1155 Heap Paths （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))

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 N (1<N≤1,000), the number of keys in the tree. Then the next line 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, 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:

8 25 70
8 25 82
8 38 52
8 38 58 60
Min Heap

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

经验总结：

emmmm  这一题其实就是 PAT 甲级 1147 Heaps 的稍微加强版，增加的就是，需要输出从根结点到叶结点的所有路径，并且输出要先输出左子树，后输出右子树，最后再判断一下这个树是大根堆，小根堆还是不是堆，终于做完啦，明天就要去考试啦，希望自己能取得一个不错的成绩，给自己加油！！ (/≧▽≦)/ *★,°*:.☆:*.°★* ヾ(^▽^*)))

AC代码

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