ðŸŽ‰ Exercism Research is now launched. Help Exercism, help science and have some fun at research.exercism.io ðŸŽ‰

# davearonson's solution

## to Zipper in the Elixir Track

Published at Jul 13 2018 · 1 comment
Instructions
Test suite
Solution

#### Note:

This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

Creating a zipper for a binary tree.

Zippers are a purely functional way of navigating within a data structure and manipulating it. They essentially contain a data structure and a pointer into that data structure (called the focus).

For example given a rose tree (where each node contains a value and a list of child nodes) a zipper might support these operations:

• `from_tree` (get a zipper out of a rose tree, the focus is on the root node)
• `to_tree` (get the rose tree out of the zipper)
• `value` (get the value of the focus node)
• `prev` (move the focus to the previous child of the same parent, returns a new zipper)
• `next` (move the focus to the next child of the same parent, returns a new zipper)
• `up` (move the focus to the parent, returns a new zipper)
• `set_value` (set the value of the focus node, returns a new zipper)
• `insert_before` (insert a new subtree before the focus node, it becomes the `prev` of the focus node, returns a new zipper)
• `insert_after` (insert a new subtree after the focus node, it becomes the `next` of the focus node, returns a new zipper)
• `delete` (removes the focus node and all subtrees, focus moves to the `next` node if possible otherwise to the `prev` node if possible, otherwise to the parent node, returns a new zipper)

## Running tests

Execute the tests with:

``````\$ elixir zipper_test.exs
``````

### Pending tests

In the test suites, all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by commenting out the relevant `@tag :pending` with a `#` symbol.

For example:

``````# @tag :pending
test "shouting" do
assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end
``````

Or, you can enable all the tests by commenting out the `ExUnit.configure` line in the test suite.

``````# ExUnit.configure exclude: :pending, trace: true
``````

For more detailed information about the Elixir track, please see the help page.

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

### zipper_test.exs

``````if !System.get_env("EXERCISM_TEST_EXAMPLES") do
end

ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)

defmodule ZipperTest do
alias BinTree, as: BT
import Zipper
use ExUnit.Case

defp bt(value, left, right), do: %BT{value: value, left: left, right: right}
defp leaf(value), do: %BT{value: value}

defp t1, do: bt(1, bt(2, nil, leaf(3)), leaf(4))
defp t2, do: bt(1, bt(5, nil, leaf(3)), leaf(4))
defp t3, do: bt(1, bt(2, leaf(5), leaf(3)), leaf(4))
defp t4, do: bt(1, leaf(2), leaf(4))
defp t5, do: bt(1, bt(2, nil, leaf(3)), bt(6, leaf(7), leaf(8)))
defp t6, do: bt(1, bt(2, nil, leaf(5)), leaf(4))

# @tag :pending
test "data is retained" do
assert t1() |> from_tree |> to_tree == t1()
end

@tag :pending
test "left, right and value" do
assert t1() |> from_tree |> left |> right |> value == 3
end

@tag :pending
assert t1() |> from_tree |> left |> left == nil
end

@tag :pending
test "tree from deep focus" do
assert t1() |> from_tree |> left |> right |> to_tree == t1()
end

@tag :pending
test "traversing up from top" do
assert t1() |> from_tree |> up == nil
end

@tag :pending
test "left, right, and up" do
assert t1() |> from_tree |> left |> up |> right |> up |> left |> right |> value == 3
end

@tag :pending
test "set_value" do
assert t1() |> from_tree |> left |> set_value(5) |> to_tree == t2()
end

@tag :pending
test "set_value after traversing up" do
assert t1() |> from_tree |> left |> right |> up |> set_value(5) |> to_tree == t2()
end

@tag :pending
test "set_left with leaf" do
assert t1() |> from_tree |> left |> set_left(leaf(5)) |> to_tree == t3()
end

@tag :pending
test "set_right with nil" do
assert t1() |> from_tree |> left |> set_right(nil) |> to_tree == t4()
end

@tag :pending
test "set_right with subtree" do
assert t1() |> from_tree |> set_right(bt(6, leaf(7), leaf(8))) |> to_tree == t5()
end

@tag :pending
test "set_value on deep focus" do
assert t1() |> from_tree |> left |> right |> set_value(5) |> to_tree == t6()
end
end``````
``````defmodule BinTree do
import Inspect.Algebra
@moduledoc """
A node in a binary tree.

`value` is the value of a node.
`left` is the left subtree (nil if no subtree).
`right` is the right subtree (nil if no subtree).
"""
@type t :: %BinTree{ value: any, left: BinTree.t | nil, right: BinTree.t | nil }
defstruct value: nil, left: nil, right: nil

# A custom inspect instance purely for the tests, this makes error messages
#
# BT[value: 3, left: BT[value: 5, right: BT[value: 6]]] becomes (3:(5::(6::)):)
def inspect(%BinTree{value: v, left: l, right: r}, opts) do
concat ["(", to_doc(v, opts),
":", (if l, do: to_doc(l, opts), else: ""),
":", (if r, do: to_doc(r, opts), else: ""),
")"]
end
end

defmodule Zipper do
alias BinTree, as: BT
defstruct data: nil, path: nil, dirs: nil
@doc """
Get a zipper focused on the root node.
"""
@spec from_tree(BT.t) :: Z.t
def from_tree(bt) do
%Zipper{ data: bt, path: [bt], dirs: [] }
end

@doc """
Get the complete tree from a zipper.
"""
@spec to_tree(Z.t) :: BT.t
def to_tree(z) do
z.data
end

@doc """
Get the value of the focus node.
"""
@spec value(Z.t) :: any
end

@doc """
Get the left child of the focus node, if any.
"""
@spec left(Z.t) :: Z.t | nil
def left(  %Zipper{path: [%BT{left: nil  }|_tail]}), do: nil
def left(z=%Zipper{path: [%BT{left: lefty}|_tail]})  do
%Zipper{ z | path: [lefty|z.path], dirs: [:left|z.dirs] }
end

@doc """
Get the right child of the focus node, if any.
"""
def right(  %Zipper{path: [%BT{right: nil   }|_tail]}), do: nil
def right(z=%Zipper{path: [%BT{right: righty}|_tail]})  do
%Zipper{ z | path: [righty|z.path], dirs: [:right|z.dirs] }
end

@doc """
Get the parent of the focus node, if any.
"""
@spec up(Z.t) :: Z.t
def up(%Zipper{dirs: []}), do: nil
def up(z=%Zipper{path: [_cur|path_rest], dirs: [_curdir|dirs_rest]}) do
%Zipper{ z | path: path_rest, dirs: dirs_rest }
end

@doc """
Set the value of the focus node.
"""
@spec set_value(Z.t, any) :: Z.t
replace_focus(z, %BT{ head | value: v })
end

@doc """
Replace the left child tree of the focus node.
"""
@spec set_left(Z.t, BT.t) :: Z.t
replace_focus(z, %BT{ head | left: l })
end

@doc """
Replace the right child tree of the focus node.
"""
@spec set_right(Z.t, BT.t) :: Z.t
replace_focus(z, %BT{ head | right: r })
end

%Zipper{ z | data: update_tree(tail, z.dirs, new_head),
end

:left  -> %BT{ path_head | left:  sub }
:right -> %BT{ path_head | right: sub }
end
update_tree(path_tail, dirs_tail, new_sub)
end
defp update_tree([], [], sub), do: sub

end``````