A1147

1147 Heaps (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))

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

判断是否为小顶堆跟大顶堆,遍历一遍判断结点与根结点的大小关系即可（判断的起始结点从2开始，1是根结点不需要比较），最后后序输出。。

#include<bits/stdc++.h>
using namespace std;
int N,K,ismax=1,ismin=1,ok;
int isheap(int heap[]){
    for(int i=2;i<K+1;i++){
        if(heap[i]<heap[i/2])   ismin=0;
        if(heap[i]>heap[i/2])   ismax=0;        
    }
}
void postorder(int heap[],int root){
    if(root>K)return;
    postorder(heap,2*root);
    postorder(heap,2*root+1);
    if(ok++)printf(" ");
    printf("%d",heap[root]);
}
int main(){
    cin>>N>>K;
    for(int i=0;i<N;i++){
        int heap[K+1];
        ismax=1,ismin=1,ok=0;
        for(int j=1;j<=K;j++){
            scanf("%d",&heap[j]);
        }
        isheap(heap);
        if(ismax)   printf("Max Heap\n");
        else if(ismin) printf("Min Heap\n");
        else printf("Not Heap\n");
        postorder(heap,1);
        printf("\n");
    }
    return 0;
}