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 <stdio.h>

#include <algorithm>

#include <set>

#include <vector>

#include <string>

#include <iostream>

#include <queue>

using namespace std;

const int maxn=;

int tree[maxn] ;

int n;

vector<int> v;

void dfs(int st){

    v.push_back(tree[st]);

    if(st*>n){

        if(st<=n){

            for(int i=;i<v.size();i++){

                printf("%d%s",v[i],i!=v.size()-?" ":"\n");

            }

        }

    }

    else{

        //v.push_back(tree[st*2+1]);

        dfs(st*+);

        //v.pop_back();

        //v.push_back(tree[st*2]);

        dfs(st*);

    }

    v.pop_back();

}

int main(){

    scanf("%d",&n);

    int ismax=,ismin=;

    for(int i=;i<=n;i++){

        scanf("%d",&tree[i]);

    }

    dfs();

    for(int i=;i<=n;i++){

        if(tree[i/]>tree[i])ismin=;

        if(tree[i/]<tree[i])ismax=;

    }

    if(ismin==)printf("Min Heap\n");

    else{

        printf("%s\n",ismax==?"Max Heap":"Not Heap");

    }

}