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:

588 70 61 96 120

Sample Output 1:

70

Sample Input 2:

788 70 61 96 120 90 65

Sample Output 2:

88

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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);}