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 ;

 }

巴特西

PAT甲级——1147 Heaps【30】

Input Specification:

Output Specification:

Sample Input:

Sample Output:

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