PAT 1066. Root of AVL Tree (25) （AVL树）

               1066. Root of AVL Tree (25)

时间限制

100 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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

提交代码

知识点：（1）AVL（平衡二叉树）。 （2） AVL树的建立，请参考这篇博文： http://blog.csdn.net/gabriel1026/article/details/6311339       。

请结合图文参考一下代码：

#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <cstring>
#define PI acos(-1)
#define inf 0x3f3f3f3f
#define SCD(a) scanf("%d",&a)
#define SCDD(a,b) scanf("%d%d",&a,&b)
#define SCF(a) scanf("%lf",&a)
#define PTD(a) printf("%d\n",a)
#define PTS(a) printf("%s\n",a)
#define MST(a,b) memset(a, b, sizeof(a))
using namespace std;
// PTA (Advanced Level) Practise 1066 Root of AVL Tree (25)

const int L = 10010;

struct AVLNode{
int data;
AVLNode* lchild;
AVLNode* rchild;
};
AVLNode* T;

void LL(AVLNode* &T)
{
AVLNode* t = T->rchild;
T->rchild = t->lchild;
t->lchild = T;
T = t;
}

void RR(AVLNode* &T)
{
AVLNode* t = T->lchild;
T->lchild = t->rchild;
t->rchild = T;
T = t;
}

void RL(AVLNode* &T)
{
RR(T->rchild);
LL(T);
}

void LR(AVLNode* &T)
{
LL(T->lchild);
RR(T);
}

int Height(AVLNode* &T)
{
if(!T)
return 0;
return max( Height(T->lchild), Height(T->rchild) ) + 1;
}

void InsertAVLNode(AVLNode* &T, int val)
{
if(!T){
T = new AVLNode;
T->data = val;
T->lchild = NULL;
T->rchild = NULL;
return;
}
if(val < T->data){
InsertAVLNode(T->lchild, val);
if(Height(T->lchild) - Height(T->rchild) == 2){
if(val < T->lchild->data)
RR(T);
else
LR(T);
}
}else{
InsertAVLNode(T->rchild, val);
if(Height(T->rchild) - Height(T->lchild) == 2){
if(val > T->rchild->data)
LL(T);
else
RL(T);
}
}
}

int main()
{
int i, b, t, j, n;
SCD(n);
for(i=0;i<n;i++){
SCD(t);
InsertAVLNode(T, t);
}
PTD(T->data);
}