考虑以下自调整BST中常用的以下向左旋转和向右旋转功能
T1, T2 and T3 are subtrees of the tree rooted with y (on left side)
or x (on right side)
y x
/ \ Right Rotation / \
x T3 – - – - – - – > T1 y
/ \ < - - - - - - - / \
T1 T2 Left Rotation T2 T3
以下哪一项是向左旋转和向右旋转操作的最严格上限。
(A) O(1)
(B) O(登录)
(C) O(登录)
(D) O(n)答案： (A)
说明：旋转操作(向左和向右旋转)需要恒定的时间，因为在那里仅更改了几个指针。以下是向左旋转和向右旋转的C实现
// A utility function to right rotate subtree rooted with y
// See the diagram given above.
struct node *rightRotate(struct node *y)
{
struct node *x = y->left;
struct node *T2 = x->right;
// Perform rotation
x->right = y;
y->left = T2;
// Update heights
y->height = max(height(y->left), height(y->right))+1;
x->height = max(height(x->left), height(x->right))+1;
// Return new root
return x;
}
// A utility function to left rotate subtree rooted with x
// See the diagram given above.
struct node *leftRotate(struct node *x)
{
struct node *y = x->right;
struct node *T2 = y->left;
// Perform rotation
y->left = x;
x->right = T2;
// Update heights
x->height = max(height(x->left), height(x->right))+1;
y->height = max(height(y->left), height(y->right))+1;
// Return new root
return y;
}
这个问题的测验