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.
Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.
Input Specification:
Each input file contains one test case. For each case, the first line contains a positive integer N (<=20) which is the total number of keys to be inserted. Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.
Output Specification:
For each test case, print the root of the resulting AVL tree in one line.
Sample Input 1:
5 88 70 61 96 120
Sample Output 1:
70
Sample Input 2:
7 88 70 61 96 120 90 65
Sample Output 2:
88
1 #include<iostream> 2 #include<vector> 3 #include<algorithm> 4 #include<queue> 5 #include<stack> 6 using namespace std; 7 8 class Node{ 9 public: 10 int value; 11 bool vis; 12 Node *left, *right; 13 Node(){left = NULL; right = NULL; vis = true;} 14 }; 15 16 /*Node* build(Node* root, int value) { 17 if(root == NULL) { 18 root = new Node(); 19 root->value = value; 20 } else if(root->value > value) root->left = build(root->left, value); 21 else root->right = build(root->right, value); 22 return root; 23 }*/ 24 25 Node* roateLeft(Node* root) { 26 Node* t = root->right; 27 root->right = t->left; 28 t->left = root; 29 return t; 30 } 31 32 Node* roateRight(Node* root){ 33 Node* t = root->left; 34 root->left = t->right; 35 t->right = root; 36 return t; 37 } 38 39 Node* roateRightLeft(Node* root){ 40 root->right = roateRight(root->right); 41 return roateLeft(root); 42 } 43 44 Node* roateLeftRight(Node* root){ 45 root->left = roateLeft(root->left); 46 return roateRight(root); 47 } 48 49 int getHeight(Node* root){ 50 if(root == NULL) return 0; 51 int l = getHeight(root->left) + 1; 52 int r = getHeight(root->right) + 1; 53 return l>r ? l : r; 54 } 55 56 Node* build(Node* root, int value){ 57 if(root == NULL) { 58 root = new Node(); 59 root->value = value; 60 } else if(root->value > value){ 61 root->left = build(root->left, value); 62 if(getHeight(root->left) - getHeight(root->right) == 2) { 63 if(value < root->left->value) root = roateRight(root); 64 else root = roateLeftRight(root); 65 } 66 }else{ 67 root->right = build(root->right, value); 68 if(getHeight(root->right) - getHeight(root->left) == 2) { 69 if(value < root->right->value) root = roateRightLeft(root); 70 else root = roateLeft(root); 71 } 72 } 73 return root; 74 } 75 76 77 Node* deleteNode(Node* root, int value){ 78 if(value < root->value){ 79 root->left = deleteNode(root->left, value); 80 if(getHeight(root->right) - getHeight(root->left) == 2) { 81 if(getHeight(root->right->right) > getHeight(root->right->left)) root = roateLeft(root); 82 else root = roateRightLeft(root); 83 } 84 } 85 else if(value > root->value){ 86 root->right = deleteNode(root->right, value); 87 if(getHeight(root->left) - getHeight(root->right) == 2) { 88 if(getHeight(root->left->left) > getHeight(root->left->right)) root = roateRight(root); 89 else root = roateLeftRight(root); 90 } 91 } 92 else{ 93 if(root->left == NULL && root->right == NULL) root = NULL; 94 else if(root->left == NULL && root->right != NULL) { 95 root->value = root->right->value; 96 root->right = NULL; 97 }else if(root->left != NULL && root->right == NULL){ 98 root->value = root->left->value; 99 root->left = NULL; 100 }else{ 101 if(getHeight(root->left) > getHeight(root->right)) { 102 Node* pre = root->left; 103 while(pre->right != NULL) pre = pre->right; 104 root->value = pre->value; 105 root->left = deleteNode(root->left, pre->value); 106 107 }else{ 108 Node* post = root->right; 109 while(post->left != NULL) post = post->left; 110 root->value = post->value; 111 root->right = deleteNode(root->right, post->value); 112 } 113 } 114 } 115 return root; 116 } 117 118 void levelOrder(Node* root){ 119 queue<Node*> q; 120 q.push(root); 121 while(!q.empty()){ 122 Node *temp = q.front(); 123 q.pop(); 124 cout<<temp->value<<" "; 125 if(temp->left != NULL) q.push(temp->left); 126 if(temp->right != NULL) q.push(temp->right); 127 } 128 } 129 130 /*void preOrder(Node* root){ 131 cout<<root->value<<" "; 132 if(root->left != NULL) preOrder(root->left); 133 if(root->right != NULL) preOrder(root->right); 134 } 135 136 void inOrder(Node* root){ 137 if(root->left != NULL) inOrder(root->left); 138 cout<<root->value<<" "; 139 if(root->right != NULL) inOrder(root->right); 140 }//中序遍历可以检测树的有效性， 遍历出来的是按照大小顺序排列的 141 142 void postOrder(Node* root){ 143 if(root->left != NULL) postOrder(root->left); 144 if(root->right != NULL) postOrder(root->right); 145 cout<<root->value<<" "; 146 }*/ 147 148 void preOrder(Node* root){ 149 stack<Node*> s; 150 s.push(root); 151 while(!s.empty()){ 152 Node* temp = s.top(); 153 cout<<temp->value<<" "; 154 s.pop(); 155 if(temp->right != NULL) s.push(temp->right); 156 if(temp->left != NULL) s.push(temp->left); 157 } 158 } 159 160 void postOrder(Node* root){ 161 stack<Node*> s; 162 s.push(root); 163 while(!s.empty()){ 164 Node* temp = s.top(); 165 if(temp->left != NULL ) { 166 s.push(temp->left); 167 temp->left = NULL; 168 } 169 else if(temp->right != NULL){ 170 s.push(temp->right); 171 temp->right = NULL; 172 }else{ 173 cout<<s.top()->value<<" "; 174 s.pop(); 175 } 176 177 } 178 } 179 180 void inOrder(Node* root){ 181 stack<Node*> s; 182 s.push(root); 183 while(!s.empty()){ 184 Node* temp = s.top(); 185 if(temp->left === 1) temp->left = 0; 186 else if(temp->left != NULL) { 187 s.push(temp->left); 188 temp->left = 1; 189 } else if(temp->left == NULL) temp->left = 1; 190 else if(temp->right != NULL) { 191 s.push(temp->right); 192 temp->right = NULL; 193 }else{ 194 cout<<s.top()->value()<<" "; 195 s.pop(); 196 } 197 } 198 } 199 int main(){ 200 Node *root = NULL; 201 int t[] = {10,5,15,3,6,13,17,2,14,16}; 202 for(int i = 0; i < 10; i++) root = build(root, t[i]); 203 levelOrder(root); 204 cout<<endl; 205 inOrder(root); 206 207 return 0;}