1155 Heap Paths （30 分）判断是否是一个堆

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

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:

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

思路：
　　1、由于输入是层序遍历，且是完全二叉树，所以使用一个数组存储树，根节点下标为1，这样i是根节点，2*i是左孩子，2*i+1是
右孩子。然后按照先右子树再左子树的顺序遍历树，并且存储遍历路径，当遇到叶子结点时候输出。
　　2、由于题目中给出的结点数目N满足1<N<=1,000，所以在遍历之前先使用第一个结点和第二个结点进行比较，做一个预判断，根据判断
结果，假设其为max heap或者min heap。再输出路径的时候再判断与假设是否一致即可，详情请看代码。

#include<iostream>
#include<vector>
#include<algorithm>
#include<queue>
#include<string>
#include<map>
#include<set>
using namespace std;
bool flag=true;
vector<int> path;
//对树进行深度遍历
void print(int tree[],int i,int n,bool isBig)
{
    //cout<<i<<" ";
    path.push_back(tree[i]);
    //cout<<tree[i]<<endl;
    if(2*i>n)
    {
        if(isBig)
        {
            // cout<<endl;
            if(path.size()>0)
                cout<<path[0];
            for(int j=1; j<path.size(); j++)
            {
                if(path[j]>path[j-1])
                    flag=false;
                cout<<" "<<path[j];
            }
            cout<<endl;

        }
        else
        {
            if(path.size()>0)
                cout<<path[0];
            for(int j=1; j<path.size(); j++)
            {
                if(path[j]<path[j-1])
                    flag=false;
                cout<<" "<<path[j];
            }
            cout<<endl;
        }
        return;
    }
    if(2*i+1<=n)
    {
        print(tree,2*i+1,n,isBig);
        path.pop_back();
    }
    if(2*i<=n)
    {
        print(tree,2*i,n,isBig);
        path.pop_back();
    }
}




int main()
{
    int n;
    scanf("%d",&n);
    int tree[n+1];
    for(int i=1; i<=n; i++)
    {
        scanf("%d",&tree[i]);
        // cout<<tree[i]<<endl;
    }
    // path.push_back(tree[1]);
    if(tree[1]<tree[2])//如果是min heap，则父节点小
    {
        print(tree,1,n,false);
        if(flag)
            cout<<"Min Heap"<<endl;
        else
            cout<<"Not Heap"<<endl;
    }
    else
    {
        print(tree,1,n,true);
        if(flag)
            cout<<"Max Heap"<<endl;
        else
            cout<<"Not Heap"<<endl;
    }

    return 0;
}