1147. Heaps (30)

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 <= 1000), 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


判断最堆只需要判断从头到尾是否是一致的双亲大于（小于）左右儿子。
代码：

#include <iostream>
#include <cstring>
#include <cstdio>
#include <map>
#define Max 1005
using namespace std;
int n,m,h[Max],flag;
bool check(bool tag)
{
    for(int i = 1;i * 2 <= n;i ++)
    {
        if(h[i] != h[i * 2] && h[i] > h[i * 2] == tag)return 0;
        if(i * 2 + 1 <= n && h[i] != h[i * 2 + 1] && h[i] > h[i * 2 + 1] == tag)return 0;
    }
    return 1;
}
void post_order(int t)
{
    if(t * 2 <= n)post_order(t * 2);
    if(t * 2 + 1 <= n)post_order(t * 2 + 1);
    if(flag ++)printf(" %d",h[t]);
    else printf("%d",h[t]);
}
int main()
{
    scanf("%d%d",&m,&n);
    while(m --)
    {
        for(int i = 1;i <= n;i ++)
        {
            scanf("%d",&h[i]);
        }
        if(check(false))puts("Max Heap");
        else if(check(true))puts("Min Heap");
        else puts("Not Heap");
        flag = 0;
        post_order(1);
        puts("");
    }
}