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
给定一个完全二叉树的层次遍历,判断该树是否为大顶堆或者小顶堆,同时写出该完全二叉树的后序排列
分为两步:
1、由完全二叉树的层次遍历得出其后序遍历
2、判断大顶堆还是小顶堆
均为DFS
#include <string>
#include <iostream>
#include <vector>
using namespace std;
int m,n;
std::vector<int> level,post;
bool result;
void posttravel(int root){
if(root>n)
return;
posttravel(2*root);
posttravel(2*root+1);
post.push_back(level[root]);
}
void dfs(bool flag,int root,int index){
if(flag==true){
if(index>n)
return;
if(root<level[index])
result=false;
dfs(flag,level[index],2*index);
dfs(flag,level[index],2*index+1);
}
else{
if(index>n)
return;
if(root>level[index])
result=false;
dfs(flag,level[index],2*index);
dfs(flag,level[index],2*index+1);
}
}
int main(){
scanf("%d %d",&m,&n);
level.resize(n+1);
for(int i=0;i<m;i++){
for(int j=1;j<=n;j++)
scanf("%d",&level[j]);
result=true;
post.clear();
posttravel(1);
dfs(true,level[1],1);
if(result==true)
cout<<"Max Heap\n";
else{
result=true;
dfs(false,level[1],1);
if(result==true)
cout<<"Min Heap\n";
else
cout<<"Not Heap\n";
}
printf("%d",post[0]);
for(int i=1;i<n;i++)
printf(" %d",post[i]);
printf("\n");
}
}