标签：后序 post fir ESS rop wiki output node dia
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.
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.
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.
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
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 }
标签：后序 post fir ESS rop wiki output node dia
原文地址：https://www.cnblogs.com/zzw1024/p/11909255.html
