Tree traversal

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Task
Tree traversal
You are encouraged to solve this task according to the task description, using any language you may know.

Implement a binary tree where each node carries an integer, and implement preoder, inorder, postorder and level-order traversal. Use those traversals to output the following tree:

         1
        / \
       /   \
      /     \
     2       3
    / \     /
   4   5   6
  /       / \
 7       8   9

The correct output should look like this:

preorder:    1 2 4 7 5 3 6 8 9
inorder:     7 4 2 5 1 8 6 9 3
postorder:   7 4 5 2 8 9 6 3 1
level-order: 1 2 3 4 5 6 7 8 9

This article has more information on traversing trees.

Contents

[edit] ACL2

(defun flatten-preorder (tree)
(if (endp tree)
nil
(append (list (first tree))
(flatten-preorder (second tree))
(flatten-preorder (third tree)))))
 
(defun flatten-inorder (tree)
(if (endp tree)
nil
(append (flatten-inorder (second tree))
(list (first tree))
(flatten-inorder (third tree)))))
 
(defun flatten-postorder (tree)
(if (endp tree)
nil
(append (flatten-postorder (second tree))
(flatten-postorder (third tree))
(list (first tree)))))
 
(defun flatten-level-r1 (tree level levels)
(if (endp tree)
levels
(let ((curr (cdr (assoc level levels))))
(flatten-level-r1
(second tree)
(1+ level)
(flatten-level-r1
(third tree)
(1+ level)
(put-assoc level
(append curr (list (first tree)))
levels))))))
 
(defun flatten-level-r2 (levels max-level)
(declare (xargs :measure (nfix (1+ max-level))))
(if (zp (1+ max-level))
nil
(append (flatten-level-r2 levels
(1- max-level))
(reverse (cdr (assoc max-level levels))))))
 
 
(defun flatten-level (tree)
(let ((levels (flatten-level-r1 tree 0 nil)))
(flatten-level-r2 levels (len levels))))

[edit] Ada

with Ada.Text_Io; use Ada.Text_Io;
with Ada.Unchecked_Deallocation;
with Ada.Containers.Doubly_Linked_Lists;
 
procedure Tree_Traversal is
type Node;
type Node_Access is access Node;
type Node is record
Left : Node_Access := null;
Right : Node_Access := null;
Data : Integer;
end record;
procedure Destroy_Tree(N : in out Node_Access) is
procedure free is new Ada.Unchecked_Deallocation(Node, Node_Access);
begin
if N.Left /= null then
Destroy_Tree(N.Left);
end if;
if N.Right /= null then
Destroy_Tree(N.Right);
end if;
Free(N);
end Destroy_Tree;
function Tree(Value : Integer; Left : Node_Access; Right : Node_Access) return Node_Access is
Temp : Node_Access := new Node;
begin
Temp.Data := Value;
Temp.Left := Left;
Temp.Right := Right;
return Temp;
end Tree;
procedure Preorder(N : Node_Access) is
begin
Put(Integer'Image(N.Data));
if N.Left /= null then
Preorder(N.Left);
end if;
if N.Right /= null then
Preorder(N.Right);
end if;
end Preorder;
procedure Inorder(N : Node_Access) is
begin
if N.Left /= null then
Inorder(N.Left);
end if;
Put(Integer'Image(N.Data));
if N.Right /= null then
Inorder(N.Right);
end if;
end Inorder;
procedure Postorder(N : Node_Access) is
begin
if N.Left /= null then
Postorder(N.Left);
end if;
if N.Right /= null then
Postorder(N.Right);
end if;
Put(Integer'Image(N.Data));
end Postorder;
procedure Levelorder(N : Node_Access) is
package Queues is new Ada.Containers.Doubly_Linked_Lists(Node_Access);
use Queues;
Node_Queue : List;
Next : Node_Access;
begin
Node_Queue.Append(N);
while not Is_Empty(Node_Queue) loop
Next := First_Element(Node_Queue);
Delete_First(Node_Queue);
Put(Integer'Image(Next.Data));
if Next.Left /= null then
Node_Queue.Append(Next.Left);
end if;
if Next.Right /= null then
Node_Queue.Append(Next.Right);
end if;
end loop;
end Levelorder;
N : Node_Access;
begin
N := Tree(1,
Tree(2,
Tree(4,
Tree(7, null, null),
null),
Tree(5, null, null)),
Tree(3,
Tree(6,
Tree(8, null, null),
Tree(9, null, null)),
null));
 
Put("preorder: ");
Preorder(N);
New_Line;
Put("inorder: ");
Inorder(N);
New_Line;
Put("postorder: ");
Postorder(N);
New_Line;
Put("level order: ");
Levelorder(N);
New_Line;
Destroy_Tree(N);
end Tree_traversal;

[edit] ALGOL 68

Translation of: C
- note the strong code structural similarities with C.

Note the changes from the original translation from C in this diff. It contains examples of syntactic sugar available in ALGOL 68.

Works with: ALGOL 68 version Standard - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
Works with: ELLA ALGOL 68 version Any (with appropriate job cards)
MODE VALUE = INT;
PROC value repr = (VALUE value)STRING: whole(value, 0);
 
MODE NODES = STRUCT ( VALUE value, REF NODES left, right);
MODE NODE = REF NODES;
 
PROC tree = (VALUE value, NODE left, right)NODE:
HEAP NODES := (value, left, right);
 
PROC preorder = (NODE node, PROC (VALUE)VOID action)VOID:
IF node ISNT NODE(NIL) THEN
action(value OF node);
preorder(left OF node, action);
preorder(right OF node, action)
FI;
 
PROC inorder = (NODE node, PROC (VALUE)VOID action)VOID:
IF node ISNT NODE(NIL) THEN
inorder(left OF node, action);
action(value OF node);
inorder(right OF node, action)
FI;
 
PROC postorder = (NODE node, PROC (VALUE)VOID action)VOID:
IF node ISNT NODE(NIL) THEN
postorder(left OF node, action);
postorder(right OF node, action);
action(value OF node)
FI;
 
PROC destroy tree = (NODE node)VOID:
postorder(node, (VALUE skip)VOID:
# free(node) - PR garbage collect hint PR #
node := (SKIP, NIL, NIL)
);
 
# helper queue for level order #
MODE QNODES = STRUCT (REF QNODES next, NODE value);
MODE QNODE = REF QNODES;
 
 
MODE QUEUES = STRUCT (QNODE begin, end);
MODE QUEUE = REF QUEUES;
 
PROC enqueue = (QUEUE queue, NODE node)VOID:
(
HEAP QNODES qnode := (NIL, node);
IF end OF queue ISNT QNODE(NIL) THEN
next OF end OF queue
ELSE
begin OF queue
FI := end OF queue := qnode
);
 
PROC queue empty = (QUEUE queue)BOOL:
begin OF queue IS QNODE(NIL);
 
PROC dequeue = (QUEUE queue)NODE:
(
NODE out := value OF begin OF queue;
QNODE second := next OF begin OF queue;
# free(begin OF queue); PR garbage collect hint PR #
QNODE(begin OF queue) := (NIL, NIL);
begin OF queue := second;
IF queue empty(queue) THEN
end OF queue := begin OF queue
FI;
out
);
 
PROC level order = (NODE node, PROC (VALUE)VOID action)VOID:
(
HEAP QUEUES queue := (QNODE(NIL), QNODE(NIL));
enqueue(queue, node);
WHILE NOT queue empty(queue)
DO
NODE next := dequeue(queue);
IF next ISNT NODE(NIL) THEN
action(value OF next);
enqueue(queue, left OF next);
enqueue(queue, right OF next)
FI
OD
);
 
PROC print node = (VALUE value)VOID:
print((" ",value repr(value)));
 
main: (
NODE node := tree(1,
tree(2,
tree(4,
tree(7, NIL, NIL),
NIL),
tree(5, NIL, NIL)),
tree(3,
tree(6,
tree(8, NIL, NIL),
tree(9, NIL, NIL)),
NIL));
 
MODE TEST = STRUCT(
STRING name,
PROC(NODE,PROC(VALUE)VOID)VOID order
);
 
PROC test = (TEST test)VOID:(
STRING pad=" "*(12-UPB name OF test);
print((name OF test,pad,": "));
(order OF test)(node, print node);
print(new line)
);
 
[]TEST test list = (
("preorder",preorder),
("inorder",inorder),
("postorder",postorder),
("level order",level order)
);
 
FOR i TO UPB test list DO test(test list[i]) OD;
 
destroy tree(node)
)

Output:

preorder :     1 2 4 7 5 3 6 8 9 
inorder :      7 4 2 5 1 8 6 9 3 
postorder :    7 4 5 2 8 9 6 3 1 
level-order :  1 2 3 4 5 6 7 8 9 

[edit] ATS

#include
"share/atspre_staload.hats"
//
(* ****** ****** *)
//
datatype
tree (a:t@ype) =
| tnil of ()
| tcons of (tree a, a, tree a)
//
(* ****** ****** *)
 
symintr ++
infixr (+) ++
overload ++ with list_append
 
(* ****** ****** *)
 
#define sing list_sing
 
(* ****** ****** *)
 
fun{
a:t@ype
} preorder
(t0: tree a): List0 a =
case t0 of
| tnil () => nil ()
| tcons (tl, x, tr) => sing(x) ++ preorder(tl) ++ preorder(tr)
 
(* ****** ****** *)
 
fun{
a:t@ype
} inorder
(t0: tree a): List0 a =
case t0 of
| tnil () => nil ()
| tcons (tl, x, tr) => inorder(tl) ++ sing(x) ++ inorder(tr)
 
(* ****** ****** *)
 
fun{
a:t@ype
} postorder
(t0: tree a): List0 a =
case t0 of
| tnil () => nil ()
| tcons (tl, x, tr) => postorder(tl) ++ postorder(tr) ++ sing(x)
 
(* ****** ****** *)
 
fun{
a:t@ype
} levelorder
(t0: tree a): List0 a = let
//
fun auxlst
(ts: List (tree(a))): List0 a =
case ts of
| list_nil () => list_nil ()
| list_cons (t, ts) =>
(
case+ t of
| tnil () => auxlst (ts)
| tcons (tl, x, tr) => cons (x, auxlst (ts ++ $list{tree(a)}(tl, tr)))
)
//
in
auxlst (sing(t0))
end // end of [levelorder]
 
(* ****** ****** *)
 
macdef
tsing(x) = tcons (tnil, ,(x), tnil)
 
(* ****** ****** *)
 
implement
main0 () = let
//
val t0 =
tcons{int}
(
tcons (tcons (tsing (7), 4, tnil ()), 2, tsing (5))
,
1
,
tcons (tcons (tsing (8), 6, tsing (9)), 3, tnil ())
)
//
in
println! ("preorder:\t", preorder(t0));
println! ("inorder:\t", inorder(t0));
println! ("postorder:\t", postorder(t0));
println! ("level-order:\t", levelorder(t0));
end (* end of [main0] *)
Output:
preorder:	1 2 4 7 5 3 6 8 9 
inorder:	7 4 2 5 1 8 6 9 3 
postorder:	7 4 5 2 8 9 6 3 1 
level-order:	1 2 3 4 5 6 7 8 9

[edit] AutoHotkey

Works with: AutoHotkey_L version 45
AddNode(Tree,1,2,3,1) ; Build global Tree
AddNode(Tree,2,4,5,2)
AddNode(Tree,3,6,0,3)
AddNode(Tree,4,7,0,4)
AddNode(Tree,5,0,0,5)
AddNode(Tree,6,8,9,6)
AddNode(Tree,7,0,0,7)
AddNode(Tree,8,0,0,8)
AddNode(Tree,9,0,0,9)
 
MsgBox % "Preorder: " PreOrder(Tree,1) ; 1 2 4 7 5 3 6 8 9
MsgBox % "Inorder: " InOrder(Tree,1) ; 7 4 2 5 1 8 6 9 3
MsgBox % "postorder: " PostOrder(Tree,1) ; 7 4 5 2 8 9 6 3 1
MsgBox % "levelorder: " LevOrder(Tree,1) ; 1 2 3 4 5 6 7 8 9
 
AddNode(ByRef Tree,Node,Left,Right,Value) {
if !isobject(Tree)
Tree := object()
 
Tree[Node, "L"] := Left
Tree[Node, "R"] := Right
Tree[Node, "V"] := Value
}
 
PreOrder(Tree,Node) {
ptree := Tree[Node, "V"] " "
. ((L:=Tree[Node, "L"]) ? PreOrder(Tree,L) : "")
. ((R:=Tree[Node, "R"]) ? PreOrder(Tree,R) : "")
return ptree
}
InOrder(Tree,Node) {
Return itree := ((L:=Tree[Node, "L"]) ? InOrder(Tree,L) : "")
. Tree[Node, "V"] " "
. ((R:=Tree[Node, "R"]) ? InOrder(Tree,R) : "")
}
PostOrder(Tree,Node) {
Return ptree := ((L:=Tree[Node, "L"]) ? PostOrder(Tree,L) : "")
. ((R:=Tree[Node, "R"]) ? PostOrder(Tree,R) : "")
. Tree[Node, "V"] " "
}
LevOrder(Tree,Node,Lev=1) {
Static ; make node lists static
i%Lev% .= Tree[Node, "V"] " " ; build node lists in every level
If (L:=Tree[Node, "L"])
LevOrder(Tree,L,Lev+1)
If (R:=Tree[Node, "R"])
LevOrder(Tree,R,Lev+1)
If (Lev > 1)
Return
While i%Lev% ; concatenate node lists from all levels
t .= i%Lev%, Lev++
Return t
}

[edit] Bracmat

(
( tree
= 1
. (2.(4.7.) (5.))
(3.6.(8.) (9.))
)
& ( preorder
= K sub
.  !arg:(?K.?sub) ?arg
& !K preorder$!sub preorder$!arg
|
)
& out$("preorder: " preorder$!tree)
& ( inorder
= K lhs rhs
.  !arg:(?K.?sub) ?arg
& (  !sub:%?lhs ?rhs
& inorder$!lhs !K inorder$!rhs inorder$!arg
| !K
)
)
& out$("inorder: " inorder$!tree)
& ( postorder
= K sub
.  !arg:(?K.?sub) ?arg
& postorder$!sub !K postorder$!arg
|
)
& out$("postorder: " postorder$!tree)
& ( levelorder
= todo tree sub
.  !arg:(.)&
|  !arg:(?tree.?todo)
& (  !tree:(?K.?sub) ?tree
& !K levelorder$(!tree.!todo !sub)
| levelorder$(!todo.)
)
)
& out$("level-order:" levelorder$(!tree.))
&
)

[edit] C

#include <stdlib.h>
#include <stdio.h>
 
typedef struct node_s
{
int value;
struct node_s* left;
struct node_s* right;
} *node;
 
node tree(int v, node l, node r)
{
node n = malloc(sizeof(struct node_s));
n->value = v;
n->left = l;
n->right = r;
return n;
}
 
void destroy_tree(node n)
{
if (n->left)
destroy_tree(n->left);
if (n->right)
destroy_tree(n->right);
free(n);
}
 
void preorder(node n, void (*f)(int))
{
f(n->value);
if (n->left)
preorder(n->left, f);
if (n->right)
preorder(n->right, f);
}
 
void inorder(node n, void (*f)(int))
{
if (n->left)
inorder(n->left, f);
f(n->value);
if (n->right)
inorder(n->right, f);
}
 
void postorder(node n, void (*f)(int))
{
if (n->left)
postorder(n->left, f);
if (n->right)
postorder(n->right, f);
f(n->value);
}
 
/* helper queue for levelorder */
typedef struct qnode_s
{
struct qnode_s* next;
node value;
} *qnode;
 
typedef struct { qnode begin, end; } queue;
 
void enqueue(queue* q, node n)
{
qnode node = malloc(sizeof(struct qnode_s));
node->value = n;
node->next = 0;
if (q->end)
q->end->next = node;
else
q->begin = node;
q->end = node;
}
 
node dequeue(queue* q)
{
node tmp = q->begin->value;
qnode second = q->begin->next;
free(q->begin);
q->begin = second;
if (!q->begin)
q->end = 0;
return tmp;
}
 
int queue_empty(queue* q)
{
return !q->begin;
}
 
void levelorder(node n, void(*f)(int))
{
queue nodequeue = {};
enqueue(&nodequeue, n);
while (!queue_empty(&nodequeue))
{
node next = dequeue(&nodequeue);
f(next->value);
if (next->left)
enqueue(&nodequeue, next->left);
if (next->right)
enqueue(&nodequeue, next->right);
}
}
 
void print(int n)
{
printf("%d ", n);
}
 
int main()
{
node n = tree(1,
tree(2,
tree(4,
tree(7, 0, 0),
0),
tree(5, 0, 0)),
tree(3,
tree(6,
tree(8, 0, 0),
tree(9, 0, 0)),
0));
 
printf("preorder: ");
preorder(n, print);
printf("\n");
 
printf("inorder: ");
inorder(n, print);
printf("\n");
 
printf("postorder: ");
postorder(n, print);
printf("\n");
 
printf("level-order: ");
levelorder(n, print);
printf("\n");
 
destroy_tree(n);
 
return 0;
}

[edit] C#

using System;
using System.Collections.Generic;
using System.Linq;
 
class Node
{
int Value;
Node Left;
Node Right;
 
Node(int value = default(int), Node left = default(Node), Node right = default(Node))
{
Value = value;
Left = left;
Right = right;
}
 
IEnumerable<int> Preorder()
{
yield return Value;
if (Left != null)
foreach (var value in Left.Preorder())
yield return value;
if (Right != null)
foreach (var value in Right.Preorder())
yield return value;
}
 
IEnumerable<int> Inorder()
{
if (Left != null)
foreach (var value in Left.Inorder())
yield return value;
yield return Value;
if (Right != null)
foreach (var value in Right.Inorder())
yield return value;
}
 
IEnumerable<int> Postorder()
{
if (Left != null)
foreach (var value in Left.Postorder())
yield return value;
if (Right != null)
foreach (var value in Right.Postorder())
yield return value;
yield return Value;
}
 
IEnumerable<int> LevelOrder()
{
var queue = new Queue<Node>();
queue.Enqueue(this);
while (queue.Any())
{
var node = queue.Dequeue();
yield return node.Value;
if (node.Left != null)
queue.Enqueue(node.Left);
if (node.Right != null)
queue.Enqueue(node.Right);
}
}
 
static void Main()
{
var tree = new Node(1, new Node(2, new Node(4, new Node(7)), new Node(5)), new Node(3, new Node(6, new Node(8), new Node(9))));
foreach (var traversal in new Func<IEnumerable<int>>[] { tree.Preorder, tree.Inorder, tree.Postorder, tree.LevelOrder })
Console.WriteLine("{0}:\t{1}", traversal.Method.Name, string.Join(" ", traversal()));
}
}

[edit] C++

Compiler: g++ (version 4.3.2 20081105 (Red Hat 4.3.2-7))

Library: Boost version 1.39.0
#include <boost/scoped_ptr.hpp>
#include <iostream>
#include <queue>
 
template<typename T>
class TreeNode {
public:
TreeNode(const T& n, TreeNode* left = NULL, TreeNode* right = NULL)
: mValue(n),
mLeft(left),
mRight(right) {}
 
T getValue() const {
return mValue;
}
 
TreeNode* left() const {
return mLeft.get();
}
 
TreeNode* right() const {
return mRight.get();
}
 
void preorderTraverse() const {
std::cout << " " << getValue();
if(mLeft) { mLeft->preorderTraverse(); }
if(mRight) { mRight->preorderTraverse(); }
}
 
void inorderTraverse() const {
if(mLeft) { mLeft->inorderTraverse(); }
std::cout << " " << getValue();
if(mRight) { mRight->inorderTraverse(); }
}
 
void postorderTraverse() const {
if(mLeft) { mLeft->postorderTraverse(); }
if(mRight) { mRight->postorderTraverse(); }
std::cout << " " << getValue();
}
 
void levelorderTraverse() const {
std::queue<const TreeNode*> q;
q.push(this);
 
while(!q.empty()) {
const TreeNode* n = q.front();
q.pop();
std::cout << " " << n->getValue();
 
if(n->left()) { q.push(n->left()); }
if(n->right()) { q.push(n->right()); }
}
}
 
protected:
T mValue;
boost::scoped_ptr<TreeNode> mLeft;
boost::scoped_ptr<TreeNode> mRight;
 
private:
TreeNode();
};
 
int main() {
TreeNode<int> root(1,
new TreeNode<int>(2,
new TreeNode<int>(4,
new TreeNode<int>(7)),
new TreeNode<int>(5)),
new TreeNode<int>(3,
new TreeNode<int>(6,
new TreeNode<int>(8),
new TreeNode<int>(9))));
 
std::cout << "preorder: ";
root.preorderTraverse();
std::cout << std::endl;
 
std::cout << "inorder: ";
root.inorderTraverse();
std::cout << std::endl;
 
std::cout << "postorder: ";
root.postorderTraverse();
std::cout << std::endl;
 
std::cout << "level-order:";
root.levelorderTraverse();
std::cout << std::endl;
 
return 0;
}

[edit] Clojure

(defn walk [node f order]
(when node
(doseq [o order]
(if (= o :visit)
(f (:val node))
(walk (node o) f order)))))
 
(defn preorder [node f]
(walk node f [:visit :left :right]))
 
(defn inorder [node f]
(walk node f [:left :visit :right]))
 
(defn postorder [node f]
(walk node f [:left :right :visit]))
 
(defn queue [& xs]
(when (seq xs)
(apply conj clojure.lang.PersistentQueue/EMPTY xs)))
 
(defn level-order [root f]
(loop [q (queue root)]
(when-not (empty? q)
(if-let [node (first q)]
(do
(f (:val node))
(recur (conj (pop q) (:left node) (:right node))))
(recur (pop q))))))
 
(defn vec-to-tree [t]
(if (vector? t)
(let [[val left right] t]
{:val val
 :left (vec-to-tree left)
 :right (vec-to-tree right)})
t))
 
(let [tree (vec-to-tree [1 [2 [4 [7]] [5]] [3 [6 [8] [9]]]])
fs '[preorder inorder postorder level-order]
pr-node #(print (format "%2d" %))]
(doseq [f fs]
(print (format "%-12s" (str f ":")))
((resolve f) tree pr-node)
(println)))

[edit] CoffeeScript

 
# In this example, we don't encapsulate binary trees as objects; instead, we have a
# convention on how to store them as arrays, and we namespace the functions that
# operate on those data structures.
binary_tree =
preorder: (tree, visit) ->
return unless tree?
[node, left, right] = tree
visit node
binary_tree.preorder left, visit
binary_tree.preorder right, visit
 
inorder: (tree, visit) ->
return unless tree?
[node, left, right] = tree
binary_tree.inorder left, visit
visit node
binary_tree.inorder right, visit
 
postorder: (tree, visit) ->
return unless tree?
[node, left, right] = tree
binary_tree.postorder left, visit
binary_tree.postorder right, visit
visit node
 
levelorder: (tree, visit) ->
q = []
q.push tree
while q.length > 0
t = q.shift()
continue unless t?
[node, left, right] = t
visit node
q.push left
q.push right
 
do ->
tree = [1, [2, [4, [7]], [5]], [3, [6, [8],[9]]]]
test_walk = (walk_function_name) ->
output = []
binary_tree[walk_function_name] tree, output.push.bind(output)
console.log walk_function_name, output.join ' '
test_walk "preorder"
test_walk "inorder"
test_walk "postorder"
test_walk "levelorder"
 

output

 
> coffee tree_traversal.coffee
preorder 1 2 4 7 5 3 6 8 9
inorder 7 4 2 5 1 8 6 9 3
postorder 7 4 5 2 8 9 6 3 1
levelorder 1 2 3 4 5 6 7 8 9
 

[edit] Common Lisp

(defun preorder (node f)
(when node
(funcall f (first node))
(preorder (second node) f)
(preorder (third node) f)))
 
(defun inorder (node f)
(when node
(inorder (second node) f)
(funcall f (first node))
(inorder (third node) f)))
 
(defun postorder (node f)
(when node
(postorder (second node) f)
(postorder (third node) f)
(funcall f (first node))))
 
(defun level-order (node f)
(loop with level = (list node)
while level
do
(setf level (loop for node in level
when node
do (funcall f (first node))
and collect (second node)
and collect (third node)))))
 
(defparameter *tree* '(1 (2 (4 (7))
(5))
(3 (6 (8)
(9)))))
 
(defun show (traversal-function)
(format t "~&~(~A~):~12,0T" traversal-function)
(funcall traversal-function *tree* (lambda (value) (format t " ~A" value))))
 
(map nil #'show '(preorder inorder postorder level-order))

Output:

preorder:    1 2 4 7 5 3 6 8 9
inorder:     7 4 2 5 1 8 6 9 3
postorder:   7 4 2 5 1 8 6 9 3
level-order: 1 2 3 4 5 6 7 8 9

[edit] D

This code is long because it's very generic.

import std.stdio, std.traits;
 
const final class Node(T) {
T data;
Node left, right;
 
this(in T data, in Node left=null, in Node right=null)
const pure nothrow {
this.data = data;
this.left = left;
this.right = right;
}
}
 
// 'static' templated opCall can't be used in Node
auto node(T)(in T data, in Node!T left=null, in Node!T right=null)
pure nothrow {
return new const(Node!T)(data, left, right);
}
 
void show(T)(in T x) {
write(x, " ");
}
 
enum Visit { pre, inv, post }
 
// 'visitor' can be any kind of callable or it uses a default visitor.
// TNode can be any kind of Node, with data, left and right fields,
// so this is more generic than a member function of Node.
void backtrackingOrder(Visit v, TNode, TyF=void*)
(in TNode node, TyF visitor=null) {
alias trueVisitor = Select!(is(TyF == void*), show, visitor);
if (node !is null) {
static if (v == Visit.pre)
trueVisitor(node.data);
backtrackingOrder!v(node.left, visitor);
static if (v == Visit.inv)
trueVisitor(node.data);
backtrackingOrder!v(node.right, visitor);
static if (v == Visit.post)
trueVisitor(node.data);
}
}
 
void levelOrder(TNode, TyF=void*)
(TNode node, TyF visitor=null,
const(TNode)[] more=[]) {
alias trueVisitor = Select!(is(TyF == void*), show, visitor);
if (node !is null) {
more ~= [node.left, node.right];
trueVisitor(node.data);
}
if (more.length)
levelOrder(more[0], visitor, more[1 .. $]);
}
 
void main() {
alias N = node;
const tree = N(1,
N(2,
N(4,
N(7)),
N(5)),
N(3,
N(6,
N(8),
N(9))));
 
write(" preOrder: ");
tree.backtrackingOrder!(Visit.pre);
write("\n inorder: ");
tree.backtrackingOrder!(Visit.inv);
write("\n postOrder: ");
tree.backtrackingOrder!(Visit.post);
write("\nlevelorder: ");
tree.levelOrder;
writeln;
}
Output:
  preOrder: 1 2 4 7 5 3 6 8 9 
   inorder: 7 4 2 5 1 8 6 9 3 
 postOrder: 7 4 5 2 8 9 6 3 1 
levelorder: 1 2 3 4 5 6 7 8 9 

[edit] Alternative Version

Translation of: Haskell

Generic as the first version, but not lazy as the Haskell version.

const struct Node(T) {
T v;
Node* l, r;
}
 
T[] preOrder(T)(in Node!T* t) pure nothrow {
return t ? t.v ~ preOrder(t.l) ~ preOrder(t.r) : [];
}
 
T[] inOrder(T)(in Node!T* t) pure nothrow {
return t ? inOrder(t.l) ~ t.v ~ inOrder(t.r) : [];
}
 
T[] postOrder(T)(in Node!T* t) pure nothrow {
return t ? postOrder(t.l) ~ postOrder(t.r) ~ t.v : [];
}
 
T[] levelOrder(T)(in Node!T* t) pure nothrow {
static T[] loop(in Node!T*[] a) pure nothrow {
if (!a.length) return [];
if (!a[0]) return loop(a[1 .. $]);
return a[0].v ~ loop(a[1 .. $] ~ [a[0].l, a[0].r]);
}
return loop([t]);
}
 
void main() {
alias N = Node!int;
auto tree = new N(1,
new N(2,
new N(4,
new N(7)),
new N(5)),
new N(3,
new N(6,
new N(8),
new N(9))));
 
import std.stdio;
writeln(preOrder(tree));
writeln(inOrder(tree));
writeln(postOrder(tree));
writeln(levelOrder(tree));
}
Output:
[1, 2, 4, 7, 5, 3, 6, 8, 9]
[7, 4, 2, 5, 1, 8, 6, 9, 3]
[7, 4, 5, 2, 8, 9, 6, 3, 1]
[1, 2, 3, 4, 5, 6, 7, 8, 9]

[edit] Alternative Lazy Version

This version is not complete, it lacks the level order visit.

import std.stdio, std.algorithm, std.range, std.string;
 
const struct Tree(T) {
T value;
Tree* left, right;
}
 
alias VisitRange(T) = InputRange!(const Tree!T);
 
VisitRange!T preOrder(T)(in Tree!T* t) /*pure nothrow*/ {
enum self = mixin("&" ~ __FUNCTION__.split(".").back);
if (t == null)
return typeof(return).init.takeNone.inputRangeObject;
return [*t]
.chain([t.left, t.right]
.filter!(t => t != null)
.map!(a => self(a))
.joiner)
.inputRangeObject;
}
 
VisitRange!T inOrder(T)(in Tree!T* t) /*pure nothrow*/ {
enum self = mixin("&" ~ __FUNCTION__.split(".").back);
if (t == null)
return typeof(return).init.takeNone.inputRangeObject;
return [t.left]
.filter!(t => t != null)
.map!(a => self(a))
.joiner
.chain([*t])
.chain([t.right]
.filter!(t => t != null)
.map!(a => self(a))
.joiner)
.inputRangeObject;
}
 
VisitRange!T postOrder(T)(in Tree!T* t) /*pure nothrow*/ {
enum self = mixin("&" ~ __FUNCTION__.split(".").back);
if (t == null)
return typeof(return).init.takeNone.inputRangeObject;
return [t.left, t.right]
.filter!(t => t != null)
.map!(a => self(a))
.joiner
.chain([*t])
.inputRangeObject;
}
 
void main() {
alias N = Tree!int;
const tree = new N(1,
new N(2,
new N(4,
new N(7)),
new N(5)),
new N(3,
new N(6,
new N(8),
new N(9))));
 
tree.preOrder.map!(t => t.value).writeln;
tree.inOrder.map!(t => t.value).writeln;
tree.postOrder.map!(t => t.value).writeln;
}
Output:
[1, 2, 4, 7, 5, 3, 6, 8, 9]
[7, 4, 2, 5, 1, 8, 6, 9, 3]
[7, 4, 5, 2, 8, 9, 6, 3, 1]

[edit] E

def btree := [1, [2, [4, [7, null, null],
null],
[5, null, null]],
[3, [6, [8, null, null],
[9, null, null]],
null]]
 
def backtrackingOrder(node, pre, mid, post) {
switch (node) {
match ==null {}
match [value, left, right] {
pre(value)
backtrackingOrder(left, pre, mid, post)
mid(value)
backtrackingOrder(right, pre, mid, post)
post(value)
}
}
}
 
def levelOrder(root, func) {
var level := [root].diverge()
while (level.size() > 0) {
for node in level.removeRun(0) {
switch (node) {
match ==null {}
match [value, left, right] {
func(value)
level.push(left)
level.push(right)
} } } } }
 
print("preorder: ")
backtrackingOrder(btree, fn v { print(" ", v) }, fn _ {}, fn _ {})
println()
 
print("inorder: ")
backtrackingOrder(btree, fn _ {}, fn v { print(" ", v) }, fn _ {})
println()
 
print("postorder: ")
backtrackingOrder(btree, fn _ {}, fn _ {}, fn v { print(" ", v) })
println()
 
print("level-order:")
levelOrder(btree, fn v { print(" ", v) })
println()

[edit] Eiffel

Works with: EiffelStudio version 7.3, Void-Safety disabled

Void-Safety has been disabled for simplicity of the code.

note
description : "Application for tree traversal demonstration"
output : "[
Prints preorder, inorder, postorder and levelorder traversal of an example binary tree.
]"

author : "Jascha Grübel"
date : "$2014-01-07$"
revision : "$1.0$"
 
class
APPLICATION
 
create
make
 
feature {NONE} -- Initialization
 
make
-- Run Tree traversal example.
local
tree:NODE
do
create tree.make (1)
tree.set_left_child (create {NODE}.make (2))
tree.set_right_child (create {NODE}.make (3))
tree.left_child.set_left_child (create {NODE}.make (4))
tree.left_child.set_right_child (create {NODE}.make (5))
tree.left_child.left_child.set_left_child (create {NODE}.make (7))
tree.right_child.set_left_child (create {NODE}.make (6))
tree.right_child.left_child.set_left_child (create {NODE}.make (8))
tree.right_child.left_child.set_right_child (create {NODE}.make (9))
 
Io.put_string ("preorder: ")
tree.print_preorder
Io.put_new_line
 
Io.put_string ("inorder: ")
tree.print_inorder
Io.put_new_line
 
Io.put_string ("postorder: ")
tree.print_postorder
Io.put_new_line
 
Io.put_string ("level-order:")
tree.print_levelorder
Io.put_new_line
 
end
 
end -- class APPLICATION
note
description : "A simple node for a binary tree"
libraries : "Relies on LINKED_LIST from EiffelBase"
author : "Jascha Grübel"
date : "$2014-01-07$"
revision : "$1.0$"
implementation : "[
All traversals but the levelorder traversal have been implemented recursively.
The levelorder traversal is solved iteratively.
]"

 
class
NODE
create
make
 
feature {NONE} -- Initialization
 
make (a_value:INTEGER)
-- Creates a node with no children.
do
value := a_value
set_right_child(Void)
set_left_child(Void)
end
 
feature -- Modification
 
set_right_child (a_node:NODE)
-- Sets `right_child' to `a_node'.
do
right_child:=a_node
end
 
set_left_child (a_node:NODE)
-- Sets `left_child' to `a_node'.
do
left_child:=a_node
end
 
feature -- Representation
 
print_preorder
-- Recursively prints the value of the node and all its children in preorder
do
Io.put_string (" " + value.out)
if has_left_child then
left_child.print_preorder
end
if has_right_child then
right_child.print_preorder
end
end
 
print_inorder
-- Recursively prints the value of the node and all its children in inorder
do
if has_left_child then
left_child.print_inorder
end
Io.put_string (" " + value.out)
if has_right_child then
right_child.print_inorder
end
end
 
print_postorder
-- Recursively prints the value of the node and all its children in postorder
do
if has_left_child then
left_child.print_postorder
end
if has_right_child then
right_child.print_postorder
end
Io.put_string (" " + value.out)
end
 
print_levelorder
-- Iteratively prints the value of the node and all its children in levelorder
local
l_linked_list:LINKED_LIST[NODE]
l_node:NODE
do
from
create l_linked_list.make
l_linked_list.extend (Current)
until
l_linked_list.is_empty
loop
l_node := l_linked_list.first
if l_node.has_left_child then
l_linked_list.extend (l_node.left_child)
end
if l_node.has_right_child then
l_linked_list.extend (l_node.right_child)
end
Io.put_string (" " + l_node.value.out)
l_linked_list.prune (l_node)
end
end
 
feature -- Access
 
value:INTEGER
-- Value stored in the node.
 
right_child:NODE
-- Reference to right child, possibly void.
 
left_child:NODE
-- Reference to left child, possibly void.
 
has_right_child:BOOLEAN
-- Test right child for existence.
do
Result := right_child /= Void
end
 
has_left_child:BOOLEAN
-- Test left child for existence.
do
Result := left_child /= Void
end
 
end
-- class NODE

[edit] Elisa

This is a generic component for binary tree traversals. More information about binary trees in Elisa are given in trees.

 
component BinaryTreeTraversals (Tree, Element);
type Tree;
type Node = Tree;
Tree (LeftTree = Tree, Element, RightTree = Tree) -> Tree;
Leaf (Element) -> Node;
Node (Tree) -> Node;
Item (Node) -> Element;
 
Preorder (Tree) -> multi (Node);
Inorder (Tree) -> multi (Node);
Postorder (Tree) -> multi (Node);
Level_order(Tree) -> multi (Node);
begin
Tree (Lefttree, Item, Righttree) = Tree: [ Lefttree; Item; Righttree ];
Leaf (anItem) = Tree (null(Tree), anItem, null(Tree) );
Node (aTree) = aTree;
Item (aNode) = aNode.Item;
 
Preorder (=null(Tree)) = no(Tree);
Preorder (T) = ( T, Preorder (T.Lefttree), Preorder (T.Righttree));
 
Inorder (=null(Tree)) = no(Tree);
Inorder (T) = ( Inorder (T.Lefttree), T, Inorder (T.Righttree));
 
Postorder (=null(Tree)) = no(Tree);
Postorder (T) = ( Postorder (T.Lefttree), Postorder (T.Righttree), T);
 
Level_order(T) = [ Queue = {T};
node = Tree:items(Queue);
[ result(node);
add(Queue, node.Lefttree) when valid(node.Lefttree);
add(Queue, node.Righttree) when valid(node.Righttree);
];
no(Tree);
];
end component BinaryTreeTraversals;
 

Tests

 
use BinaryTreeTraversals (Tree, integer);
 
BT = Tree(
Tree(
Tree(Leaf(7), 4, null(Tree)), 2 , Leaf(5)), 1,
Tree(
Tree(Leaf(8), 6, Leaf(9)), 3 ,null(Tree)));
 
{Item(Preorder(BT))}?
{ 1, 2, 4, 7, 5, 3, 6, 8, 9}
 
{Item(Inorder(BT))}?
{ 7, 4, 2, 5, 1, 8, 6, 9, 3}
 
{Item(Postorder(BT))}?
{ 7, 4, 5, 2, 8, 9, 6, 3, 1}
 
{Item(Level_order(BT))}?
{ 1, 2, 3, 4, 5, 6, 7, 8, 9}
 

[edit] Erlang

-module(tree_traversal).
-export([main/0]).
-export([preorder/2, inorder/2, postorder/2, levelorder/2]).
-export([tnode/0, tnode/1, tnode/3]).
 
-define(NEWLINE, io:format("~n")).
 
tnode() -> {}.
tnode(V) -> {node, V, {}, {}}.
tnode(V,L,R) -> {node, V, L, R}.
 
preorder(_,{}) -> ok;
preorder(F,{node,V,L,R}) ->
F(V), preorder(F,L), preorder(F,R).
 
inorder(_,{}) -> ok;
inorder(F,{node,V,L,R}) ->
inorder(F,L), F(V), inorder(F,R).
 
postorder(_,{}) -> ok;
postorder(F,{node,V,L,R}) ->
postorder(F,L), postorder(F,R), F(V).
 
levelorder(_, []) -> [];
levelorder(F, [{}|T]) -> levelorder(F, T);
levelorder(F, [{node,V,L,R}|T]) ->
F(V), levelorder(F, T++[L,R]);
levelorder(F, X) -> levelorder(F, [X]).
 
main() ->
Tree = tnode(1,
tnode(2,
tnode(4, tnode(7), tnode()),
tnode(5, tnode(), tnode())),
tnode(3,
tnode(6, tnode(8), tnode(9)),
tnode())),
F = fun(X) -> io:format("~p ",[X]) end,
preorder(F, Tree), ?NEWLINE,
inorder(F, Tree), ?NEWLINE,
postorder(F, Tree), ?NEWLINE,
levelorder(F, Tree), ?NEWLINE.

Output:

1 2 4 7 5 3 6 8 9 
7 4 2 5 1 8 6 9 3 
7 4 5 2 8 9 6 3 1 
1 2 3 4 5 6 7 8 9 

[edit] Euphoria

constant VALUE = 1, LEFT = 2, RIGHT = 3
 
constant tree = {1,
{2,
{4,
{7, 0, 0},
0},
{5, 0, 0}},
{3,
{6,
{8, 0, 0},
{9, 0, 0}},
0}}
 
procedure preorder(object tree)
if sequence(tree) then
printf(1,"%d ",{tree[VALUE]})
preorder(tree[LEFT])
preorder(tree[RIGHT])
end if
end procedure
 
procedure inorder(object tree)
if sequence(tree) then
inorder(tree[LEFT])
printf(1,"%d ",{tree[VALUE]})
inorder(tree[RIGHT])
end if
end procedure
 
procedure postorder(object tree)
if sequence(tree) then
postorder(tree[LEFT])
postorder(tree[RIGHT])
printf(1,"%d ",{tree[VALUE]})
end if
end procedure
 
procedure lo(object tree, sequence more)
if sequence(tree) then
more &= {tree[LEFT],tree[RIGHT]}
printf(1,"%d ",{tree[VALUE]})
end if
if length(more) > 0 then
lo(more[1],more[2..$])
end if
end procedure
 
procedure level_order(object tree)
lo(tree,{})
end procedure
 
puts(1,"preorder: ")
preorder(tree)
puts(1,'\n')
 
puts(1,"inorder: ")
inorder(tree)
puts(1,'\n')
 
puts(1,"postorder: ")
postorder(tree)
puts(1,'\n')
 
puts(1,"level-order: ")
level_order(tree)
puts(1,'\n')

Output:

preorder:    1 2 4 7 5 3 6 8 9
inorder:     7 4 2 5 1 8 6 9 3
postorder:   7 4 5 2 8 9 6 3 1
level-order: 1 2 3 4 5 6 7 8 9

[edit] F#

open System
open System.IO
 
type Tree<'a> =
| Tree of '
a * Tree<'a> * Tree<'a>
| Empty
 
let rec inorder tree =
seq {
match tree with
| Tree(x, left, right) ->
yield! inorder left
yield x
yield! inorder right
| Empty -> ()
}
 
let rec preorder tree =
seq {
match tree with
| Tree(x, left, right) ->
yield x
yield! preorder left
yield! preorder right
| Empty -> ()
}
 
let rec postorder tree =
seq {
match tree with
| Tree(x, left, right) ->
yield! postorder left
yield! postorder right
yield x
| Empty -> ()
}
 
let levelorder tree =
let rec loop queue =
seq {
match queue with
| [] -> ()
| (Empty::tail) -> yield! loop tail
| (Tree(x, l, r)::tail) ->
yield x
yield! loop (tail @ [l; r])
}
loop [tree]
 
[<EntryPoint>]
let main _ =
let tree =
Tree (1,
Tree (2,
Tree (4,
Tree (7, Empty, Empty),
Empty),
Tree (5, Empty, Empty)),
Tree (3,
Tree (6,
Tree (8, Empty, Empty),
Tree (9, Empty, Empty)),
Empty))
 
let show x = printf "%d " x
 
printf "preorder: "
preorder tree |> Seq.iter show
printf "\ninorder: "
inorder tree |> Seq.iter show
printf "\npostorder: "
postorder tree |> Seq.iter show
printf "\nlevel-order: "
levelorder tree |> Seq.iter show
0

[edit] Factor

USING: accessors combinators deques dlists fry io kernel
math.parser ;
IN: rosetta.tree-traversal
 
TUPLE: node data left right ;
 
CONSTANT: example-tree
T{ node f 1
T{ node f 2
T{ node f 4
T{ node f 7 f f }
f
}
T{ node f 5 f f }
}
T{ node f 3
T{ node f 6
T{ node f 8 f f }
T{ node f 9 f f }
}
f
}
}
 
: preorder ( node quot: ( data -- ) -- )
[ [ data>> ] dip call ]
[ [ left>> ] dip over [ preorder ] [ 2drop ] if ]
[ [ right>> ] dip over [ preorder ] [ 2drop ] if ]
2tri ; inline recursive
 
: inorder ( node quot: ( data -- ) -- )
[ [ left>> ] dip over [ inorder ] [ 2drop ] if ]
[ [ data>> ] dip call ]
[ [ right>> ] dip over [ inorder ] [ 2drop ] if ]
2tri ; inline recursive
 
: postorder ( node quot: ( data -- ) -- )
[ [ left>> ] dip over [ postorder ] [ 2drop ] if ]
[ [ right>> ] dip over [ postorder ] [ 2drop ] if ]
[ [ data>> ] dip call ]
2tri ; inline recursive
 
: (levelorder) ( dlist quot: ( data -- ) -- )
over deque-empty? [ 2drop ] [
[ dup pop-front ] dip {
[ [ data>> ] dip call drop ]
[ drop left>> [ swap push-back ] [ drop ] if* ]
[ drop right>> [ swap push-back ] [ drop ] if* ]
[ nip (levelorder) ]
} 3cleave
] if ; inline recursive
 
: levelorder ( node quot: ( data -- ) -- )
[ 1dlist ] dip (levelorder) ; inline
 
: levelorder2 ( node quot: ( data -- ) -- )
[ 1dlist ] dip
[ dup deque-empty? not ] swap '[
dup pop-front
[ data>> @ ]
[ left>> [ over push-back ] when* ]
[ right>> [ over push-back ] when* ] tri
] while drop ; inline
 
: main ( -- )
example-tree [ number>string write " " write ] {
[ "preorder: " write preorder nl ]
[ "inorder: " write inorder nl ]
[ "postorder: " write postorder nl ]
[ "levelorder: " write levelorder nl ]
[ "levelorder2: " write levelorder2 nl ]
} 2cleave ;

[edit] Fantom

 
class Tree
{
readonly Int label
readonly Tree? left
readonly Tree? right
 
new make (Int label, Tree? left := null, Tree? right := null)
{
this.label = label
this.left = left
this.right = right
}
 
Void preorder(|Int->Void| func)
{
func(label)
left?.preorder(func) // ?. will not call method if 'left' is null
right?.preorder(func)
}
 
Void postorder(|Int->Void| func)
{
left?.postorder(func)
right?.postorder(func)
func(label)
}
 
Void inorder(|Int->Void| func)
{
left?.inorder(func)
func(label)
right?.inorder(func)
}
 
Void levelorder(|Int->Void| func)
{
Tree[] nodes := [this]
while (nodes.size > 0)
{
Tree cur := nodes.removeAt(0)
func(cur.label)
if (cur.left != null) nodes.add (cur.left)
if (cur.right != null) nodes.add (cur.right)
}
}
}
 
class Main
{
public static Void main ()
{
tree := Tree(1,
Tree(2, Tree(4, Tree(7)), Tree(5)),
Tree(3, Tree(6, Tree(8), Tree(9))))
List result := [,]
collect := |Int a -> Void| { result.add(a) }
tree.preorder(collect)
echo ("preorder: " + result.join(" "))
result = [,]
tree.inorder(collect)
echo ("inorder: " + result.join(" "))
result = [,]
tree.postorder(collect)
echo ("postorder: " + result.join(" "))
result = [,]
tree.levelorder(collect)
echo ("levelorder: " + result.join(" "))
}
}
 

Output:

preorder:    1 2 4 7 5 3 6 8 9
inorder:     7 4 2 5 1 8 6 9 3
postorder:   7 4 5 2 8 9 6 3 1
levelorder:  1 2 3 4 5 6 7 8 9

[edit] Forth

\ binary tree (dictionary)
: node ( l r data -- node ) here >r , , , r> ;
: leaf ( data -- node ) 0 0 rot node ;
 
: >data ( node -- ) @ ;
: >right ( node -- ) cell+ @ ;
: >left ( node -- ) cell+ cell+ @ ;
 
: preorder ( xt tree -- )
dup 0= if 2drop exit then
2dup >data swap execute
2dup >left recurse
>right recurse ;
 
: inorder ( xt tree -- )
dup 0= if 2drop exit then
2dup >left recurse
2dup >data swap execute
>right recurse ;
 
: postorder ( xt tree -- )
dup 0= if 2drop exit then
2dup >left recurse
2dup >right recurse
>data swap execute ;
 
: max-depth ( tree -- n )
dup 0= if exit then
dup >left recurse
swap >right recurse max 1+ ;
 
defer depthaction
: depthorder ( depth tree -- )
dup 0= if 2drop exit then
over 0=
if >data depthaction drop
else over 1- over >left recurse
swap 1- swap >right recurse
then ;
 
: levelorder ( xt tree -- )
swap is depthaction
dup max-depth 0 ?do
i over depthorder
loop drop ;
 
7 leaf 0 4 node
5 leaf 2 node
8 leaf 9 leaf 6 node
0 3 node 1 node value tree
 
cr ' . tree preorder \ 1 2 4 7 5 3 6 8 9
cr ' . tree inorder \ 7 4 2 5 1 8 6 9 3
cr ' . tree postorder \ 7 4 5 2 8 9 6 3 1
cr tree max-depth . \ 4
cr ' . tree levelorder \ 1 2 3 4 5 6 7 8 9

[edit] FunL

Translation of: Haskell
data Tree = Empty | Node( value, left, right )
 
def
preorder( Empty ) = []
preorder( Node(v, l, r) ) = [v] + preorder( l ) + preorder( r )
 
inorder( Empty ) = []
inorder( Node(v, l, r) ) = inorder( l ) + [v] + inorder( r )
 
postorder( Empty ) = []
postorder( Node(v, l, r) ) = postorder( l ) + postorder( r ) + [v]
 
levelorder( x ) =
def
loop( [] ) = []
loop( Empty  : xs ) = loop( xs )
loop( Node(v, l, r) : xs ) = v : loop( xs + [l, r] )
 
loop( [x] )
 
tree = Node( 1,
Node( 2,
Node( 4,
Node( 7, Empty, Empty ),
Empty ),
Node( 5, Empty, Empty ) ),
Node( 3,
Node( 6,
Node( 8, Empty, Empty ),
Node( 9, Empty, Empty ) ),
Empty ) )
 
println( preorder(tree) )
println( inorder(tree) )
println( postorder(tree) )
println( levelorder(tree) )
Output:
[1, 2, 4, 7, 5, 3, 6, 8, 9]
[7, 4, 2, 5, 1, 8, 6, 9, 3]
[7, 4, 5, 2, 8, 9, 6, 3, 1]
[1, 2, 3, 4, 5, 6, 7, 8, 9]

[edit] Go

[edit] Individually allocated nodes

Translation of: C

This is like many examples on this page.

package main
 
import "fmt"
 
type node struct {
value int
left, right *node
}
 
func (n *node) iterPreorder(visit func(int)) {
if n == nil {
return
}
visit(n.value)
n.left.iterPreorder(visit)
n.right.iterPreorder(visit)
}
 
func (n *node) iterInorder(visit func(int)) {
if n == nil {
return
}
n.left.iterInorder(visit)
visit(n.value)
n.right.iterInorder(visit)
}
 
func (n *node) iterPostorder(visit func(int)) {
if n == nil {
return
}
n.left.iterPostorder(visit)
n.right.iterPostorder(visit)
visit(n.value)
}
 
func (n *node) iterLevelorder(visit func(int)) {
if n == nil {
return
}
for queue := []*node{n}; ; {
n = queue[0]
visit(n.value)
copy(queue, queue[1:])
queue = queue[:len(queue)-1]
if n.left != nil {
queue = append(queue, n.left)
}
if n.right != nil {
queue = append(queue, n.right)
}
if len(queue) == 0 {
return
}
}
}
 
func main() {
tree := &node{1,
&node{2,
&node{4,
&node{7, nil, nil},
nil},
&node{5, nil, nil}},
&node{3,
&node{6,
&node{8, nil, nil},
&node{9, nil, nil}},
nil}}
fmt.Print("preorder: ")
tree.iterPreorder(visitor)
fmt.Println()
fmt.Print("inorder: ")
tree.iterInorder(visitor)
fmt.Println()
fmt.Print("postorder: ")
tree.iterPostorder(visitor)
fmt.Println()
fmt.Print("level-order: ")
tree.iterLevelorder(visitor)
fmt.Println()
}
 
func visitor(value int) {
fmt.Print(value, " ")
}
Output:
preorder:    1 2 4 7 5 3 6 8 9
inorder:     7 4 2 5 1 8 6 9 3
postorder:   7 4 5 2 8 9 6 3 1
level-order: 1 2 3 4 5 6 7 8 9

[edit] Flat slice

Alternative representation. Like Wikipedia Binary tree#Arrays

package main
 
import "fmt"
 
// flat, level-order representation.
// for node at index k, left child has index 2k, right child has index 2k+1.
// a value of -1 means the node does not exist.
type tree []int
 
func main() {
t := tree{1, 2, 3, 4, 5, 6, -1, 7, -1, -1, -1, 8, 9}
visitor := func(n int) {
fmt.Print(n, " ")
}
fmt.Print("preorder: ")
t.iterPreorder(visitor)
fmt.Print("\ninorder: ")
t.iterInorder(visitor)
fmt.Print("\npostorder: ")
t.iterPostorder(visitor)
fmt.Print("\nlevel-order: ")
t.iterLevelorder(visitor)
fmt.Println()
}
 
func (t tree) iterPreorder(visit func(int)) {
var traverse func(int)
traverse = func(k int) {
if k >= len(t) || t[k] == -1 {
return
}
visit(t[k])
traverse(2*k + 1)
traverse(2*k + 2)
}
traverse(0)
}
 
func (t tree) iterInorder(visit func(int)) {
var traverse func(int)
traverse = func(k int) {
if k >= len(t) || t[k] == -1 {
return
}
traverse(2*k + 1)
visit(t[k])
traverse(2*k + 2)
}
traverse(0)
}
 
func (t tree) iterPostorder(visit func(int)) {
var traverse func(int)
traverse = func(k int) {
if k >= len(t) || t[k] == -1 {
return
}
traverse(2*k + 1)
traverse(2*k + 2)
visit(t[k])
}
traverse(0)
}
 
func (t tree) iterLevelorder(visit func(int)) {
for _, n := range t {
if n != -1 {
visit(n)
}
}
}

[edit] Groovy

Uses Groovy Node and NodeBuilder classes

def preorder;
preorder = { Node node ->
([node] + node.children().collect { preorder(it) }).flatten()
}
 
def postorder;
postorder = { Node node ->
(node.children().collect { postorder(it) } + [node]).flatten()
}
 
def inorder;
inorder = { Node node ->
def kids = node.children()
if (kids.empty) [node]
else if (kids.size() == 1 && kids[0].'@right') [node] + inorder(kids[0])
else inorder(kids[0]) + [node] + (kids.size()>1 ? inorder(kids[1]) : [])
}
 
def levelorder = { Node node ->
def nodeList = []
def level = [node]
while (!level.empty) {
nodeList += level
def nextLevel = level.collect { it.children() }.flatten()
level = nextLevel
}
nodeList
}
 
class BinaryNodeBuilder extends NodeBuilder {
protected Object postNodeCompletion(Object parent, Object node) {
assert node.children().size() < 3
node
}
}

Verify that BinaryNodeBuilder will not allow a node to have more than 2 children

try {
new BinaryNodeBuilder().'1' {
a {}
b {}
c {}
}
println 'not limited to binary tree\r\n'
} catch (org.codehaus.groovy.transform.powerassert.PowerAssertionError e) {
println 'limited to binary tree\r\n'
}

Test case #1 (from the task definition)

//               1
// / \
// 2 3
// / \ /
// 4 5 6
// / / \
// 7 8 9
def tree1 = new BinaryNodeBuilder().
'1' {
'2' {
'4' { '7' {} }
'5' {}
}
'3' {
'6' { '8' {}; '9' {} }
}
}

Test case #2 (tests single right child)

//               1
// / \
// 2 3
// / \ /
// 4 5 6
// \ / \
// 7 8 9
def tree2 = new BinaryNodeBuilder().
'1' {
'2' {
'4' { '7'(right:true) {} }
'5' {}
}
'3' {
'6' { '8' {}; '9' {} }
}
}

Run tests:

def test = { tree ->
println "preorder: ${preorder(tree).collect{it.name()}}"
println "preorder: ${tree.depthFirst().collect{it.name()}}"
 
println "postorder: ${postorder(tree).collect{it.name()}}"
 
println "inorder: ${inorder(tree).collect{it.name()}}"
 
println "level-order: ${levelorder(tree).collect{it.name()}}"
println "level-order: ${tree.breadthFirst().collect{it.name()}}"
 
println()
}
test(tree1)
test(tree2)

Output:

limited to binary tree

preorder:    [1, 2, 4, 7, 5, 3, 6, 8, 9]
preorder:    [1, 2, 4, 7, 5, 3, 6, 8, 9]
postorder:   [7, 4, 5, 2, 8, 9, 6, 3, 1]
inorder:     [7, 4, 2, 5, 1, 8, 6, 9, 3]
level-order: [1, 2, 3, 4, 5, 6, 7, 8, 9]
level-order: [1, 2, 3, 4, 5, 6, 7, 8, 9]

preorder:    [1, 2, 4, 7, 5, 3, 6, 8, 9]
preorder:    [1, 2, 4, 7, 5, 3, 6, 8, 9]
postorder:   [7, 4, 5, 2, 8, 9, 6, 3, 1]
inorder:     [4, 7, 2, 5, 1, 8, 6, 9, 3]
level-order: [1, 2, 3, 4, 5, 6, 7, 8, 9]
level-order: [1, 2, 3, 4, 5, 6, 7, 8, 9]

[edit] Haskell

data Tree a = Empty
| Node { value :: a,
left :: Tree a,
right :: Tree a }
 
preorder, inorder, postorder, levelorder :: Tree a -> [a]
 
preorder Empty = []
preorder (Node v l r) = [v]
++ preorder l
++ preorder r
 
inorder Empty = []
inorder (Node v l r) = inorder l
++ [v]
++ inorder r
 
postorder Empty = []
postorder (Node v l r) = postorder l
++ postorder r
++ [v]
 
levelorder x = loop [x]
where loop [] = []
loop (Empty  : xs) = loop xs
loop (Node v l r : xs) = v : loop (xs ++ [l,r])
 
tree :: Tree Int
tree = Node 1
(Node 2
(Node 4
(Node 7 Empty Empty)
Empty)
(Node 5 Empty Empty))
(Node 3
(Node 6
(Node 8 Empty Empty)
(Node 9 Empty Empty))
Empty)
 
main :: IO ()
main = do print $ preorder tree
print $ inorder tree
print $ postorder tree
print $ levelorder tree

Output:

[1,2,4,7,5,3,6,8,9]
[7,4,2,5,1,8,6,9,3]
[7,4,5,2,8,9,6,3,1]
[1,2,3,4,5,6,7,8,9]

[edit] Icon and Unicon

procedure main()
bTree := [1, [2, [4, [7]], [5]], [3, [6, [8], [9]]]]
showTree(bTree, preorder|inorder|postorder|levelorder)
end
 
procedure showTree(tree, f)
writes(image(f),":\t")
every writes(" ",f(tree)[1])
write()
end
 
procedure preorder(L)
if \L then suspend L | preorder(L[2|3])
end
 
procedure inorder(L)
if \L then suspend inorder(L[2]) | L | inorder(L[3])
end
 
procedure postorder(L)
if \L then suspend postorder(L[2|3]) | L
end
 
procedure levelorder(L)
if \L then {
queue := [L]
while nextnode := get(queue) do {
every put(queue, \nextnode[2|3])
suspend nextnode
}
}
end

Output:

->bintree
procedure preorder:      1 2 4 7 5 3 6 8 9
procedure inorder:       7 4 2 5 1 8 6 9 3
procedure postorder:     7 4 5 2 8 9 6 3 1
procedure levelorder:    1 2 3 4 5 6 7 8 9
->

[edit] J

preorder=: ]S:0
postorder=: ([:; postorder&.>@}.) , >@{.
levelorder=: ;@({::L:1 _~ [: (/: #@>) <S:1@{::)
inorder=: ([:; inorder&.>@(''"_`(1&{)@.(1<#))) , >@{. , [:; inorder&.>@}.@}.

Required example:

N2=: conjunction def '(<m),(<n),<y'
N1=: adverb def '(<m),<y'
L=: adverb def '<m'
 
tree=: 1 N2 (2 N2 (4 N1 (7 L)) 5 L) 3 N1 6 N2 (8 L) 9 L

This tree is organized in a pre-order fashion

    preorder tree
1 2 4 7 5 3 6 8 9

post-order is not that much different from pre-order, except that the children must extracted before the parent.

    postorder tree
7 4 5 2 8 9 6 3 1

Implementing in-order is more complex because we must sometimes test whether we have any leaves, instead of relying on J's implicit looping over lists

    inorder tree
7 4 2 5 1 8 6 9 3

level-order can be accomplished by constructing a map of the locations of the leaves, sorting these map locations by their non-leaf indices and using the result to extract all leaves from the tree. Elements at the same level with the same parent will have the same sort keys and thus be extracted in preorder fashion, which works just fine.

    levelorder tree
1 2 3 4 5 6 7 8 9


For J novices, here's the tree instance with a few redundant parenthesis:

    tree=: 1 N2 (2 N2 (4 N1 (7 L)) (5 L)) (3 N1 (6 N2 (8 L) (9 L)))

Syntactically, N2 is a binary node expressed as m N2 n y. N1 is a node with a single child, expressed as m N2 y. L is a leaf node, expressed as m L. In all three cases, the parent value (m) for the node appears on the left, and the child tree(s) appear on the right. (And n must be parenthesized if it is not a single word.)

[edit] Java

Works with: Java version 1.5+
import java.util.Queue;
import java.util.LinkedList;
public class TreeTraverse
{
private static class Node<T>
{
public Node<T> left;
public Node<T> right;
public T data;
public Node(T data)
{
this.data = data;
}
public Node<T> getLeft()
{
return this.left;
}
public void setLeft(Node<T> left)
{
this.left = left;
}
public Node<T> getRight()
{
return this.right;
}
public void setRight(Node<T> right)
{
this.right = right;
}
}
public static void preorder(Node<?> n)
{
if (n != null)
{
System.out.print(n.data + " ");
preorder(n.getLeft());
preorder(n.getRight());
}
}
public static void inorder(Node<?> n)
{
if (n != null)
{
inorder(n.getLeft());
System.out.print(n.data + " ");
inorder(n.getRight());
}
}
public static void postorder(Node<?> n)
{
if (n != null)
{
postorder(n.getLeft());
postorder(n.getRight());
System.out.print(n.data + " ");
}
}
public static void levelorder(Node<?> n)
{
Queue<Node<?>> nodequeue = new LinkedList<Node<?>>();
if (n != null)
nodequeue.add(n);
while (!nodequeue.isEmpty())
{
Node<?> next = nodequeue.remove();
System.out.print(next.data + " ");
if (next.getLeft() != null)
{
nodequeue.add(next.getLeft());
}
if (next.getRight() != null)
{
nodequeue.add(next.getRight());
}
}
}
public static void main(final String[] args)
{
Node<Integer> one = new Node<Integer>(1);
Node<Integer> two = new Node<Integer>(2);
Node<Integer> three = new Node<Integer>(3);
Node<Integer> four = new Node<Integer>(4);
Node<Integer> five = new Node<Integer>(5);
Node<Integer> six = new Node<Integer>(6);
Node<Integer> seven = new Node<Integer>(7);
Node<Integer> eight = new Node<Integer>(8);
Node<Integer> nine = new Node<Integer>(9);
one.setLeft(two);
one.setRight(three);
two.setLeft(four);
two.setRight(five);
three.setLeft(six);
four.setLeft(seven);
six.setLeft(eight);
six.setRight(nine);
preorder(one);
System.out.println();
inorder(one);
System.out.println();
postorder(one);
System.out.println();
levelorder(one);
System.out.println();
}
}

Output:

1 2 4 7 5 3 6 8 9 
7 4 2 5 1 8 6 9 3 
7 4 5 2 8 9 6 3 1 
1 2 3 4 5 6 7 8 9 

[edit] JavaScript

inspired by Ruby

function BinaryTree(value, left, right) {
this.value = value;
this.left = left;
this.right = right;
}
BinaryTree.prototype.preorder = function(f) {this.walk(f,['this','left','right'])}
BinaryTree.prototype.inorder = function(f) {this.walk(f,['left','this','right'])}
BinaryTree.prototype.postorder = function(f) {this.walk(f,['left','right','this'])}
BinaryTree.prototype.walk = function(func, order) {
for (var i in order)
switch (order[i]) {
case "this": func(this.value); break;
case "left": if (this.left) this.left.walk(func, order); break;
case "right": if (this.right) this.right.walk(func, order); break;
}
}
BinaryTree.prototype.levelorder = function(func) {
var queue = [this];
while (queue.length != 0) {
var node = queue.shift();
func(node.value);
if (node.left) queue.push(node.left);
if (node.right) queue.push(node.right);
}
}
 
// convenience function for creating a binary tree
function createBinaryTreeFromArray(ary) {
var left = null, right = null;
if (ary[1]) left = createBinaryTreeFromArray(ary[1]);
if (ary[2]) right = createBinaryTreeFromArray(ary[2]);
return new BinaryTree(ary[0], left, right);
}
 
var tree = createBinaryTreeFromArray([1, [2, [4, [7]], [5]], [3, [6, [8],[9]]]]);
 
print("*** preorder ***"); tree.preorder(print);
print("*** inorder ***"); tree.inorder(print);
print("*** postorder ***"); tree.postorder(print);
print("*** levelorder ***"); tree.levelorder(print);

[edit] Julia

tree = {1, {2, {4, {7,{},{}},
{}},
{5, {},{}}},
{3, {6, {8,{},{}},
{9,{},{}}},
{}}}
 
preorder(t,f) = if !isempty(t)
f(t[1]) ; preorder(t[2],f) ; preorder(t[3],f)
end
 
inorder(t,f) = if !isempty(t)
inorder(t[2],f) ; f(t[1]) ; inorder(t[3],f)
end
 
postorder(t,f) = if !isempty(t)
postorder(t[2],f) ; postorder(t[3],f) ; f(t[1])
end
 
levelorder(t,f) = while !isempty(t)
t = mapreduce(x->isa(x,Number)? (f(x);{}): x, vcat, t)
end
Output:
julia> for f in {preorder, inorder, postorder, levelorder}
         f(tree, x->print(x," ")) ; println("<- $f")
       end
1 2 4 7 5 3 6 8 9 <- preorder
7 4 2 5 1 8 6 9 3 <- inorder
7 4 5 2 8 9 6 3 1 <- postorder
1 2 3 4 5 6 7 8 9 <- levelorder

[edit]

; nodes are [data left right], use "first" to get data
 
to node.left :node
if empty? butfirst :node [output []]
output first butfirst :node
end
to node.right :node
if empty? butfirst :node [output []]
if empty? butfirst butfirst :node [output []]
output first butfirst butfirst :node
end
to max :a :b
output ifelse :a > :b [:a] [:b]
end
to tree.depth :tree
if empty? :tree [output 0]
output 1 + max tree.depth node.left :tree tree.depth node.right :tree
end
 
to pre.order :tree :action
if empty? :tree [stop]
invoke :action first :tree
pre.order node.left :tree :action
pre.order node.right :tree :action
end
to in.order :tree :action
if empty? :tree [stop]
in.order node.left :tree :action
invoke :action first :tree
in.order node.right :tree :action
end
to post.order :tree :action
if empty? :tree [stop]
post.order node.left :tree :action
post.order node.right :tree :action
invoke :action first :tree
end
to at.depth :n :tree :action
if empty? :tree [stop]
ifelse :n = 1 [invoke :action first :tree] [
at.depth :n-1 node.left  :tree :action
at.depth :n-1 node.right :tree :action
]
end
to level.order :tree :action
for [i 1 [tree.depth :tree]] [at.depth :i :tree :action]
end
 
make "tree [1 [2 [4 [7]]
[5]]
[3 [6 [8]
[9]]]]
 
pre.order :tree [(type ? "| |)] (print)
in.order :tree [(type ? "| |)] (print)
post.order :tree [(type ? "| |)] (print)
level.order :tree [(type ? "| |)] (print)

[edit] Logtalk

 
:- object(tree_traversal).
 
:- public(orders/1).
orders(Tree) :-
write('Pre-order: '), pre_order(Tree), nl,
write('In-order: '), in_order(Tree), nl,
write('Post-order: '), post_order(Tree), nl,
write('Level-order: '), level_order(Tree).
 
:- public(orders/0).
orders :-
tree(Tree),
orders(Tree).
 
tree(
t(1,
t(2,
t(4,
t(7, t, t),
t
),
t(5, t, t)
),
t(3,
t(6,
t(8, t, t),
t(9, t, t)
),
t
)
)
).
 
pre_order(t).
pre_order(t(Value, Left, Right)) :-
write(Value), write(' '),
pre_order(Left),
pre_order(Right).
 
in_order(t).
in_order(t(Value, Left, Right)) :-
in_order(Left),
write(Value), write(' '),
in_order(Right).
 
post_order(t).
post_order(t(Value, Left, Right)) :-
post_order(Left),
post_order(Right),
write(Value), write(' ').
 
level_order(t).
level_order(t(Value, Left, Right)) :-
% write tree root value
write(Value), write(' '),
% write rest of the tree
level_order([Left, Right], Tail-Tail).
 
level_order([], Trees-[]) :-
( Trees \= [] ->
% print next level
level_order(Trees, Tail-Tail)
; % no more levels
true
).
level_order([Tree| Trees], Rest0) :-
( Tree = t(Value, Left, Right) ->
write(Value), write(' '),
% collect the subtrees to print the next level
append(Rest0, [Left, Right| Tail]-Tail, Rest1),
% continue printing the current level
level_order(Trees, Rest1)
; % continue printing the current level
level_order(Trees, Rest0)
).
 
% use difference-lists for constant time append
append(List1-Tail1, Tail1-Tail2, List1-Tail2).
 
:- end_object.
 

Sample output:

 
| ?- ?- tree_traversal::orders.
Pre-order: 1 2 4 7 5 3 6 8 9
In-order: 7 4 2 5 1 8 6 9 3
Post-order: 7 4 5 2 8 9 6 3 1
Level-order: 1 2 3 4 5 6 7 8 9
yes
 

[edit] Mathematica

preorder[a_Integer] := a; 
preorder[a_[b__]] := Flatten@{a, preorder /@ {b}};
inorder[a_Integer] := a;
inorder[a_[b_, c_]] := Flatten@{inorder@b, a, inorder@c};
inorder[a_[b_]] := Flatten@{inorder@b, a}; postorder[a_Integer] := a;
postorder[a_[b__]] := Flatten@{postorder /@ {b}, a};
levelorder[a_] :=
Flatten[Table[Level[a, {n}], {n, 0, Depth@a}]] /. {b_Integer[__] :>
b};

Example:

preorder[1[2[4[7], 5], 3[6[8, 9]]]]
inorder[1[2[4[7], 5], 3[6[8, 9]]]]
postorder[1[2[4[7], 5], 3[6[8, 9]]]]
levelorder[1[2[4[7], 5], 3[6[8, 9]]]]

Output:

{1, 2, 4, 7, 5, 3, 6, 8, 9}

{7, 4, 2, 5, 1, 8, 6, 9, 3}

{7, 4, 5, 2, 8, 9, 6, 3, 1}

{1, 2, 3, 4, 5, 6, 7, 8, 9}

[edit] Nimrod

import queues, sequtils
 
type
Node[T] = ref TNode[T]
TNode[T] = object
data: T
left, right: Node[T]
 
proc newNode[T](data: T; left, right: Node[T] = nil): Node[T] =
Node[T](data: data, left: left, right: right)
 
proc preorder[T](n: Node[T]): seq[T] =
if n == nil: @[]
else: @[n.data] & preorder(n.left) & preorder(n.right)
 
proc inorder[T](n: Node[T]): seq[T] =
if n == nil: @[]
else: inorder(n.left) & @[n.data] & inorder(n.right)
 
proc postorder[T](n: Node[T]): seq[T] =
if n == nil: @[]
else: postorder(n.left) & postorder(n.right) & @[n.data]
 
proc levelorder[T](n: Node[T]): seq[T] =
result = @[]
var queue = initQueue[Node[T]]()
queue.enqueue(n)
while queue.len > 0:
let next = queue.dequeue()
result.add next.data
if next.left != nil: queue.enqueue(next.left)
if next.right != nil: queue.enqueue(next.right)
 
let tree = 1.newNode(
2.newNode(
4.newNode(
7.newNode),
5.newNode),
3.newNode(
6.newNode(
8.newNode,
9.newNode)))
 
echo preorder tree
echo inorder tree
echo postorder tree
echo levelorder tree

Output:

@[1, 2, 4, 7, 5, 3, 6, 8, 9]
@[7, 4, 2, 5, 1, 8, 6, 9, 3]
@[7, 4, 5, 2, 8, 9, 6, 3, 1]
@[1, 2, 3, 4, 5, 6, 7, 8, 9]

[edit] Objeck

 
use Collection;
 
class Test {
function : Main(args : String[]) ~ Nil {
one := Node->New(1);
two := Node->New(2);
three := Node->New(3);
four := Node->New(4);
five := Node->New(5);
six := Node->New(6);
seven := Node->New(7);
eight := Node->New(8);
nine := Node->New(9);
 
one->SetLeft(two); one->SetRight(three);
two->SetLeft(four); two->SetRight(five);
three->SetLeft(six); four->SetLeft(seven);
six->SetLeft(eight); six->SetRight(nine);
 
"Preorder: "->Print(); Preorder(one);
"\nInorder: "->Print(); Inorder(one);
"\nPostorder: "->Print(); Postorder(one);
"\nLevelorder: "->Print(); Levelorder(one);
"\n"->Print();
}
 
function : Preorder(node : Node) ~ Nil {
if(node <> Nil) {
System.IO.Console->Print(node->GetData())->Print(", ");
Preorder(node->GetLeft());
Preorder(node->GetRight());
};
}
 
function : Inorder(node : Node) ~ Nil {
if(node <> Nil) {
Inorder(node->GetLeft());
System.IO.Console->Print(node->GetData())->Print(", ");
Inorder(node->GetRight());
};
}
 
function : Postorder(node : Node) ~ Nil {
if(node <> Nil) {
Postorder(node->GetLeft());
Postorder(node->GetRight());
System.IO.Console->Print(node->GetData())->Print(", ");
};
}
 
function : Levelorder(node : Node) ~ Nil {
nodequeue := Collection.Queue->New();
if(node <> Nil) {
nodequeue->Add(node);
};
 
while(nodequeue->IsEmpty() = false) {
next := nodequeue->Remove()->As(Node);
System.IO.Console->Print(next->GetData())->Print(", ");
if(next->GetLeft() <> Nil) {
nodequeue->Add(next->GetLeft());
};
 
if(next->GetRight() <> Nil) {
nodequeue->Add(next->GetRight());
};
};
}
}
 
class Node from BasicCompare {
@left : Node;
@right : Node;
@data : Int;
 
New(data : Int) {
Parent();
@data := data;
}
 
method : public : GetData() ~ Int {
return @data;
}
 
method : public : SetLeft(left : Node) ~ Nil {
@left := left;
}
 
method : public : GetLeft() ~ Node {
return @left;
}
 
method : public : SetRight(right : Node) ~ Nil {
@right := right;
}
 
method : public : GetRight() ~ Node {
return @right;
}
 
method : public : Compare(rhs : Compare) ~ Int {
right : Node := rhs->As(Node);
if(@data = right->GetData()) {
return 0;
}
else if(@data < right->GetData()) {
return -1;
};
 
return 1;
}
}
 

Output:

Preorder: 1, 2, 4, 7, 5, 3, 6, 8, 9, 
Inorder: 7, 4, 2, 5, 1, 8, 6, 9, 3, 
Postorder: 7, 4, 5, 2, 8, 9, 6, 3, 1, 
Levelorder: 1, 2, 3, 4, 5, 6, 7, 8, 9, 

[edit] OCaml

type 'a tree = Empty
| Node of 'a * 'a tree * 'a tree
 
let rec preorder f = function
Empty -> ()
| Node (v,l,r) -> f v;
preorder f l;
preorder f r
 
let rec inorder f = function
Empty -> ()
| Node (v,l,r) -> inorder f l;
f v;
inorder f r
 
let rec postorder f = function
Empty -> ()
| Node (v,l,r) -> postorder f l;
postorder f r;
f v
 
let levelorder f x =
let queue = Queue.create () in
Queue.add x queue;
while not (Queue.is_empty queue) do
match Queue.take queue with
Empty -> ()
| Node (v,l,r) -> f v;
Queue.add l queue;
Queue.add r queue
done
 
let tree =
Node (1,
Node (2,
Node (4,
Node (7, Empty, Empty),
Empty),
Node (5, Empty, Empty)),
Node (3,
Node (6,
Node (8, Empty, Empty),
Node (9, Empty, Empty)),
Empty))
 
let () =
preorder (Printf.printf "%d ") tree; print_newline ();
inorder (Printf.printf "%d ") tree; print_newline ();
postorder (Printf.printf "%d ") tree; print_newline ();
levelorder (Printf.printf "%d ") tree; print_newline ()

Output:

1 2 4 7 5 3 6 8 9 
7 4 2 5 1 8 6 9 3 
2 4 7 5 3 6 8 9 1 
1 2 3 4 5 6 7 8 9 

[edit] ooRexx

 
one = .Node~new(1);
two = .Node~new(2);
three = .Node~new(3);
four = .Node~new(4);
five = .Node~new(5);
six = .Node~new(6);
seven = .Node~new(7);
eight = .Node~new(8);
nine = .Node~new(9);
 
one~left = two
one~right = three
two~left = four
two~right = five
three~left = six
four~left = seven
six~left = eight
six~right = nine
 
out = .array~new
.treetraverser~preorder(one, out);
say "Preorder: " out~toString("l", ", ")
out~empty
.treetraverser~inorder(one, out);
say "Inorder: " out~toString("l", ", ")
out~empty
.treetraverser~postorder(one, out);
say "Postorder: " out~toString("l", ", ")
out~empty
.treetraverser~levelorder(one, out);
say "Levelorder:" out~toString("l", ", ")
 
 
::class node
::method init
expose left right data
use strict arg data
left = .nil
right = .nil
 
::attribute left
::attribute right
::attribute data
 
::class treeTraverser
::method preorder class
use arg node, out
if node \== .nil then do
out~append(node~data)
self~preorder(node~left, out)
self~preorder(node~right, out)
end
 
::method inorder class
use arg node, out
if node \== .nil then do
self~inorder(node~left, out)
out~append(node~data)
self~inorder(node~right, out)
end
 
::method postorder class
use arg node, out
if node \== .nil then do
self~postorder(node~left, out)
self~postorder(node~right, out)
out~append(node~data)
end
 
::method levelorder class
use arg node, out
 
if node == .nil then return
nodequeue = .queue~new
nodequeue~queue(node)
loop while \nodequeue~isEmpty
next = nodequeue~pull
out~append(next~data)
if next~left \= .nil then
nodequeue~queue(next~left)
if next~right \= .nil then
nodequeue~queue(next~right)
end
 

Output:

Preorder:   1, 2, 4, 7, 5, 3, 6, 8, 9
Inorder:    7, 4, 2, 5, 1, 8, 6, 9, 3
Postorder:  7, 4, 5, 2, 8, 9, 6, 3, 1
Levelorder: 1, 2, 3, 4, 5, 6, 7, 8, 9

[edit] Oz

declare
Tree = n(1
n(2
n(4 n(7 e e) e)
n(5 e e))
n(3
n(6 n(8 e e) n(9 e e))
e))
 
fun {Concat Xs}
{FoldR Xs Append nil}
end
 
fun {Preorder T}
case T of e then nil
[] n(V L R) then
{Concat [[V]
{Preorder L}
{Preorder R}]}
end
end
 
fun {Inorder T}
case T of e then nil
[] n(V L R) then
{Concat [{Inorder L}
[V]
{Inorder R}]}
end
end
 
fun {Postorder T}
case T of e then nil
[] n(V L R) then
{Concat [{Postorder L}
{Postorder R}
[V]]}
end
end
 
local
fun {Collect Queue}
case Queue of nil then nil
[] e|Xr then {Collect Xr}
[] n(V L R)|Xr then
V|{Collect {Append Xr [L R]}}
end
end
in
fun {Levelorder T}
{Collect [T]}
end
end
in
{Show {Preorder Tree}}
{Show {Inorder Tree}}
{Show {Postorder Tree}}
{Show {Levelorder Tree}}

[edit] Perl

Tree nodes are represented by 3-element arrays: [0] - the value; [1] - left child; [2] - right child.

sub preorder
{
my $t = shift or return ();
return ($t->[0], preorder($t->[1]), preorder($t->[2]));
}
 
sub inorder
{
my $t = shift or return ();
return (inorder($t->[1]), $t->[0], inorder($t->[2]));
}
 
sub postorder
{
my $t = shift or return ();
return (postorder($t->[1]), postorder($t->[2]), $t->[0]);
}
 
sub depth
{
my @ret;
my @a = ($_[0]);
while (@a) {
my $v = shift @a or next;
push @ret, $v->[0];
push @a, @{$v}[1,2];
}
return @ret;
}
 
my $x = [1,[2,[4,[7]],[5]],[3,[6,[8],[9]]]];
 
print "pre: @{[preorder($x)]}\n";
print "in: @{[inorder($x)]}\n";
print "post: @{[postorder($x)]}\n";
print "depth: @{[depth($x)]}\n";

Output:

pre:   1 2 4 7 5 3 6 8 9
in:    7 4 2 5 1 8 6 9 3
post:  7 4 5 2 8 9 6 3 1
depth: 1 2 3 4 5 6 7 8 9

[edit] Perl 6

class TreeNode {
has TreeNode $.parent;
has TreeNode $.left;
has TreeNode $.right;
has $.value;
 
method pre-order {
gather {
take $.value;
take $.left.pre-order if $.left;
take $.right.pre-order if $.right
}
}
 
method in-order {
gather {
take $.left.in-order if $.left;
take $.value;
take $.right.in-order if $.right;
}
}
 
method post-order {
gather {
take $.left.post-order if $.left;
take $.right.post-order if $.right;
take $.value;
}
}
 
method level-order {
my TreeNode @queue = (self);
gather while @queue.elems {
my $n = @queue.shift;
take $n.value;
@queue.push($n.left) if $n.left;
@queue.push($n.right) if $n.right;
}
}
}
 
my TreeNode $root .= new( value => 1,
left => TreeNode.new( value => 2,
left => TreeNode.new( value => 4, left => TreeNode.new(value => 7)),
right => TreeNode.new( value => 5)
),
right => TreeNode.new( value => 3,
left => TreeNode.new( value => 6,
left => TreeNode.new(value => 8),
right => TreeNode.new(value => 9)
)
)
);
 
say "preorder: ",$root.pre-order.join(" ");
say "inorder: ",$root.in-order.join(" ");
say "postorder: ",$root.post-order.join(" ");
say "levelorder:",$root.level-order.join(" ");
Output:
preorder:  1 2 4 7 5 3 6 8 9
inorder:   7 4 2 5 1 8 6 9 3
postorder: 7 4 5 2 8 9 6 3 1
levelorder:1 2 3 4 5 6 7 8 9

[edit] PicoLisp

(de preorder (Node Fun)
(when Node
(Fun (car Node))
(preorder (cadr Node) Fun)
(preorder (caddr Node) Fun) ) )
 
(de inorder (Node Fun)
(when Node
(inorder (cadr Node) Fun)
(Fun (car Node))
(inorder (caddr Node) Fun) ) )
 
(de postorder (Node Fun)
(when Node
(postorder (cadr Node) Fun)
(postorder (caddr Node) Fun)
(Fun (car Node)) ) )
 
(de level-order (Node Fun)
(for (Q (circ Node) Q)
(let N (fifo 'Q)
(Fun (car N))
(and (cadr N) (fifo 'Q @))
(and (caddr N) (fifo 'Q @)) ) ) )
 
(setq *Tree
(1
(2 (4 (7)) (5))
(3 (6 (8) (9))) ) )
 
(for Order '(preorder inorder postorder level-order)
(prin (align -13 (pack Order ":")))
(Order *Tree printsp)
(prinl) )

Output:

preorder:    1 2 4 7 5 3 6 8 9 
inorder:     7 4 2 5 1 8 6 9 3 
postorder:   7 4 5 2 8 9 6 3 1 
level-order: 1 2 3 4 5 6 7 8 9 

[edit] Prolog

Works with SWI-Prolog.

tree :-
Tree= [1,
[2,
[4,
[7, nil, nil],
nil],
[5, nil, nil]],
[3,
[6,
[8, nil, nil],
[9,nil, nil]],
nil]],
 
write('preorder  : '), preorder(Tree), nl,
write('inorder  : '), inorder(Tree), nl,
write('postorder  : '), postorder(Tree), nl,
write('level-order : '), level_order([Tree]).
 
preorder(nil).
preorder([Node, FG, FD]) :-
format('~w ', [Node]),
preorder(FG),
preorder(FD).
 
 
inorder(nil).
inorder([Node, FG, FD]) :-
inorder(FG),
format('~w ', [Node]),
inorder(FD).
 
postorder(nil).
postorder([Node, FG, FD]) :-
postorder(FG),
postorder(FD),
format('~w ', [Node]).
 
 
level_order([]).
 
level_order(A) :-
level_order_(A, U-U, S),
level_order(S).
 
level_order_([], S-[],S).
 
level_order_([[Node, FG, FD] | T], CS, FS) :-
format('~w ', [Node]),
append_dl(CS, [FG, FD|U]-U, CS1),
level_order_(T, CS1, FS).
 
level_order_([nil | T], CS, FS) :-
level_order_(T, CS, FS).
 
 
append_dl(X-Y, Y-Z, X-Z).
 

Output :

?- tree.
preorder    : 1 2 4 7 5 3 6 8 9 
inorder     : 7 4 2 5 1 8 6 9 3 
postorder   : 7 4 5 2 8 9 6 3 1 
level-order : 1 2 3 4 5 6 7 8 9 
true .

[edit] PureBasic

Works with: PureBasic version 4.5+
Structure node
value.i
*left.node
*right.node
EndStructure
 
Structure queue
List q.i()
EndStructure
 
DataSection
tree:
Data.s "1(2(4(7),5),3(6(8,9)))"
EndDataSection
 
;Convenient routine to interpret string data to construct a tree of integers.
Procedure createTree(*n.node, *tPtr.Character)
Protected num.s, *l.node, *ntPtr.Character
 
Repeat
Select *tPtr\c
Case '0' To '9'
num + Chr(*tPtr\c)
Case '('
*n\value = Val(num): num = ""
*ntPtr = *tPtr + 1
If *ntPtr\c = ','
ProcedureReturn *tPtr
Else
*l = AllocateMemory(SizeOf(node))
*n\left = *l: *tPtr = createTree(*l, *ntPtr)
EndIf
Case ')', ',', #Null
If num: *n\value = Val(num): EndIf
ProcedureReturn *tPtr
EndSelect
 
If *tPtr\c = ','
*l = AllocateMemory(SizeOf(node)):
*n\right = *l: *tPtr = createTree(*l, *tPtr + 1)
EndIf
*tPtr + 1
ForEver
EndProcedure
 
Procedure enqueue(List q.i(), element)
LastElement(q())
AddElement(q())
q() = element
EndProcedure
 
Procedure dequeue(List q.i())
Protected element
If FirstElement(q())
element = q()
DeleteElement(q())
EndIf
ProcedureReturn element
EndProcedure
 
Procedure onVisit(*n.node)
Print(Str(*n\value) + " ")
EndProcedure
 
Procedure preorder(*n.node) ;recursive
onVisit(*n)
If *n\left
preorder(*n\left)
EndIf
If *n\right
preorder(*n\right)
EndIf
EndProcedure
 
Procedure inorder(*n.node) ;recursive
If *n\left
inorder(*n\left)
EndIf
onVisit(*n)
If *n\right
inorder(*n\right)
EndIf
EndProcedure
 
Procedure postorder(*n.node) ;recursive
If *n\left
postorder(*n\left)
EndIf
If *n\right
postorder(*n\right)
EndIf
onVisit(*n)
EndProcedure
 
Procedure levelorder(*n.node)
Dim q.queue(1)
Protected readQueue = 1, writeQueue, *currNode.node
 
enqueue(q(writeQueue)\q(),*n) ;start queue off with root
Repeat
readQueue ! 1: writeQueue ! 1
While ListSize(q(readQueue)\q())
*currNode = dequeue(q(readQueue)\q())
If *currNode\left
enqueue(q(writeQueue)\q(),*currNode\left)
EndIf
If *currNode\right
enqueue(q(writeQueue)\q(),*currNode\right)
EndIf
onVisit(*currNode)
Wend
Until ListSize(q(writeQueue)\q()) = 0
EndProcedure
 
If OpenConsole()
Define root.node
createTree(root,?tree)
 
Print("preorder: ")
preorder(root)
PrintN("")
Print("inorder: ")
inorder(root)
PrintN("")
Print("postorder: ")
postorder(root)
PrintN("")
Print("levelorder: ")
levelorder(root)
PrintN("")
 
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
Input()
CloseConsole()
EndIf

Sample output:

preorder: 1 2 4 7 5 3 6 8 9
inorder: 7 4 2 5 1 8 6 9 3
postorder: 7 4 5 2 8 9 6 3 1
levelorder: 1 2 3 4 5 6 7 8 9

[edit] Python

from collections import namedtuple
from sys import stdout
 
Node = namedtuple('Node', 'data, left, right')
tree = Node(1,
Node(2,
Node(4,
Node(7, None, None),
None),
Node(5, None, None)),
Node(3,
Node(6,
Node(8, None, None),
Node(9, None, None)),
None))
 
def printwithspace(i):
stdout.write("%i " % i)
 
def preorder(node, visitor = printwithspace):
if node is not None:
visitor(node.data)
preorder(node.left, visitor)
preorder(node.right, visitor)
 
def inorder(node, visitor = printwithspace):
if node is not None:
inorder(node.left, visitor)
visitor(node.data)
inorder(node.right, visitor)
 
def postorder(node, visitor = printwithspace):
if node is not None:
postorder(node.left, visitor)
postorder(node.right, visitor)
visitor(node.data)
 
def levelorder(node, more=None, visitor = printwithspace):
if node is not None:
if more is None:
more = []
more += [node.left, node.right]
visitor(node.data)
if more:
levelorder(more[0], more[1:], visitor)
 
stdout.write(' preorder: ')
preorder(tree)
stdout.write('\n inorder: ')
inorder(tree)
stdout.write('\n postorder: ')
postorder(tree)
stdout.write('\nlevelorder: ')
levelorder(tree)
stdout.write('\n')

Sample output:

  preorder: 1 2 4 7 5 3 6 8 9 
   inorder: 7 4 2 5 1 8 6 9 3 
 postorder: 7 4 5 2 8 9 6 3 1 
levelorder: 1 2 3 4 5 6 7 8 9 

[edit] Qi

 
(set *tree* [1 [2 [4 [7]]
[5]]
[3 [6 [8]
[9]]]])
 
(define inorder
[] -> []
[V] -> [V]
[V L] -> (append (inorder L)
[V])
[V L R] -> (append (inorder L)
[V]
(inorder R)))
 
(define postorder
[] -> []
[V] -> [V]
[V L] -> (append (postorder L)
[V])
[V L R] -> (append (postorder L)
(postorder R)
[V]))
 
(define preorder
[] -> []
[V] -> [V]
[V L] -> (append [V]
(preorder L))
[V L R] -> (append [V]
(preorder L)
(preorder R)))
 
(define levelorder-0
[] -> []
[[] | Q] -> (levelorder-0 Q)
[[V | LR] | Q] -> [V | (levelorder-0 (append Q LR))])
 
(define levelorder
Node -> (levelorder-0 [Node]))
 
(preorder (value *tree*))
(postorder (value *tree*))
(inorder (value *tree*))
(levelorder (value *tree*))
 

Output:

[1 2 4 7 5 3 6 8 9]
[7 4 2 5 1 8 6 9 3]
[7 4 5 2 8 9 6 3 1]
[1 2 3 4 5 6 7 8 9]

[edit] Racket

 
#lang racket
 
(define the-tree ; Node: (list <data> <left> <right>)
'(1 (2 (4 (7 #f #f) #f) (5 #f #f)) (3 (6 (8 #f #f) (9 #f #f)) #f)))
 
(define (preorder tree visit)
(let loop ([t tree])
(when t (visit (car t)) (loop (cadr t)) (loop (caddr t)))))
(define (inorder tree visit)
(let loop ([t tree])
(when t (loop (cadr t)) (visit (car t)) (loop (caddr t)))))
(define (postorder tree visit)
(let loop ([t tree])
(when t (loop (cadr t)) (loop (caddr t)) (visit (car t)))))
(define (levelorder tree visit)
(let loop ([trees (list tree)])
(unless (null? trees)
((compose1 loop (curry filter values) append*)
(for/list ([t trees] #:when t) (visit (car t)) (cdr t))))))
 
(define (run order)
(printf "~a:" (object-name order))
(order the-tree (λ(x) (printf " ~s" x)))
(newline))
(for-each run (list preorder inorder postorder levelorder))
 

Output:

preorder: 1 2 4 7 5 3 6 8 9
inorder: 7 4 2 5 1 8 6 9 3
postorder: 7 4 5 2 8 9 6 3 1
levelorder: 1 2 3 4 5 6 7 8 9

[edit] REXX

 
/* REXX ***************************************************************
* Tree traversal
= 1
= / \
= / \
= / \
= 2 3
= / \ /
= 4 5 6
= / / \
= 7 8 9
=
= The correct output should look like this:
= preorder: 1 2 4 7 5 3 6 8 9
= level-order: 1 2 3 4 5 6 7 8 9
= postorder: 7 4 5 2 8 9 6 3 1
= inorder: 7 4 2 5 1 8 6 9 3
 
* 17.06.2012 Walter Pachl not thoroughly tested
**********************************************************************/

debug=0
wl_soll=1 2 4 7 5 3 6 8 9
il_soll=7 4 2 5 1 8 6 9 3
pl_soll=7 4 5 2 8 9 6 3 1
ll_soll=1 2 3 4 5 6 7 8 9
 
Call mktree
wl.=''; wl='' /* preorder */
ll.=''; ll='' /* level-order */
il='' /* inorder */
pl='' /* postorder */
 
/**********************************************************************
* First walk the tree and construct preorder and level-order lists
**********************************************************************/

done.=0
lvl=1
z=root
Call note z
Do Until z=0
z=go_next(z)
Call note z
End
Call show 'preorder: ',wl,wl_soll
Do lvl=1 To 4
ll=ll ll.lvl
End
Call show 'level-order:',ll,ll_soll
 
/**********************************************************************
* Next construct postorder list
**********************************************************************/

done.=0
ridone.=0
z=lbot(root)
Call notep z
Do Until z=0
br=brother(z)
If br>0 &,
done.br=0 Then Do
ridone.br=1
z=lbot(br)
Call notep z
End
Else
z=father(z)
Call notep z
End
Call show 'postorder: ',pl,pl_soll
 
/**********************************************************************
* Finally construct inorder list
**********************************************************************/

done.=0
ridone.=0
z=lbot(root)
Call notei z
Do Until z=0
z=father(z)
Call notei z
ri=node.z.0rite
If ridone.z=0 Then Do
ridone.z=1
If ri>0 Then Do
z=lbot(ri)
Call notei z
End
End
End
 
/**********************************************************************
* And now show the results and check them for correctness
**********************************************************************/

Call show 'inorder: ',il,il_soll
 
Exit
 
show: Parse Arg Which,have,soll
/**********************************************************************
* Show our result and show it it's correct
**********************************************************************/

have=space(have)
If have=soll Then
tag=''
Else
tag='*wrong*'
Say which have tag
If tag<>'' Then
Say '------------>'soll 'is the expected result'
Return
 
brother: Procedure Expose node.
/**********************************************************************
* Return the right node of this node's father or 0
**********************************************************************/

Parse arg no
nof=node.no.0father
brot1=node.nof.0rite
Return brot1
 
notei: Procedure Expose debug il done.
/**********************************************************************
* append the given node to il
**********************************************************************/

Parse Arg nd
If nd<>0 &,
done.nd=0 Then
il=il nd
If debug Then
Say 'notei' nd
done.nd=1
Return
 
notep: Procedure Expose debug pl done.
/**********************************************************************
* append the given node to pl
**********************************************************************/

Parse Arg nd
If nd<>0 &,
done.nd=0 Then Do
pl=pl nd
If debug Then
Say 'notep' nd
End
done.nd=1
Return
 
father: Procedure Expose node.
/**********************************************************************
* Return the father of the argument
* or 0 if the root is given as argument
**********************************************************************/

Parse Arg nd
Return node.nd.0father
 
lbot: Procedure Expose node.
/**********************************************************************
* From node z: Walk down on the left side until you reach the bottom
* and return the bottom node
* If z has no left son (at the bottom of the tree) returm itself
**********************************************************************/

Parse Arg z
Do i=1 To 100
If node.z.0left<>0 Then
z=node.z.0left
Else
Leave
End
Return z
 
note:
/**********************************************************************
* add the node to the preorder list unless it's already there
* add the node to the level list
**********************************************************************/

If z<>0 &, /* it's a node */
done.z=0 Then Do /* not yet done */
wl=wl z /* add it to the preorder list*/
ll.lvl=ll.lvl z /* add it to the level list */
done.z=1 /* remember it's done */
End
Return
 
go_next: Procedure Expose node. lvl
/**********************************************************************
* find the next node to visit in the treewalk
**********************************************************************/

next=0
Parse arg z
If node.z.0left<>0 Then Do /* there is a left son */
If node.z.0left.done=0 Then Do /* we have not visited it */
next=node.z.0left /* so we go there */
node.z.0left.done=1 /* note we were here */
lvl=lvl+1 /* increase the level */
End
End
If next=0 Then Do /* not moved yet */
If node.z.0rite<>0 Then Do /* there is a right son */
If node.z.0rite.done=0 Then Do /* we have not visited it */
next=node.z.0rite /* so we go there */
node.z.0rite.done=1 /* note we were here */
lvl=lvl+1 /* increase the level */
End
End
End
If next=0 Then Do /* not moved yet */
next=node.z.0father /* go to the father */
lvl=lvl-1 /* decrease the level */
End
Return next /* that's the next node */
/* or zero if we are done */
 
mknode: Procedure Expose node.
/**********************************************************************
* create a new node
**********************************************************************/

Parse Arg name
z=node.0+1
node.z.0name=name
node.z.0father=0
node.z.0left =0
node.z.0rite =0
node.0=z
Return z /* number of the node just created */
 
attleft: Procedure Expose node.
/**********************************************************************
* make son the left son of father
**********************************************************************/

Parse Arg son,father
node.son.0father=father
z=node.father.0left
If z<>0 Then Do
node.z.0father=son
node.son.0left=z
End
node.father.0left=son
Return
 
attrite: Procedure Expose node.
/**********************************************************************
* make son the right son of father
**********************************************************************/

Parse Arg son,father
node.son.0father=father
z=node.father.0rite
If z<>0 Then Do
node.z.0father=son
node.son.0rite=z
End
node.father.0rite=son
le=node.father.0left
If le>0 Then
node.le.0brother=node.father.0rite
Return
 
mktree: Procedure Expose node. root
/**********************************************************************
* build the tree according to the task
**********************************************************************/

node.=0
a=mknode('A'); root=a
b=mknode('B'); Call attleft b,a
c=mknode('C'); Call attrite c,a
d=mknode('D'); Call attleft d,b
e=mknode('E'); Call attrite e,b
f=mknode('F'); Call attleft f,c
g=mknode('G'); Call attleft g,d
h=mknode('H'); Call attleft h,f
i=mknode('I'); Call attrite i,f
Call show_tree 1
Return
 
show_tree: Procedure Expose node.
/**********************************************************************
* Show the tree
* f
* l1 1 r1
* l r l r
* l r l r l r l r
* 12345678901234567890
**********************************************************************/

Parse Arg f
l.=''
l.1=overlay(f ,l.1, 9)
 
l1=node.f.0left  ;l.2=overlay(l1 ,l.2, 5)
/*b1=node.f.0brother  ;l.2=overlay(b1 ,l.2, 9) */
r1=node.f.0rite  ;l.2=overlay(r1 ,l.2,13)
 
l1g=node.l1.0left  ;l.3=overlay(l1g ,l.3, 3)
/*b1g=node.l1.0brother  ;l.3=overlay(b1g ,l.3, 5) */
r1g=node.l1.0rite  ;l.3=overlay(r1g ,l.3, 7)
 
l2g=node.r1.0left  ;l.3=overlay(l2g ,l.3,11)
/*b2g=node.r1.0brother  ;l.3=overlay(b2g ,l.3,13) */
r2g=node.r1.0rite  ;l.3=overlay(r2g ,l.3,15)
 
l1ls=node.l1g.0left  ;l.4=overlay(l1ls,l.4, 2)
/*b1ls=node.l1g.0brother ;l.4=overlay(b1ls,l.4, 3) */
r1ls=node.l1g.0rite  ;l.4=overlay(r1ls,l.4, 4)
 
l1rs=node.r1g.0left  ;l.4=overlay(l1rs,l.4, 6)
/*b1rs=node.r1g.0brother ;l.4=overlay(b1rs,l.4, 7) */
r1rs=node.r1g.0rite  ;l.4=overlay(r1rs,l.4, 8)
 
l2ls=node.l2g.0left  ;l.4=overlay(l2ls,l.4,10)
/*b2ls=node.l2g.0brother ;l.4=overlay(b2ls,l.4,11) */
r2ls=node.l2g.0rite  ;l.4=overlay(r2ls,l.4,12)
 
l2rs=node.r2g.0left  ;l.4=overlay(l2rs,l.4,14)
/*b2rs=node.r2g.0brother ;l.4=overlay(b2rs,l.4,15) */
r2rs=node.r2g.0rite  ;l.4=overlay(r2rs,l.4,16)
Do i=1 To 4
Say translate(l.i,' ','0')
Say ''
End
Return
Output:
        1

    2       3

  4   5   6

 7       8 9

preorder:    1 2 4 7 5 3 6 8 9
level-order: 1 2 3 4 5 6 7 8 9
postorder:   7 4 5 2 8 9 6 3 1
inorder:     7 4 2 5 1 8 6 9 3

[edit] Ruby

class BinaryTreeNode
def initialize(value, left=nil, right=nil)
@value, @left, @right = value, left, right
end
attr_reader :value, :left, :right
 
def self.from_array(nested_list)
value, left, right = nested_list
if value
self.new(value, self.from_array(left), self.from_array(right))
end
end
 
def walk_nodes(order, &block)
order.each do |node|
case node
when :left then left && left.walk_nodes(order, &block)
when :self then yield self
when :right then right && right.walk_nodes(order, &block)
end
end
end
 
def each_preorder(&b)  ; walk_nodes([:self, :left, :right], &b) ; end
def each_inorder(&b)  ; walk_nodes([:left, :self, :right], &b) ; end
def each_postorder(&b) ; walk_nodes([:left, :right, :self], &b) ; end
 
def each_levelorder
queue = [self]
until queue.empty?
node = queue.shift
yield node
queue << node.left if node.left
queue << node.right if node.right
end
end
end
 
root = BinaryTreeNode.from_array [1, [2, [4, 7], [5]], [3, [6, [8], [9]]]]
 
%w{each_preorder each_inorder each_postorder each_levelorder}.each {|mthd|
printf "%-11s ", mthd[5..-1] + ':'
root.send(mthd) {|node| print "#{node.value} "}
puts
}

Output:

preorder:   1 2 4 7 5 3 6 8 9
inorder:    7 4 2 5 1 8 6 9 3
postorder:  7 4 5 2 8 9 6 3 1
levelorder: 1 2 3 4 5 6 7 8 9

[edit] Scala

Works with: Scala version 2.11.x
case class IntNode(value: Int, left: Option[IntNode] = None, right: Option[IntNode] = None) {
 
def preorder(f: IntNode => Unit) {
f(this)
left.map(_.preorder(f)) // Same as: if(left.isDefined) left.get.preorder(f)
right.map(_.preorder(f))
}
 
def postorder(f: IntNode => Unit) {
left.map(_.postorder(f))
right.map(_.postorder(f))
f(this)
}
 
def inorder(f: IntNode => Unit) {
left.map(_.inorder(f))
f(this)
right.map(_.inorder(f))
}
 
def levelorder(f: IntNode => Unit) {
 
def loVisit(ls: List[IntNode]): Unit = ls match {
case Nil => None
case node :: rest => f(node); loVisit(rest ++ node.left ++ node.right)
}
 
loVisit(List(this))
}
}
 
object TreeTraversal extends App {
implicit def intNode2SomeIntNode(n: IntNode) = Some[IntNode](n)
 
val tree = IntNode(1,
IntNode(2,
IntNode(4,
IntNode(7)),
IntNode(5)),
IntNode(3,
IntNode(6,
IntNode(8),
IntNode(9))))
 
List(
" preorder: " -> tree.preorder _, // `_` denotes the function value of type `IntNode => Unit` (returning nothing)
" inorder: " -> tree.inorder _,
" postorder: " -> tree.postorder _,
"levelorder: " -> tree.levelorder _) foreach {
case (name, func) =>
val s = new StringBuilder(name)
func(n => s ++= n.value.toString + " ")
println(s)
}
}
Output:
  preorder: 1 2 4 7 5 3 6 8 9 
   inorder: 7 4 2 5 1 8 6 9 3 
 postorder: 7 4 5 2 8 9 6 3 1 
levelorder: 1 2 3 4 5 6 7 8 9 

[edit] Tcl

Works with: Tcl version 8.6
or
Library: TclOO
oo::class create tree {
# Basic tree data structure stuff...
variable val l r
constructor {value {left {}} {right {}}} {
set val $value
set l $left
set r $right
}
method value {} {return $val}
method left {} {return $l}
method right {} {return $r}
destructor {
if {$l ne ""} {$l destroy}
if {$r ne ""} {$r destroy}
}
 
# Traversal methods
method preorder {varName script {level 0}} {
upvar [incr level] $varName var
set var $val
uplevel $level $script
if {$l ne ""} {$l preorder $varName $script $level}
if {$r ne ""} {$r preorder $varName $script $level}
}
method inorder {varName script {level 0}} {
upvar [incr level] $varName var
if {$l ne ""} {$l inorder $varName $script $level}
set var $val
uplevel $level $script
if {$r ne ""} {$r inorder $varName $script $level}
}
method postorder {varName script {level 0}} {
upvar [incr level] $varName var
if {$l ne ""} {$l postorder $varName $script $level}
if {$r ne ""} {$r postorder $varName $script $level}
set var $val
uplevel $level $script
}
method levelorder {varName script} {
upvar 1 $varName var
set nodes [list [self]]; # A queue of nodes to process
while {[llength $nodes] > 0} {
set nodes [lassign $nodes n]
set var [$n value]
uplevel 1 $script
if {[$n left] ne ""} {lappend nodes [$n left]}
if {[$n right] ne ""} {lappend nodes [$n right]}
}
}
}

Note that in Tcl it is conventional to handle performing something “for each element” by evaluating a script in the caller's scope for each node after setting a caller-nominated variable to the value for that iteration. Doing this transparently while recursing requires the use of a varying ‘level’ parameter to upvar and uplevel, but makes for compact and clear code.

Demo code to satisfy the official challenge instance:

# Helpers to make construction and listing of a whole tree simpler
proc Tree nested {
lassign $nested v l r
if {$l ne ""} {set l [Tree $l]}
if {$r ne ""} {set r [Tree $r]}
tree new $v $l $r
}
proc Listify {tree order} {
set list {}
$tree $order v {
lappend list $v
}
return $list
}
 
# Make a tree, print it a few ways, and destroy the tree
set t [Tree {1 {2 {4 7} 5} {3 {6 8 9}}}]
puts "preorder: [Listify $t preorder]"
puts "inorder: [Listify $t inorder]"
puts "postorder: [Listify $t postorder]"
puts "level-order: [Listify $t levelorder]"
$t destroy

Output:

preorder:    1 2 4 7 5 3 6 8 9
inorder:     7 4 2 5 1 8 6 9 3
postorder:   7 4 5 2 8 9 6 3 1
level-order: 1 2 3 4 5 6 7 8 9

[edit] UNIX Shell

Bash (also "sh" on most Unix systems) has arrays. We implement a node as an association between three arrays: left, right, and value.

left=()
right=()
value=()
 
# node node#, left#, right#, value
#
# if value is empty, use node#
 
node() {
nx=${1:-'Missing node index'}
leftx=${2}
rightx=${3}
val=${4:-$1}
value[$nx]="$val"
left[$nx]="$leftx"
right[$nx]="$rightx"
}
 
# define the tree
 
node 1 2 3
node 2 4 5
node 3 6
node 4 7
node 5
node 6 8 9
node 7
node 8
node 9
 
# walk NODE# ORDER
 
walk() {
local nx=${1-"Missing index"}
shift
for branch in "$@" ; do
case "$branch" in
left) if [[ "${left[$nx]}" ]]; then walk ${left[$nx]} $@ ; fi ;;
right) if [[ "${right[$nx]}" ]]; then walk ${right[$nx]} $@ ; fi ;;
self) printf "%d " "${value[$nx]}" ;;
esac
done
}
 
apush() {
local var="$1"
eval "$var=( \"\${$var[@]}\" \"$2\" )"
}
 
showname() {
printf "%-12s " "$1:"
}
 
showdata() {
showname "$1"
shift
walk "$@"
echo ''
}
 
preorder() { showdata $FUNCNAME $1 self left right ; }
inorder() { showdata $FUNCNAME $1 left self right ; }
postorder() { showdata $FUNCNAME $1 left right self ; }
levelorder() {
showname 'level-order'
queue=( $1 )
x=0
while [[ $x < ${#queue[*]} ]]; do
value="${queue[$x]}"
printf "%d " "$value"
for more in "${left[$value]}" "${right[$value]}" ; do
if [[ -n "$more" ]]; then
apush queue "$more"
fi
done
 : $((x++))
done
echo ''
}
 
preorder 1
inorder 1
postorder 1
levelorder 1

The output:

preorder:    1 2 4 7 5 3 6 8 9 
inorder: 7 4 2 5 1 8 6 9 3
postorder: 7 4 5 2 8 9 6 3 1
level-order: 1 2 3 4 5 6 7 8 9

[edit] Ursala

Ursala has built-in notation for trees and is perfect for whipping up little tree walking functions. This source listing shows the tree depicted above declared as a constant, followed by declarations of four functions applicable to trees of any type. The main program applies all four of them to the tree and makes a list of their results, each of which is a list of natural numbers. The compiler directive #cast %nLL induces the compile-time side effect of displaying the result on standard output as a list of lists of naturals.

tree = 
 
1^:<
2^: <4^: <7^: <>, 0>, 5^: <>>,
3^: <6^: <8^: <>, 9^: <>>, 0>>
 
pre = ~&dvLPCo
post = ~&vLPdNCTo
in = ~&vvhPdvtL2CTiQo
lev = ~&iNCaadSPfavSLiF3RTaq
 
#cast %nLL
 
main = <.pre,in,post,lev> tree

output:

<
   <1,2,4,7,5,3,6,8,9>,
   <7,4,2,5,1,8,6,9,3>,
   <7,4,5,2,8,9,6,3,1>,
   <1,2,3,4,5,6,7,8,9>>

[edit] zkl

class Node{ var [mixin=Node]left,right; var v;
fcn init(val,[Node]l=Void,[Node]r=Void) { v,left,right=vm.arglist }
}
 
class BTree{ var [mixin=Node] root;
fcn init(r){ root=r }
const VISIT=Void, LEFT="left", RIGHT="right";
fcn preOrder { traverse(VISIT,LEFT, RIGHT) }
fcn inOrder { traverse(LEFT, VISIT,RIGHT) }
fcn postOrder { traverse(LEFT, RIGHT,VISIT) }
fcn [private] traverse(order){ //--> list of Nodes
sink:=List();
fcn(sink,[Node]n,order){
if(n){ foreach o in (order){
if(VISIT==o) sink.write(n);
else self.fcn(sink,n.setVar(o),order); // actually get var
}}
}(sink,root,vm.arglist);
sink
}
fcn levelOrder{ // breadth first
sink:=List(); q:=List(root);
while(q){
n:=q.pop(0); l:=n.left; r:=n.right;
sink.write(n);
if(l) q.append(l);
if(r) q.append(r);
}
sink
}
}

It is easy to convert to lazy by replacing "sink.write" with "vm.yield" and wrapping the traversal with a Utils.Generator.

t:=BTree(Node(1,
Node(2,
Node(4,Node(7)),
Node(5)),
Node(3,
Node(6, Node(8),Node(9)))));
 
t.preOrder() .apply("v").println(" preorder");
t.inOrder() .apply("v").println(" inorder");
t.postOrder() .apply("v").println(" postorder");
t.levelOrder().apply("v").println(" level-order");

The "apply("v")" extracts the contents of var v from each node.

Output:
L(1,2,4,7,5,3,6,8,9)  preorder
L(7,4,2,5,1,8,6,9,3)  inorder
L(7,4,5,2,8,9,6,3,1)  postorder
L(1,2,3,4,5,6,7,8,9)  level-order
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