PAT_A1155#Heap Paths

Source:

PAT A1155 Heap Paths (30 分)

Description:

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 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

Keys：

• 堆（Heap）；
• 完全二叉树（Complete Binary Tree）；
• 深度优先搜索（Depth First Search）；

Attention:

• 完全二叉树采用静态存储，CBTree[1...n]，从2/n+1开始为叶子结点；
• 采用RNL遍历

Code:

/*
Data: 2019-08-03 19:57:18
Problem: PAT_A1155#Heap Paths
AC: 33:40

题目大意：
层次遍历给出一棵完全二叉树，
输出根结点到各个叶子结点的路径，并判断是否为堆
输出顺序：从最右叶子到最左叶子
基本思路：
根右左的顺序遍历二叉树并存储路径，到达叶子结点时打印路径
若父亲大于孩子，则非小根堆；
若父亲小于孩子，则非大根堆；
*/
#include<cstdio>
#include<vector>
using namespace std;
const int M=1e3+10;
int n,heap[M],Max=1,Min=1;
vector<int> path;

void Travel(int root)
{
    if(root > n)
        return;
    path.push_back(heap[root]);
    if(root!=1 && heap[root]>heap[root/2])
        Max=0;
    if(root!=1 && heap[root]<heap[root/2])
        Min=0;
    if(root > n/2)
        for(int i=0; i<path.size(); i++)
            printf("%d%c", path[i], i==path.size()-1?'\n':' ');
    Travel(root*2+1);
    Travel(root*2);
    path.pop_back();
}

int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("Test.txt", "r", stdin);
#endif // ONLINE_JUDGE

    scanf("%d", &n);
    for(int i=1; i<=n; i++)
        scanf("%d", &heap[i]);
    Travel(1);
    if(Max) printf("Max Heap");
    else if(Min)    printf("Min Heap");
    else    printf("Not Heap");

    return 0;
}