- 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
- #include <iostream>
- #include <vector>
- #include <queue>
- #include <algorithm>
- using namespace std;
- int n, m;
- vector<int>level, post;
- struct Node
- {
- int val;
- Node *l, *r;
- Node(int a = 0) :val(a), l(nullptr), r(nullptr) {}
- };
- Node* creatTree(bool &flag, const bool isMax)
- {
- Node* root = new Node(level[0]);
- int k = 1;
- queue<Node*>q;
- q.push(root);
- while (k <m)
- {
- Node *p = q.front();
- q.pop();
- p->l = new Node(level[k++]);
- if (isMax && p->val<p->l->val || !isMax && p->val>p->l->val)
- flag = false;
- q.push(p->l);
- if (k>= m)break;
- p->r = new Node(level[k++]);
- if (isMax && p->val <p->r->val || !isMax && p->val> p->r->val)
- flag = false;
- q.push(p->r);
- }
- return root;
- }
- void postOrder(Node *root)
- {
- if (root == nullptr)
- return;
- postOrder(root->l);
- postOrder(root->r);
- post.push_back(root->val);
- }
- int main()
- {
- cin>> n>> m;
- while (n--)
- {
- level.clear();
- level.resize(m);
- post.clear();
- int minN = INT32_MAX, maxN = -1;
- for (int i = 0; i <m; ++i)
- {
- cin>> level[i];
- minN = minN <level[i] ? minN : level[i];
- maxN = maxN> level[i] ? maxN : level[i];
- }
- bool flag = true, isMax = false;
- Node *root = nullptr;
- if (level[0] == minN)// 小根堆
- {
- isMax = false;
- root = creatTree(flag, isMax);
- }
- else if (level[0] == maxN)
- {
- isMax = true;
- root = creatTree(flag, isMax);
- }
- else
- {
- flag = false;
- root = creatTree(flag, isMax);
- }
- postOrder(root);
- if (flag && isMax)
- printf("Max Heap\n");
- else if (flag && !isMax)
- printf("Min Heap\n");
- else
- printf("Not Heap\n");
- for (int i = 0; i <m; ++i)
- cout << (i == 0 ? "":" ") << post[i];
- cout << endl;
- }
- return 0;
- }
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
- #include <iostream>
- #include <vector>
- using namespace std;
- int n, m;
- vector<int>level, post;
- void postOrder(int index)
- {
- if (index>= m)return;
- postOrder(index * 2 + 1);
- postOrder(index * 2 + 2);
- post.push_back(level[index]);
- }
- int main()
- {
- cin>> n>> m;
- while (n--)
- {
- level.resize(m);
- for (int i = 0; i <m; ++i)
- cin>> level[i];
- bool isMaxHeap = level[0]>= level[1] ? true : false;
- bool flag = true;
- for (int i = 0; i <(m - 1) / 2 && flag; ++i)
- {
- int L = i * 2 + 1, R = i * 2 + 2;
- if (isMaxHeap && (level[i] < level[L] || R < m && level[i] < level[R]))
- flag = false;
- if (!isMaxHeap && (level[i]> level[L] || R<m && level[i]> level[R]))
- flag = false;
- }
- if (flag && isMaxHeap)
- printf("Max Heap\n");
- else if (flag && !isMaxHeap)
- printf("Min Heap\n");
- else
- printf("Not Heap\n");
- postOrder(0);
- for (int i = 0; i < m; ++i)
- cout << (i == 0 ? "":" ") << post[i];
- cout << endl;
- }
- return 0;
- }
来源: http://www.bubuko.com/infodetail-3298291.html