PAT甲级——1147 Heaps【30】

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 = ) :val(a), l(nullptr), r(nullptr) {}
 };
 Node* creatTree(bool &flag, const bool isMax)
 {
     Node* root = new Node(level[]);
     int k = ;
     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 = -;
         for (int i = ; 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[] == minN)//小根堆
         {
             isMax = false;
             root = creatTree(flag, isMax);
         }
         else if (level[] == 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 = ; i < m; ++i)
             cout << (i ==  ? "" : " ") << post[i];
         cout << endl;
     }
     return ;
 }

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 *  + );
     postOrder(index *  + );
     post.push_back(level[index]);
 }
 int main()
 {
     cin >> n >> m;
     while (n--)
     {
         level.resize(m);
         for (int i = ; i < m; ++i)
             cin >> level[i];
         bool isMaxHeap = level[] >= level[] ? true : false;
         bool flag = true;
         for (int i = ; i < (m - ) /  && flag; ++i)
         {
             int L = i *  + , R = i *  + ;
             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();
         for (int i = ; i < m; ++i)
             cout << (i ==  ? "" : " ") << post[i];
         cout << endl;
     }
     return ;
 }