1155 Heap Paths （30 分）
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题意：
给你一棵完全二叉树的层序遍历，即可以得到一个堆，需要你从右子树开始镜像的输出从根到叶，并判断是大顶堆还是小顶堆还是不是堆
思路：
dfs生成堆，并注意到达叶子结点的标志
完全二叉树判断某个结点是否为叶子结点的标志是该节点root的左子节点的编号root*2是否大于结点总个数 n
中间利用几个bool变量来判断是什么堆 （注意堆的根节点的数组下标一定要从1开始）
#include<iostream>
#include<vector>
using namespace std;
const int maxn=1005;
bool max_flag=false,min_flag=false,not_flag=false;
int level[maxn];
vector<int>path;
int n;
void dfs(int root)
{
path.push_back(level[root]);
if(root*2>n)//表示该结点为叶子结点
{
for(int i=0;i<path.size();i++)
{
printf("%d",path[i]);
if(i>0)
{
if(path[i]<=path[i-1])
max_flag=true;
else if(path[i]>=path[i-1])
min_flag=true;
if(min_flag==true&&max_flag==true)
not_flag=true;
}
if(i<path.size()-1)
printf(" ");
else
printf("\n");
}
}
else
{
if(root*2+1<=n)//右子树先
dfs(root*2+1);
if(root*2<=n)//再左子树
dfs(root*2);
}
path.pop_back();
}
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;i++)
{//注意这里要从1开始
scanf("%d",&level[i]);
}
dfs(1);//1号位进入
if(not_flag)
printf("Not Heap\n");
else
{
if(max_flag)
printf("Max Heap\n");
else if(min_flag)
printf("Min Heap\n");
}
}