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:

588 70 61 96 120

Sample Output 1:

70

Sample Input 2:

788 70 61 96 120 90 65

Sample Output 2:

88

1 #include 
     
       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 }