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

一直一个树，我们要判断是最大堆，最小堆，还是不是堆，并且打印后序遍历。

通过0位和1位确定堆是如何的，然后进行判断其他节点是否符合，不符合打印不是，否则打印是

#include <iostream>
using namespace std;
int M, N, tree[2000], judge, start;
void dfs(int index) {
    if(2 * index + 1 < N) {
        if(judge == 1 && tree[index] < tree[2 * index + 1]) judge = -1;
        if(judge == 0 && tree[index] > tree[2 * index + 1]) judge = -1;
        dfs(2 * index + 1);
    }
    if(2 * index + 2 < N) {
        if(judge == 1 && tree[index] < tree[2 * index + 2]) judge = -1;
        if(judge == 0 && tree[index] > tree[2 * index + 2]) judge = -1;
        dfs(2 * index + 2);
    }
}
void post(int index) {
    if(index >= N) return;
    post(2 * index + 1);
    post(2 * index + 2);
    if(start) {
        printf("%d", tree[index]);
        start = !start;
    } else printf(" %d", tree[index]);
}
int main() {
    cin >> M >> N;
    while(M--) {
        for(int i = 0; i < N; i++) cin >> tree[i];
        judge = tree[0] > tree[1]; // judge 1 大根 0 根 -1 不是
        dfs(0);
        if(judge == 1) cout << "Max Heap" << endl;
        else if(judge == 0) cout << "Min Heap" << endl;
        else cout << "Not Heap" << endl;
        start = 1;
        post(0);
        cout << endl;
    }
    return 0;
}