1155 Heap Paths (30 分)——甲级（堆+dfs回溯）

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<N≤1,000), the number of keys in the tree. Then the next line 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, 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

题目大意：给出一颗完全二叉树的层序遍历，从左到右输出所有从根节点到叶子节点的路径，并判断是否为最大堆或最小堆。
思路：判断堆与上题类似。输出路径用dfs。

代码如下：

#include <stdio.h>
int n, ans[20], a[1001];
int is_max = 1, is_min = 1;
void dfs(int index, int cnt)
{
    if(index > n) return ;/* 空结点返回 */
    if(2*index <= n)/* 判断是否为堆 */
    {
        if(a[index] > a[2*index]) is_min = 0;
        if(a[index] < a[2*index]) is_max = 0;
        if(2*index+1 <= n)
        {
            if(a[index] > a[2*index+1]) is_min = 0;
            if(a[index] < a[2*index+1]) is_max = 0;
        }
    }
    ans[cnt] = a[index];/* 记录答案 */
    if(index*2 > n)/* 如果已经是叶子节点 */
    {
        int i;
        for(i=1; i<=cnt; i++)
            printf("%d%c", ans[i], i == cnt ? '\n':' ');
        return ;
    }
    dfs(index*2+1, cnt+1);/* 递归右子树 */
    dfs(index*2, cnt+1);/* 递归左子树 */
}
int main()
{
    scanf("%d", &n);
    int i;
    for(i=1; i<=n; i++) scanf("%d", &a[i]);
    dfs(1, 1);
    if(is_max == 1) printf("Max Heap\n");
    else if(is_min == 1) printf("Min Heap\n");
    else printf("Not Heap\n");
    return 0;
}