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
代码：
#include <cstdio>
int queryCnt,n;
int CBT[1005];
void postOrderTraversal(int root)
{
if(root>n) return;
postOrderTraversal(root*2);
postOrderTraversal(root*2+1);
printf("%d",CBT[root]);
if(root==1) printf("\n");//因为是后序遍历，最后访问根节点，而根节点的下标固定为1
else printf(" ");
}
int main()
{
scanf("%d%d",&queryCnt,&n);
for(int i=0;i<queryCnt;i++){
for(int j=1;j<=n;j++)
scanf("%d",&CBT[j]);
//判断，层序遍历完全二叉树的非叶结点
int flag=CBT[1]>CBT[2]?1:0;//大顶堆标记为1，小顶堆标记为0。题目保证结点个数至少有两个。
for(int j=1;j<=n/2;j++){
if(flag==1){
if(CBT[j]<CBT[j*2] || (j*2+1<=n && CBT[j]<CBT[j*2+1])){
flag=-1;
break;
}
}
if(flag==0){
if(CBT[j]>CBT[j*2] || (j*2+1<=n && CBT[j]>CBT[j*2+1])){
flag=-1;
break;
}
}
}
if(flag==1) printf("Max Heap\n");
else if(flag==0) printf("Min Heap\n");
else printf("Not Heap\n");
//输出后续序列
postOrderTraversal(1);
}
return 0;
}
