#include <stdio.h>
#include <stdlib.h>
typedef int ElementType;
typedef struct AVLNode *AVLTree; /* AVL树类型 */
typedef struct AVLNode{
ElementType Data; /* 结点数据 */
AVLTree Left; /* 指向左子树 */
AVLTree Right; /* 指向右子树 */
int Height; /* 树高 */
}AVLNode;
int Max ( int a, int b );
int GetHeight(AVLTree T);
AVLTree SingleLeftRotation ( AVLTree A );
AVLTree DoubleLeftRightRotation ( AVLTree A );
AVLTree SingleRightRotation ( AVLTree A );
AVLTree DoubleRightLeftRotation ( AVLTree A );
AVLTree Insert( AVLTree T, ElementType X );
int main(int argc, char const *argv[])
{
// freopen("test.txt", "r", stdin);
int N, tmp;
scanf("%d", &N);
AVLTree AVL = NULL;
for (int i = 0; i < N; ++i){
scanf("%d", &tmp);
AVL = Insert(AVL, tmp);
}
printf("%d\n", AVL->Data);
return 0;
}
int Max ( int a, int b )
{
return a > b ? a : b;
}
int GetHeight(AVLTree T)
{
if(!T)
return 0;
else
return T->Height;
}
AVLTree SingleLeftRotation ( AVLTree A )
{ /* 注意:A必须有一个左子结点B */
/* 将A与B做左单旋,更新A与B的高度,返回新的根结点B */
AVLTree B = A->Left;
A->Left = B->Right;
B->Right = A;
A->Height = Max( GetHeight(A->Left), GetHeight(A->Right) ) + 1;
B->Height = Max( GetHeight(B->Left), A->Height ) + 1;
return B;
}
AVLTree DoubleLeftRightRotation ( AVLTree A )
{ /* 注意:A必须有一个左子结点B,且B必须有一个右子结点C */
/* 将A、B与C做两次单旋,返回新的根结点C */
/* 将B与C做右单旋,C被返回 */
A->Left = SingleRightRotation(A->Left);
/* 将A与C做左单旋,C被返回 */
return SingleLeftRotation(A);
}
AVLTree SingleRightRotation ( AVLTree A )
{
AVLTree B = A->Right;
A->Right = B->Left;
B->Left = A;
A->Height = Max( GetHeight(A->Left), GetHeight(A->Right) ) + 1;
B->Height = Max( GetHeight(B->Right), A->Height) + 1;
return B;
}
AVLTree DoubleRightLeftRotation ( AVLTree A )
{
A->Right = SingleLeftRotation(A->Right);
return SingleRightRotation(A);
}
AVLTree Insert( AVLTree T, ElementType X )
{ /* 将X插入AVL树T中,并且返回调整后的AVL树 */
if ( !T ) { /* 若插入空树,则新建包含一个结点的树 */
T = (AVLTree)malloc(sizeof(struct AVLNode));
T->Data = X;
T->Height = 0;
T->Left = T->Right = NULL;
} /* if (插入空树) 结束 */
else if ( X < T->Data ) {
/* 插入T的左子树 */
T->Left = Insert( T->Left, X);
/* 如果需要左旋 */
if ( GetHeight(T->Left)-GetHeight(T->Right) == 2 )
if ( X < T->Left->Data )
T = SingleLeftRotation(T); /* 左单旋 */
else
T = DoubleLeftRightRotation(T); /* 左-右双旋 */
} /* else if (插入左子树) 结束 */
else if ( X > T->Data ) {
/* 插入T的右子树 */
T->Right = Insert( T->Right, X );
/* 如果需要右旋 */
if ( GetHeight(T->Left)-GetHeight(T->Right) == -2 )
if ( X > T->Right->Data )
T = SingleRightRotation(T); /* 右单旋 */
else
T = DoubleRightLeftRotation(T); /* 右-左双旋 */
} /* else if (插入右子树) 结束 */
/* else X == T->Data,无须插入 */
/* 更新树高 */
T->Height = Max( GetHeight(T->Left), GetHeight(T->Right) ) + 1;
return T;
}
04-树5 Root of AVL Tree
最新推荐文章于 2022-04-16 10:25:58 发布