题目地址
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<algorithm>
#include<string>
#include<math.h>
#include<map>
#include<vector>
using namespace std;
const int maxn=10010;
int n,a[maxn];
void dfs1(int i){
    if(i>n) return;
    if(i*2>n&&i*2+1>n){
        int t=i;
        vector<int>v;
        while(t>=1){
            v.push_back(a[t]);t/=2;
        }
        for(int j=v.size()-1;j>=0;j--){
            if(j!=v.size()-1) cout<<" ";
            cout<<v[j];
        }
        cout<<endl;
    }
    dfs1(i*2+1);dfs1(i*2);
}
bool heap=1;
void max_dfs(int i){
    if(i>n) return;
    if(i*2<=n&&a[i*2]>a[i]) heap=0;
    if(i*2+1<=n&&a[i*2+1]>a[i]) heap=0;
    max_dfs(i*2);max_dfs(i*2+1);
}
void min_dfs(int i){
    if(i>n) return;
    if(i*2<=n&&a[i*2]<a[i]) heap=0;
    if(i*2+1<=n&&a[i*2+1]<a[i]) heap=0;
    min_dfs(i*2);min_dfs(i*2+1);
}
int main(){
    cin>>n;
    for(int i=1;i<=n;i++) cin>>a[i];
    dfs1(1);
    if(a[1]>a[n])
    {
        max_dfs(1);
        if(heap) cout<<"Max Heap"<<endl;
        else cout<<"Not Heap"<<endl;
    }
    else {
        min_dfs(1);
        if(heap) cout<<"Min Heap"<<endl;
        else cout<<"Not Heap"<<endl;
    }
}