A1147. Heaps

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

#include<iostream>
#include<cstdio>
using namespace std;
int N, M, tree[10010];
int isMaxheap(){
    for(int k = N / 2; k >= 1; k--){
        int max;
        if(2*k + 1 <= N && tree[2*k+1] > tree[2*k]){
            max = tree[2*k + 1];
        }else{
            max = tree[2*k];
        }
        if(tree[k] < max)
            return 0;
    }
    return 1;
}
int isMinheap(){
    for(int k = N / 2; k >= 1; k--){
        int min;
        if(2*k+1 <= N && tree[2*k+1] < tree[2*k]){
            min = tree[2*k+1];
        }else min = tree[2*k];
        if(tree[k] > min)
            return 0;
    }
    return 1;
}
int cnt = 0;
void postOrder(int root){
    if(root > N)
        return;
    postOrder(root*2);
    postOrder(root*2 + 1);
    cnt++;
    if(cnt == N)
        printf("%d\n", tree[root]);
    else printf("%d ", tree[root]);
}
int main(){
    scanf("%d%d", &M, &N);
    for(int i = 0; i < M; i++){
        for(int i = 1; i <= N; i++){
            scanf("%d", &tree[i]);
        }
        if(isMaxheap()){
            printf("Max Heap\n");
        }else if(isMinheap()){
            printf("Min Heap\n");
        }else{
            printf("Not Heap\n");
        }
        cnt = 0;
        postOrder(1);
    }
    cin >> N;
    return 0;
}

总结：

1、题意：检查每个给出的序列是否是一个大根堆或者小根堆。