124 lines
3.5 KiB
Elixir
124 lines
3.5 KiB
Elixir
defmodule MbBinaryTree do
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@moduledoc """
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Documentation for `MbBinaryTree`.
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"""
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@type t :: nil | nonempty_maybe_improper_list()
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@spec new(any) :: t
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@doc """
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Create a new tree with a root node.
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## Examples
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iex> MbBinaryTree.new(4)
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[4, nil, nil]
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"""
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def new(root) do
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[root, nil, nil]
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end
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@spec is_tree?(any) :: boolean
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@doc """
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Test whether argument is a valid binary tree.
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## Examples
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iex> MbBinaryTree.new(19) |> MbBinaryTree.is_tree?()
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true
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iex> MbBinaryTree.is_tree?([12])
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false
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iex> MbBinaryTree.is_tree?(12)
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false
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iex> MbBinaryTree.is_tree?([12, [4, MbBinaryTree.new(2), MbBinaryTree.new(5)], [26, MbBinaryTree.new(14), [28, MbBinaryTree.new(27), MbBinaryTree.new(30)]]])
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"""
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def is_tree?(nil), do: true
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def is_tree?([_, nil, nil]), do: true
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def is_tree?([_, nil, right]), do: is_tree?(right)
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def is_tree?([_, left, nil]), do: is_tree?(left)
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def is_tree?([_, left, right]), do: is_tree?(left) && is_tree?(right)
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def is_tree?(_), do: false
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@spec left(t) :: t
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@doc """
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Get the left child of a tree.
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## Examples
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iex> MbBinaryTree.left([1, MbBinaryTree.new(2), MbBinaryTree.new(3)])
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[2, nil, nil]
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iex> MbBinaryTree.new(12) |> MbBinaryTree.left()
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nil
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iex> MbBinaryTree.left([12, [4, MbBinaryTree.new(2), MbBinaryTree.new(5)], [26, MbBinaryTree.new(14), [28, MbBinaryTree.new(27), MbBinaryTree.new(30)]]])
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[4, [2, nil, nil], [5, nil, nil]]
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"""
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def left([_, left | _]), do: left
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def left(_), do: nil
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@spec right(t) :: t
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@doc """
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Get the right child of a tree.
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## Examples
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iex> MbBinaryTree.right([1, MbBinaryTree.new(2), MbBinaryTree.new(3)])
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[3, nil, nil]
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iex> MbBinaryTree.new(12) |> MbBinaryTree.right()
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nil
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iex> MbBinaryTree.right([12, [4, MbBinaryTree.new(2), MbBinaryTree.new(5)], [26, MbBinaryTree.new(14), [28, MbBinaryTree.new(27), MbBinaryTree.new(30)]]])
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[26, [14, nil, nil], [28, [27, nil, nil], [30, nil, nil]]]
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"""
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def right([_, _, right]), do: right
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def right(_), do: nil
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@spec update_left(t, t) :: t
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@doc """
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Update the left child of a tree.
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## Examples
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iex> MbBinaryTree.update_left([1, MbBinaryTree.new(2), MbBinaryTree.new(3)], MbBinaryTree.new(4))
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[1, [4, nil, nil], [3, nil, nil]]
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iex> MbBinaryTree.new(12) |> MbBinaryTree.update_left(MbBinaryTree.new(4))
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[12, [4, nil, nil], nil]
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"""
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def update_left([node, _left, right], new_left), do: [node, new_left, right]
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@spec update_right(t, t) :: t
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@doc """
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Update the right child of a tree.
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## Examples
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iex> MbBinaryTree.update_right([1, MbBinaryTree.new(2), MbBinaryTree.new(3)], MbBinaryTree.new(4))
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[1, [2, nil, nil], [4, nil, nil]]
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iex> MbBinaryTree.new(12) |> MbBinaryTree.update_right(MbBinaryTree.new(4))
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[12, nil, [4, nil, nil]]
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"""
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def update_right([node, left, _right], new_right), do: [node, left, new_right]
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@doc """
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Calculate the depth of a binary tree.
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## Examples
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iex> MbBinaryTree.depth(nil)
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0
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iex> MbBinaryTree.depth([1, nil, nil])
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1
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iex> MbBinaryTree.depth([1, [2, nil, nil], [3, nil, nil]])
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2
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iex> MbBinaryTree.depth([1, [2, nil, nil], [3, [4, nil, nil], [5, nil, nil]]])
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3
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iex> MbBinaryTree.depth([12, [4, MbBinaryTree.new(2), MbBinaryTree.new(5)], [26, MbBinaryTree.new(14), [28, MbBinaryTree.new(27), MbBinaryTree.new(30)]]])
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4
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"""
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def depth(tree) do
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case tree do
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nil -> 0
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[_, nil, nil] -> 1
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[_, left, right] -> 1 + max(depth(left), depth(right))
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end
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end
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end
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