标签：rate bool pac avl each must size insert test
An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.
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Now given a sequence of insertions, you are supposed to output the level-order traversal sequence of the resulting AVL tree, and to tell if it is a complete binary tree.
Each input file contains one test case. For each case, the first line contains a positive integer N (≤ 20). Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.
For each test case, insert the keys one by one into an initially empty AVL tree. Then first print in a line the level-order traversal sequence of the resulting AVL tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line. Then in the next line, print YES if the tree is complete, or NO if not.
5
88 70 61 63 65
70 63 88 61 65
YES
8
88 70 61 96 120 90 65 68
88 65 96 61 70 90 120 68
NO判断是否完全二叉树：
层序遍历时，若前面已经出现过空子树，而后面又发现了非空子树，则不是完全二叉树。
平衡二叉树的旋转：
1、右单旋
2、左单旋
3、左右双旋
4、右左双旋
1 #include <iostream> 2 #include <vector> 3 #include <queue> 4 using namespace std; 5 6 typedef struct Node *Tree; 7 struct Node 8 { 9 int data; 10 Tree left; 11 Tree right; 12 }; 13 14 Tree insert(Tree T, int data); 15 int getHeight(Tree T); 16 Tree LL(Tree T); 17 Tree LR(Tree T); 18 Tree RR(Tree T); 19 Tree RL(Tree T); 20 vector<int> levelOrder(Tree T, bool& isComplete); 21 22 int main() 23 { 24 int N, i, t; 25 cin >> N; 26 Tree root = NULL; 27 for (i = 0; i < N; i++) 28 { 29 cin >> t; 30 root = insert(root, t); 31 } 32 bool isComplete; 33 vector<int> v = levelOrder(root, isComplete); 34 cout << v[0]; 35 for (i = 1; i < v.size(); i++) 36 cout << " " << v[i]; 37 printf("\n%s", isComplete ? "YES" : "NO"); 38 return 0; 39 } 40 41 Tree insert(Tree T, int data) 42 { 43 if (T == NULL) 44 { 45 T = new Node; 46 T->data = data; 47 T->left = T->right = NULL; 48 } 49 else if (data < T->data) 50 { 51 T->left = insert(T->left, data); 52 if (getHeight(T->left) - getHeight(T->right) == 2) 53 { 54 if (data < T->left->data) 55 T = LL(T); 56 else 57 T = LR(T); 58 } 59 } 60 else 61 { 62 T->right = insert(T->right, data); 63 if (getHeight(T->right) - getHeight(T->left) == 2) 64 { 65 if (data > T->right->data) 66 T = RR(T); 67 else 68 T = RL(T); 69 } 70 } 71 return T; 72 } 73 74 int getHeight(Tree T) 75 { 76 if (T == NULL) return 0; 77 int a = getHeight(T->left); 78 int b = getHeight(T->right); 79 return (a > b) ? (a + 1) : (b + 1); 80 } 81 82 Tree LL(Tree T) 83 { 84 Tree tmp = T->left; 85 T->left = tmp->right; 86 tmp->right = T; 87 return tmp; 88 } 89 90 Tree LR(Tree T) 91 { 92 T->left = RR(T->left); 93 return LL(T); 94 } 95 96 Tree RR(Tree T) 97 { 98 Tree tmp = T->right; 99 T->right = tmp->left; 100 tmp->left = T; 101 return tmp; 102 } 103 104 Tree RL(Tree T) 105 { 106 T->right = LL(T->right); 107 return RR(T); 108 } 109 110 vector<int> levelOrder(Tree T, bool& isComplete) 111 { 112 vector<int> v; 113 isComplete = true; 114 queue<Tree> q; 115 q.push(T); 116 bool hasEmpty = false; 117 while (!q.empty()) 118 { 119 Tree T = q.front(); 120 q.pop(); 121 v.push_back(T->data); 122 if (T->left != NULL) 123 { 124 q.push(T->left); 125 //已经出现过空子树但是现在子树又不空，那么不是完全二叉树 126 if (hasEmpty) isComplete = false; 127 } 128 else 129 hasEmpty = true; 130 if (T->right != NULL) 131 { 132 q.push(T->right); 133 if (hasEmpty) isComplete = false; 134 } 135 else 136 hasEmpty = true; 137 } 138 return v; 139 }
标签：rate bool pac avl each must size insert test
原文地址：https://www.cnblogs.com/lxc1910/p/9534466.html
