pat甲级 1155 Heap Paths （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))

One thing for sure is that all the keys along any path from the root to a leaf in a max/min heap must be in non-increasing/non-decreasing order.

Your job is to check every path in a given complete binary tree, in order to tell if it is a heap or not.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (1), the number of keys in the tree. Then the next line contains Ndistinct 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, first print all the paths from the root to the leaves. Each path occupies a line, with all the numbers separated by a space, and no extra space at the beginning or the end of the line. The paths must be printed in the following order: for each node in the tree, all the paths in its right subtree must be printed before those in its left subtree.

Finally 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.

Sample Input 1:

8
98 72 86 60 65 12 23 50

Sample Output 1:

98 86 23
98 86 12
98 72 65
98 72 60 50
Max Heap

Sample Input 2:

8
8 38 25 58 52 82 70 60

Sample Output 2:

8 25 70
8 25 82
8 38 52
8 38 58 60
Min Heap

Sample Input 3:

8
10 28 15 12 34 9 8 56

Sample Output 3:

10 15 8
10 15 9
10 28 34
10 28 12 56
Not Heap

考察堆的性质，总的来说很简单。
代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#define MAX 1000
#define DMAX 10000
using namespace std;
typedef long long ll;
int n;
int big,small;
int heap[MAX + 1],t[MAX + 1];
void print(int h) {
    for(int i = 0;i <= h;i ++) {
        printf("%d",t[i]);
        putchar(i < h ? ' ' : '
');
    }
}
void traversal(int k,int h) {
    if(k > n) {
        return ;
    }
    t[h] = heap[k];
    if(k * 2 > n) print(h);
    if(h) {
        if(t[h] > t[h - 1]) small = 1;
        else if(t[h] < t[h - 1]) big = 1;
    }
    traversal(k * 2 + 1,h + 1);
    traversal(k * 2,h + 1);
}
int main() {
    scanf("%d",&n);
    for(int i = 1;i <= n;i ++) {
        scanf("%d",&heap[i]);
    }
    traversal(1,0);
    if(big == small) puts("Not Heap");
    else if(big) puts("Max Heap");
    else puts("Min Heap");
}