1147 Heaps （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))

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
思路
　　计算每个序列的最大值和最小值，因为如果是大顶堆，则第一个元素一定是这个序列的最大值，如果是小顶堆，则
这个序列的第一个元素一定是最小值，根据计算出的最大、最小值，初步判断这是一个大顶堆还是一个小顶堆。然后再
根据层次遍历序列进行验证，看是否满足堆的条件。

#include<iostream>
#include<string>
#include<vector>
#include<cmath>
#include<algorithm>
using namespace std;

int judge(int a[],int n,int flag)
{
    if(flag==-1)
        return -1;

    for(int i=1; i<=n/2; i++)
    {
        int j=2*i;
        if(j<n&&a[j]>a[j+1])
            j++;
        if(flag==1&&j<=n&&a[i]<a[j])
            return -1;
        else if(flag==0&&j<=n&&a[i]>a[j])
            return -1;
    }
    return flag;
}
vector<int> result;
void postOrder(int a[],int n,int root)
{
    if(root>n)
        return;
    postOrder(a,n,2*root);
    postOrder(a,n,2*root+1);
    result.push_back(a[root]);
}


int main()
{
    int m,n;
    scanf("%d%d",&m,&n);
    for(int i=0; i<m; i++)
    {
        int a[n+1],maxV=-10000,minV=10000,flag;
        for(int i=1; i<n+1; i++)
        {
            scanf("%d",&a[i]);
            minV=min(a[i],minV);
            maxV=max(a[i],maxV);
        }
        if(a[1]==maxV)
            flag=1;
        else if(a[1]==minV)
            flag=0;
        else
        {
            flag=-1;
        }
        flag=judge(a,n,flag);
        if(flag==1)
        {
            printf("Max Heap\n");
        }
        else if(flag==0)
        {
            printf("Min Heap\n");
        }
        else
        {
            printf("Not Heap\n");
        }
        result.clear();
        postOrder(a,n,1);
        printf("%d",result[0]);
        for(int i=1; i<n; i++)
            printf(" %d",result[i]);
        printf("\n");
    }
    return 0;
}