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 ythe 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

#include <stdio.h>
struct Node {int val;int height;struct Node *left;struct Node *right;
};
int max(int a, int b) {             //返回两者较大者return a > b ?

a : b; } int height(struct Node* root) { //为了兼容空树，树高度不能直接返回根节点的height属性 if (root == NULL) { return -1; } else { return root->height; } } struct Node* RRrotation(struct Node* k1) { //右右旋转 struct Node* k2 = k1->right; //k2为根节点k1的右儿子 k1->right = k2->left; //将k2的左儿子连接到k1的右子节点 k2->left = k1; //将k1连接到k2的左子节点 k1->height = max(height(k1->left), height(k1->right)) + 1; //更新节点高度，仅仅有k1，k2节点高度变化 k2->height = max(height(k2->left), height(k2->right)) + 1; return k2; } struct Node* LLrotation(struct Node* k1) { //左左旋转 struct Node* k2 = k1->left; k1->left = k2->right; k2->right = k1; k1->height = max(height(k1->left), height(k1->right)) + 1; k2->height = max(height(k2->left), height(k2->right)) + 1; return k2; } struct Node* RLrotation(struct Node* k1) { //右左旋转 //分两步：先对根节点的右子树做左左旋转。再对根做右右旋转 k1->right = LLrotation(k1->right); return RRrotation(k1); } struct Node* LRrotation(struct Node* k1) { //左右旋转 k1->left = RRrotation(k1->left); return LLrotation(k1); } struct Node* insertAvlTree(struct Node* node, struct Node* root) { if (root == NULL) { root = node; return root; } if (node->val > root->val) { root->right = insertAvlTree(node, root->right); //插入右子树 if (height(root->right) - height(root->left) == 2) { if (node->val > root->right->val) { //假设插入右子树的右子树，进行右右旋转 root = RRrotation(root); } else if (node->val < root->right->val) { //进行右左旋转 root = RLrotation(root); } } } else if (node->val < root->val) { //插入左子树情况与上面相似 root->left = insertAvlTree(node, root->left); if (height(root->left) - height(root->right) == 2) { if (node->val < root->left->val) { root = LLrotation(root); } else if(node->val > root->left->val) { root = LRrotation(root); } } } //递归中不断更新插入节点到根节点路径上全部节点的高度 root->height = max(height(root->left), height(root->right)) + 1; return root; } int main() { freopen("test.txt", "r", stdin); int n; scanf("%d", &n); struct Node nodes[20]; struct Node *root = NULL; for (int i = 0; i < n; ++i) { //初始化一个节点。并插入AVL树中 scanf("%d", &nodes[i].val); nodes[i].height = 0; //孤立的节点高度为0 nodes[i].left = NULL; nodes[i].right = NULL; root = insertAvlTree(&nodes[i], root); } printf("%d", root->val); return 0; }

题目链接：http://www.patest.cn/contests/mooc-ds/04-%E6%A0%914