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 (≤) 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 using namespace std; 3 struct node { 4 int val; 5 struct node *left, *right; 6 }; 7 node *rotateLeft(node *root) { 8 node *t = root->right; 9 root->right = t->left; 10 t->left = root; 11 return t; 12 } 13 node *rotateRight(node *root) { 14 node *t = root->left; 15 root->left = t->right; 16 t->right = root; 17 return t; 18 } 19 node *rotateLeftRight(node *root) { 20 root->left = rotateLeft(root->left); 21 return rotateRight(root); 22 } 23 node *rotateRightLeft(node *root) { 24 root->right = rotateRight(root->right); 25 return rotateLeft(root); 26 } 27 int getHeight(node *root) { 28 if(root == NULL) return 0; 29 return max(getHeight(root->left), getHeight(root->right)) + 1; 30 } 31 node *insert(node *root, int val) { 32 if(root == NULL) { 33 root = new node(); 34 root->val = val; 35 root->left = root->right = NULL; 36 } else if(val < root->val) { 37 root->left = insert(root->left, val); 38 if(getHeight(root->left) - getHeight(root->right) == 2) 39 root = val < root->left->val ? rotateRight(root) : rotateLeftRight(root); 40 } else { 41 root->right = insert(root->right, val); 42 if(getHeight(root->left) - getHeight(root->right) == -2) 43 root = val > root->right->val ? rotateLeft(root) : rotateRightLeft(root); 44 } 45 return root; 46 } 47 int main() { 48 int n, val; 49 scanf("%d", &n); 50 node *root = NULL; 51 for(int i = 0; i < n; i++) { 52 scanf("%d", &val); 53 root = insert(root, val); 54 } 55 printf("%d", root->val); 56 return 0; 57 }