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

AVL樹的旋轉。

#include <bits/stdc++.h>
using namespace std;

const int maxn = 101000;
struct Node {
  int val;
  int son[2];
  int height;
}s[maxn];
int root, sz;
int n;

int add(int x) {
  s[sz].val = x;
  s[sz].son[0] = s[sz].son[1] = -1;
  s[sz].height = 0;
  sz ++;
  return sz - 1;
}

int Height(int id) {
  if(id == -1) return -1;
  return s[id].height;
}

int R(int k2) {
  int k1 = s[k2].son[0];
  s[k2].son[0] = s[k1].son[1];
  s[k1].son[1] = k2;
  s[k2].height = max(Height(s[k2].son[0]), Height(s[k2].son[1])) + 1;
  s[k1].height = max(Height(s[k1].son[0]), Height(s[k1].son[1])) + 1;
  return k1;
}

int L(int k2) {
  int k1 = s[k2].son[1];
  s[k2].son[1] = s[k1].son[0];
  s[k1].son[0] = k2;
  s[k2].height = max(Height(s[k2].son[0]), Height(s[k2].son[1])) + 1;
  s[k1].height = max(Height(s[k1].son[0]), Height(s[k1].son[1])) + 1;
  return k1;
}

int RL(int k3) {
  int k1 = s[k3].son[1];
  s[k3].son[1] = R(k1);
  return L(k3);
}

int LR(int k3) {
  int k1 = s[k3].son[0];
  s[k3].son[0] = L(k1);
  return R(k3);
}

int Insert(int id, int val) {
  if(id == -1) {
    id = add(val);
  } else if(val < s[id].val) {
    s[id].son[0] = Insert(s[id].son[0], val);
    if(Height(s[id].son[0]) - Height(s[id].son[1]) == 2) { // 需要調整
      if(val < s[s[id].son[0]].val) id = R(id);
      else id = LR(id);
    }
  } else {
    s[id].son[1] = Insert(s[id].son[1], val);
    if(Height(s[id].son[1]) - Height(s[id].son[0]) == 2) { // 需要調整
      if(val > s[s[id].son[1]].val) id = L(id);
      else id = RL(id);
    }
  }
  s[id].height = max(Height(s[id].son[0]), Height(s[id].son[1])) + 1;
  return id;
}

int main() {
  scanf("%d", &n);
  root = -1;
  for(int i = 1; i <= n; i ++) {
    int x;
    scanf("%d", &x);
    root = Insert(root, x);
   // cout << root << endl;
  }
  cout << s[root].val << endl;
  return 0;
}