1066. Root of AVL Tree (25)-PAT甲级真题（AVL树）

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

题目大意：AVL树是自平衡二叉搜索树。在AVL树中，任何节点的两个子子树的高度最多相差一个；如果在任何时候它们相差多于一个，则重新平衡以恢复此属性。图1-4说明了旋转规则～现在给出一系列插入，要求输出根节点的值～

分析：写出建AVL（平衡二叉搜索树）的代码模版即可，rotateLeft表示左旋，rotateRight表示右旋，rotateLeftRight表示先左旋后右旋，rotateRightLeft表示先右旋后左旋，getHeight表示获取传入结点的子树的高度，insert表示插入建树的过程，如果root为空，直接新建结点插入即可～如果当前要插入的值小于root->val，则插入root的左子树；如果当前要插入的值大于root->val，则插入root的右子树～如果插入后左右子树高度差大于1，再根据值的大小比较进行旋转调整使树平衡～插入完成后返回root指针赋值给main函数里的root～最后输出root的val值～

#include <iostream>
using namespace std;
struct node {
    int val;
    struct node *left, *right;
};
node *rotateLeft(node *root) {
    node *t = root->right;
    root->right = t->left;
    t->left = root;
    return t;
}
node *rotateRight(node *root) {
    node *t = root->left;
    root->left = t->right;
    t->right = root;
    return t;
}
node *rotateLeftRight(node *root) {
    root->left = rotateLeft(root->left);
    return rotateRight(root);
}
node *rotateRightLeft(node *root) {
    root->right = rotateRight(root->right);
    return rotateLeft(root);
}
int getHeight(node *root) {
    if(root == NULL) return 0;
    return max(getHeight(root->left), getHeight(root->right)) + 1;
}
node *insert(node *root, int val) {
    if(root == NULL) {
        root = new node();
        root->val = val;
        root->left = root->right = NULL;
    } else if(val < root->val) {
        root->left = insert(root->left, val);
        if(getHeight(root->left) - getHeight(root->right) == 2)
            root = val < root->left->val ? rotateRight(root) : rotateLeftRight(root);
    } else {
        root->right = insert(root->right, val);
        if(getHeight(root->left) - getHeight(root->right) == -2)
            root = val > root->right->val ? rotateLeft(root) : rotateRightLeft(root);
    }
    return root;
}
int main() {
    int n, val;
    scanf("%d", &n);
    node *root = NULL;
    for(int i = 0; i < n; i++) {
        scanf("%d", &val);
        root = insert(root, val);
    }
    printf("%d", root->val);
    return 0;
}

#include <iostream>

using namespace std;

struct node {

int val;

struct node *left, *right;

};

node *rotateLeft(node *root) {

node *t = root->right;

root->right = t->left;

t->left = root;

return t;

}

node *rotateRight(node *root) {

node *t = root->left;

root->left = t->right;

t->right = root;

return t;

}

node *rotateLeftRight(node *root) {

root->left = rotateLeft(root->left);

return rotateRight(root);

}

node *rotateRightLeft(node *root) {

root->right = rotateRight(root->right);

return rotateLeft(root);

}

int getHeight(node *root) {

if(root == NULL) return 0;

return max(getHeight(root->left), getHeight(root->right)) + 1;

}

node *insert(node *root, int val) {

if(root == NULL) {

root = new node();

root->val = val;

root->left = root->right = NULL;

} else if(val < root->val) {

root->left = insert(root->left, val);

if(getHeight(root->left) - getHeight(root->right) == 2)

root = val < root->left->val ? rotateRight(root) : rotateLeftRight(root);

} else {

root->right = insert(root->right, val);

if(getHeight(root->left) - getHeight(root->right) == -2)

root = val > root->right->val ? rotateLeft(root) : rotateRightLeft(root);

}

return root;

}

int main() {

int n, val;

scanf("%d", &n);

node *root = NULL;

for(int i = 0; i < n; i++) {

scanf("%d", &val);

root = insert(root, val);

}

printf("%d", root->val);

return 0;

}

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