PAT 甲级 1147 Heaps

1147 Heaps （30 point(s)）

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

经验总结：

emmmm  可以说是很简单的一道30分题了，其实就是求二叉树的后序遍历序列（这里要利用完全二叉树下标的特性），在遍历的同时，顺便判断一下父结点与子结点之间的大小关系，最后输出堆的属性以及后序遍历序列，就结束啦~

AC代码

#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
const int maxn=1010;
int n,m,k,a[maxn],post[maxn],num=0;
bool ismax,ismin;
void postorder(int s)
{
	if(s>n)
		return ;
	if(s*2<=n)
	{
		if(a[s]<=a[s*2])
			ismax=false;
		if(a[s]>=a[s*2])
			ismin=false;
		postorder(s*2);
	}
	if((s*2+1)<=n)
	{
		if(a[s]<=a[s*2+1])
			ismax=false;
		if(a[s]>=a[s*2+1])
			ismin=false;
		postorder(s*2+1);
	}
	post[num++]=a[s];
}
int main()
{
	scanf("%d%d",&m,&n);
	for(int i=0;i<m;++i)
	{
		for(int j=1;j<=n;++j)
			scanf("%d",&a[j]);
		num=0;
		ismax=true;
		ismin=true;
		postorder(1);
		if(ismax==true)
			printf("Max Heap\n");
		else if(ismin==true)
			printf("Min Heap\n");
		else
			printf("Not Heap\n");
		for(int j=0;j<n;++j)
			printf("%d%c",post[j],j<n-1?' ':'\n');
	}
	return 0;
}