Have you heard about trees?

When performing DFS on a binary tree, you can traverse it in 3 possible orders.

  • Root, left node, right node (Pre-order)
  • Left node, Root, right node (In-order)
  • Left node, right node, root (Post-order)

Check wikipedia to know more.

For this challenge, you have to provide a program that, given the pre and in order traverses of a tree returns the original tree.

Example 1:

Inputs Preorder:

[1 2 3 4 5 6 7]

In order:

[2 1 4 3 6 5 7]


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


Result notation

[a [b c]]

Node a is the parent of nodes b and c. However in this one

[a [b [c]]]

Node a is the parent of node b, but it's b in this case the parent of c.

More considerations

  • The tree might not be balanced.
  • For every 2 traverses, the original tree is unique.
  • Submissions can be programs and functions.
  • The input format has to be a sequence of numbers representing the order in which the nodes are visited.
  • The output format must be exactly as specified above.
  • Shortest code in bytes wins.

Good luck

  • \$\begingroup\$ Are the elements guaranteed to be distinct? \$\endgroup\$ Oct 3, 2015 at 21:16
  • \$\begingroup\$ So in the result, if there's only a single child, it's not defined whether the child is the left or the right? \$\endgroup\$ Oct 4, 2015 at 9:36

1 Answer 1


Haskell, 114 bytes

[a]#_=show a
(a:b)#c|(d,_:e)<-span(/=a)c,(f,g)<-splitAt(length d)b=[a]#c++" ["++f#d++' ':g#e++"]"

Example run:

*Main> [1,2,3,4,5,6,7]?[2,1,4,3,6,5,7]
"[1 [2 3 [4 5 [6 7]]]]"

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