PAT (Advanced Level) Practice 1147 Heaps (30分) （最大最小堆的判断 两种方法）

1.题目

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

2.题目分析

可以使用make_heap建堆在进行比较，因为给的是树的层序，也可以从下向上看，大根堆是根节点比左右节点都大，小根堆反之。

3.代码

方法一（输出回车的方式很SB……）

#include<iostream>
#include<vector>
#include <functional> 
#include <algorithm>
using namespace std;
void output(vector<int>list,int i,int n,int &space)
{
	if (i > n)return;
	output(list, 2 * i, n,space);
	output(list, 2 * i+1, n,space);
	printf("%s%d", space == 0 ? "" : " ", list[i - 1]);
	space++;

}
int main()
{
	int m, n,temp;
	scanf("%d %d", &m, &n);
	for (int i = 0; i < m; i++)
	{
		vector<int>list;
		vector<int>tries;
		int space = 0;
		bool ismax = true;
		bool ismin = true;
		for (int j = 0; j < n; j++)
		{
			scanf("%d", &temp);
			list.push_back(temp);
			tries.push_back(temp);
		}
		make_heap(tries.begin(), tries.end(), less<int>());
		for (int j = 0; j < n; j++)
			if (tries[j] != list[j])ismax = false;
		if (ismax) { printf("Max Heap
"); output(list, 1, n, space); printf("
"); continue; }
		make_heap(tries.begin(), tries.end(), greater<int>());
		for (int j = 0; j < n; j++)
			if (tries[j] != list[j])ismin = false;
		if (ismin) { printf("Min Heap
"); output(list, 1, n, space); printf("
");  continue; }
		printf("Not Heap
"); output(list, 1, n, space); printf("
");
	}

}

 方法二：学习柳神代码（https://blog.csdn.net/liuchuo/article/details/79810648）

相当佩服

#include<iostream>
using namespace std;
int a[1010];
int m,n;
void output(int i)
{
	if (i > n)return;
	output (2 * i);
	output( 2 * i+1);
	printf("%d%s", a[i], i == 1 ? "
" : " ");
}
int main()
{
	scanf("%d %d", &m, &n);
	for (int i = 0; i < m; i++)
	{
		bool ismax = true, ismin = true;
		for (int j = 1; j <=n; j++)
			scanf("%d", &a[j]);
		for (int j = n; j > 1; j--)
		{
			if (a[j] > a[j / 2])ismax = false;
			if (a[j] < a[j / 2])ismin = false;
		}
		if (ismax)printf("Max Heap
");
		else if (ismin)printf("Min Heap
");
		else printf("Not Heap
");
		output(1);
	}
}