&12-2 查找二叉搜索树

#1，定理

在一棵高度为h的二叉搜索树上，动态集合上的操作SEARCH、MINIMUM、MAXIMUM、SUCCESSOR和PREDECESSOR可以在O(h)时间内完成。

#2，伪代码

分别是搜索，迭代形式的搜索，取最小值，取最大值，找后继，找前驱。

//x is an element of the tree, k is the key of element we want to search.
TREE-SEARCH(x,k)
if x==NULL or k==x.key
    return x;

if k<x.key
    return TREE-SEARCH(x.left,k);
else
    return TREE_SEARCH(x.right,k);

ITERATIVE_TREE_SEARCH(x,k)
while x!=NULL and k!=x.key
    if k<x.key
        x=x.left;
    else
        x=x.right;
return x;

TREE-MINIMUM(x)
while x.left!=NULL
    x=x.left;
return x;

TREE-MAXIMUM(x)
while x.right!=NULL
    x=x.right;
return x;

TREE-SUCCESSOR(x)
if x.right!=NULL
    return TREE_MINIMUM(x.right);
y=x.p;
while y!=NULL and x==y.right
    x=y;
    y=y.p;
return y;

TERR-PREDECESSOR(x)
if x.left!=NULL
    return MAXIMUM(x.left);
y=x.p;
while y!=NULL and x==y.right
    x=y;
    y=y.p;
return y;