in the tree. Then the next line 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, 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 <iostream>
#include <vector>
#include <cmath>

using namespace std;
int n;
int heap[1005];
int l;
vector<int> v;
int status = -1;// 初始化为-1,0为min,1为max，2为状态翻转

int judge(int a, int b) {
    if (a < b) return 0;
    else
        return 1;
}

void print_route(int m) {
    if (m * 2 > n && m * 2 + 1 > n) {
        if (m <= n) {
            for (int i = 1; i < v.size(); ++i) {
                if (status == -1)
                    status = judge(v[i - 1], v[i]);
                if (status != judge(v[i - 1], v[i]))
                    status = 2;
                if (i - 1 == 0)
                    cout << v[i - 1];
                else
                    cout << " " << v[i - 1];
            }
            cout << " " << v[v.size() - 1] << endl;
        }
    } else {
        v.push_back(heap[m * 2 + 1]);
        print_route(m * 2 + 1);
        v.pop_back();
        v.push_back(heap[m * 2]);
        print_route(m * 2);
        v.pop_back();
    }
}

int main() {
    cin >> n;
    for (int i = 1; i <= n; ++i)
        cin >> heap[i];
    v.push_back(heap[1]);
    print_route(1);
    if (status == 2)
        cout << "Not Heap";
    else if (status == 1)
        cout << "Max Heap";
    else
        cout << "Min Heap";
    return 0;
}