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.
Ada
<lang 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;</lang>
C
<lang 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;
}</lang>
E
<lang 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()</lang>
Forth
<lang 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 </lang>
Haskell
<lang 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</lang>
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]
Java
<lang java5>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 left;
}
public void setLeft(Node<T> left) {
this.left = left;
}
public Node<T> getRight() {
return 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(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();
}
}</lang> 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
Python
<lang 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') </lang>
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
Ruby
<lang ruby>class BinaryTreeNode
def initialize(value, left=nil, right=nil) @value = value @left = left @right = right end attr_reader :value, :left, :right
def each_preorder(&block) yield self left.each_preorder(&block) if left right.each_preorder(&block) if right end
def each_inorder(&block) left.each_inorder(&block) if left yield self right.each_inorder(&block) if right end
def each_postorder(&block) left.each_postorder(&block) if left right.each_postorder(&block) if right yield self 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.new(1,
BinaryTreeNode.new(2,
BinaryTreeNode.new(4,
BinaryTreeNode.new(7)
),
BinaryTreeNode.new(5)
),
BinaryTreeNode.new(3,
BinaryTreeNode.new(6,
BinaryTreeNode.new(8),
BinaryTreeNode.new(9)
)
)
)
print "preorder: " root.each_preorder {|node| print "#{node.value} "} puts print "inorder: " root.each_inorder {|node| print "#{node.value} "} puts print "postorder: " root.each_postorder {|node| print "#{node.value} "} puts print "levelorder: " root.each_levelorder {|node| print "#{node.value} "} puts</lang> 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
Tcl
<lang tcl>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]} }
}
}</lang>
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: <lang tcl># 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</lang> 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