PAT甲级——1147 Heaps30

Posted 2020-11-22 zzw1024

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

第一种方法，比较笨，重建整棵树，然后判断是否时大根堆和小根堆，然后再遍历出后序遍历

 1 #include <iostream>
 2 #include <vector>
 3 #include <queue>
 4 #include <algorithm>
 5 using namespace std;
 6 int n, m;
 7 vector<int>level, post;
 8 struct Node
 9 {
10     int val;
11     Node *l, *r;
12     Node(int a = 0) :val(a), l(nullptr), r(nullptr) {}
13 };
14 Node* creatTree(bool &flag, const bool isMax)
15 {
16     Node* root = new Node(level[0]);
17     int k = 1;
18     queue<Node*>q;
19     q.push(root);
20     while (k < m)
21     {
22         Node *p = q.front();
23         q.pop();
24         p->l = new Node(level[k++]);
25         if (isMax && p->val<p->l->val || !isMax && p->val>p->l->val)
26             flag = false;
27         q.push(p->l);
28         if (k >= m)break;
29         p->r = new Node(level[k++]);
30         if (isMax && p->val < p->r->val || !isMax && p->val > p->r->val)
31             flag = false;
32         q.push(p->r);
33     }
34     return root;
35 }
36 void postOrder(Node *root)
37 {
38     if (root == nullptr)
39         return;
40     postOrder(root->l);
41     postOrder(root->r);
42     post.push_back(root->val);
43 }
44 int main()
45 {
46     cin >> n >> m;
47     while (n--)
48     {
49         level.clear();
50         level.resize(m);
51         post.clear();
52         int minN = INT32_MAX, maxN = -1;
53         for (int i = 0; i < m; ++i)
54         {
55             cin >> level[i];
56             minN = minN < level[i] ? minN : level[i];
57             maxN = maxN > level[i] ? maxN : level[i];
58         }
59         bool flag = true, isMax = false;
60         Node *root = nullptr;
61         if (level[0] == minN)//小根堆
62         {
63             isMax = false;
64             root = creatTree(flag, isMax);
65         }
66         else if (level[0] == maxN)
67         {
68             isMax = true;
69             root = creatTree(flag, isMax);
70         }
71         else
72         {
73             flag = false;
74             root = creatTree(flag, isMax);
75         }
76         postOrder(root);
77         if (flag && isMax)
78             printf("Max Heap
");
79         else if (flag && !isMax)
80             printf("Min Heap
");
81         else
82             printf("Not Heap
");
83         for (int i = 0; i < m; ++i)
84             cout << (i == 0 ? "" : " ") << post[i];
85         cout << endl;
86     }
87     return 0;
88 }

第二种方法，简单点，通过完全二叉树的性质，直接判断并得出后序遍历结果

 1 #include <iostream>
 2 #include <vector>
 3 using namespace std;
 4 int n, m;
 5 vector<int>level, post;
 6 void postOrder(int index)
 7 {
 8     if (index >= m)return;
 9     postOrder(index * 2 + 1);
10     postOrder(index * 2 + 2);
11     post.push_back(level[index]);
12 }
13 int main()
14 {
15     cin >> n >> m;
16     while (n--)
17     {
18         level.resize(m);
19         for (int i = 0; i < m; ++i)
20             cin >> level[i];
21         bool isMaxHeap = level[0] >= level[1] ? true : false;
22         bool flag = true;
23         for (int i = 0; i < (m - 1) / 2 && flag; ++i)
24         {
25             int L = i * 2 + 1, R = i * 2 + 2;
26             if (isMaxHeap && (level[i] < level[L] || R < m && level[i] < level[R]))
27                 flag = false;
28             if (!isMaxHeap && (level[i] > level[L] || R<m && level[i] > level[R]))
29                 flag = false;
30         }
31         if (flag && isMaxHeap)
32             printf("Max Heap
");
33         else if (flag && !isMaxHeap)
34             printf("Min Heap
");
35         else
36             printf("Not Heap
");
37         postOrder(0);
38         for (int i = 0; i < m; ++i)
39             cout << (i == 0 ? "" : " ") << post[i];
40         cout << endl;
41     }
42     return 0;
43 }