PAT_A1155#Heap Paths

Address:

https://pintia.cn/problem-sets/994805342720868352/problems/1071785408849047552

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:

 1 /*
 2 Data: 2019-05-06 21:04:46
 3 Problem: PAT_A1155#Heap Paths
 4 AC: 48:00
 5 */
 6 
 7 #include<cstdio>
 8 #include<vector>
 9 #include<cmath>
10 using namespace std;
11 const int M=1e3+10;
12 int heap[M], n, isMax=1,isMin=1;
13 vector<int> path;
14 
15 void DFS(int fa, int root)
16 {
17     if(fa != 0)
18     {
19         if(heap[fa]>heap[root])     isMin=0;
20         if(heap[fa]<heap[root])     isMax=0;
21     }
22     path.push_back(heap[root]);
23     if(root>n/2)
24     {
25         for(int i=0; i<path.size(); i++)
26             printf("%d%c", path[i], i==path.size()-1?'n':' ');
27         return;
28     }
29     if(root*2+1<=n)
30     {
31         DFS(root, root*2+1);
32         path.pop_back();
33     }
34     if(root*2<=n)
35     {
36         DFS(root, root*2);
37         path.pop_back();
38     }
39 }
40 
41 int main()
42 {
43 #ifdef    ONLINE_JUDGE
44 #else
45     freopen("Test.txt", "r", stdin);
46 #endif
47 
48     scanf("%d", &n);
49     for(int i=1; i<=n; i++)
50         scanf("%d", &heap[i]);
51     DFS(0,1);
52     if(isMax)
53         printf("Max Heapn");
54     else if(isMin)
55         printf("Min Heapn");
56     else
57         printf("Not Heapn");
58 
59     return 0;
60 }

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