04-07-2011
Binary tree
In computer science, a binary tree is a tree data structure in which each node has at most two child nodes, usually distinguished as "left" and "right". Nodes with children are parent nodes, and child nodes may contain references to their parents. Outside the tree, there is often a reference to the "root" node (the ancestor of all nodes), if it exists. Any node in the data structure can be reached by starting at root node and repeatedly following references to either the left or right child.
Binary trees are used to implement binary search trees and binary heaps.
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tsearch(3C) tsearch(3C)
NAME
tsearch(), tfind(), tdelete(), twalk() - manage binary search trees
SYNOPSIS
DESCRIPTION
and are routines for manipulating binary search trees. They are generalized from Knuth (6.2.2) Algorithms T and D. All comparisons are
done with a user-supplied routine, compar. This routine is called with two arguments, the pointers to the elements being compared. It
returns an integer less than, equal to, or greater than 0, according to whether the first argument is to be considered less than, equal to
or greater than the second argument. The comparison function need not compare every byte, so arbitrary data may be contained in the ele-
ments in addition to the values being compared.
is used to build and access the tree. key is a pointer to an entry to be accessed or stored. If there is an entry in the tree equal to
the value pointed to by key, a pointer to the previous key associated with this found entry is returned. Otherwise, key is inserted, and a
pointer to it returned. Note that since the value returned is a pointer to key and key itself is a pointer, the value returned is a
pointer to a pointer. Only pointers are copied, so the calling routine must store the data. rootp points to a variable that points to the
root of the tree. A NULL value for the variable pointed to by rootp denotes an empty tree; in this case, the variable is set to point to
the entry which will be at the root of the new tree.
Like searches for an entry in the tree, returning a pointer to it if found. However, if it is not found, returns a NULL pointer. The
arguments for are the same as for
deletes a node from a binary search tree. Arguments are the same as for The variable pointed to by rootp is changed if the deleted node
was the root of the tree. returns a pointer to the parent of the deleted node, or a NULL pointer if the node is not found.
traverses a binary search tree. root is the root of the tree to be traversed. (Any node in a tree may be used as the root for a walk
below that node.) action is the name of a routine to be invoked at each node. This routine is, in turn, called with three arguments:
o First argument is the address of the node being visited.
o Second argument is a value from an enumeration data type (defined in the header file), depending on whether this is the first,
second or third time that the node has been visited (during a depth-first, left-to-right traversal of the tree), or whether the
node is a leaf.
o Third argument is the level of the node in the tree, with the root being level zero.
EXAMPLES
The following code reads strings, and stores structures containing a pointer to each string and a count of its length. It then walks the
tree, printing out the stored strings and their lengths in alphabetical order.
RETURN VALUE
A NULL pointer is returned by if there is not enough space available to create a new node.
A NULL pointer is returned by and if rootp is NULL on entry.
If the datum is found, both and return a pointer to it. If not, returns NULL, and returns a pointer to the inserted item.
WARNINGS
The root argument to is one level of indirection less than the rootp arguments to and
Two nomenclatures are used to refer to the order in which tree nodes are visited. uses preorder, postorder and endorder to respectively
refer to visiting a node before any of its children, after its left child and before its right and after both its children. The alternate
nomenclature uses preorder, inorder, and postorder to refer to the same visits, which could result in some confusion over the meaning of
postorder. If the calling function alters the pointer to the root, results are unpredictable.
SEE ALSO
bsearch(3C), hsearch(3C), lsearch(3C), thread_safety(5).
STANDARDS CONFORMANCE
tsearch(3C)