&12-2 Find binary search tree

#1, theorem

On a two-fork search tree with a height of H, the operation Search, MINIMUM, MAXIMUM, successor, and predecessor on the dynamic collection can be completed in O (h) time.

#2, pseudo-code

Search, iterative form of search, take the minimum value, take the maximum value, find the successor, find the precursor.

1 //x is a element of the tree, K is the key of element we want to search.2tree-SEARCH (x,k)3 ifX==null or k==X.key4     returnx;5 6 ifk<X.key7     returntree-SEARCH (x.left,k);8 Else9     returnTree_search (X.RIGHT,K);

Tree-search

1 Iterative_tree_search (x,k) 2  while X!=null and k!=x.key3     if k<x.key4         x=  X.left; 5     Else 6         x=x.right; 7 return x;

Iterative_tree_search

1 tree-MINIMUM (x)2 while x.left!=NULL3     x=x.left; 4 return x;

Tree-minimum

1 tree-MAXIMUM (x)2 while x.right!=NULL3     x= X.right; 4 return x;

Tree-maximum

1 tree-successor (x)2if x.right!=NULL3     return Tree_minimum (x.right); 4 y=x.p; 5  while Y!=null and x==y.right6     x=y; 7     y=y.p; 8 return y;

Tree-successor

1 terr-predecessor (x)2if x.left!=NULL3     return MAXIMUM (x.left); 4 y=x.p; 5  while Y!=null and x==y.right6     x=y; 7     y=y.p; 8 return y;

Terr-predecessor

&12-2 Find binary search tree