1155 Heap Paths-PAT甲级

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

题目中给出的树为完全二叉树 的层次遍历形式，我们只需要将其按照先遍历右子树，在遍历左子树的顺序输出从根结点到叶子结点的路径即可。其次判断是大顶堆还是小顶堆，按照定义判断即可

满分代码如下：

#include<bits/stdc++.h>
using namespace std;
const int N=1005;
int heap[N];
int n;
vector<int>path;
int flagb=0,flags=0;
void check(){
	flagb=0,flags=0;
	for(int i=1;i<=n/2;i++){
		if(i*2<=n){
			if(heap[i]>=heap[2*i]){
				flagb=1;
			}else{
				flags=1;
			}
		}
		if(2*i+1<=n){
			if(heap[i]>=heap[2*i+1]){
				flagb=1;
			}else{
				flags=1;
			}
		}
	}
}
void dfs(int root){
	if(root>n){
		return;
	}
	path.push_back(heap[root]);
	if(root*2>n){
		//没有左子树
		for(int i=0;i<path.size();i++){
			if(i!=0) printf(" ");
			printf("%d",path[i]);
		} 
		printf("\n");
	}
	dfs(2*root+1);
	dfs(2*root);
	path.pop_back();
	
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d",&heap[i]);
	}
    dfs(1);
    check();
    if(flagb==1&&flags==0){
    	printf("Max Heap\n");
	}else if(flagb==0&&flags==1){
		printf("Min Heap\n");
	}else{
		printf("Not Heap\n");
	}
	return 0;
}