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\n");
79 else if (flag && !isMax)
80 printf("Min Heap\n");
81 else
82 printf("Not Heap\n");
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\n");
33 else if (flag && !isMaxHeap)
34 printf("Min Heap\n");
35 else
36 printf("Not Heap\n");
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 }
原文地址：https://www.cnblogs.com/zzw1024/p/11909255.html