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Contents
defmodule SaddlePoints do
@doc """
Parses a string representation of a matrix
to a list of rows
"""
@spec rows(String.t()) :: [[integer]]
def rows(str) do
str
|> String.split("\n")
|> Enum.map(&parse_row/1)
end
defp parse_row(str) do
str
|> String.split(" ")
|> Enum.map(&String.to_integer/1)
end
@doc """
Parses a string representation of a matrix
to a list of columns
"""
@spec columns(String.t()) :: [[integer]]
def columns(str) do
str
|> rows
|> List.zip()
|> Enum.map(&Tuple.to_list/1)
end
@doc """
Calculates all the saddle points from a string
representation of a matrix
"""
@spec saddle_points(String.t()) :: [{integer, integer}]
def saddle_points(str) do
rows = rows(str)
columns = columns(str)
rows
|> generate_coordinates
|> Enum.filter(&is_saddle_point?(&1, rows, columns))
end
defp is_saddle_point?(point, rows, columns) do
max_in_row?(point, rows) && min_in_column?(point, columns)
end
defp max_in_row?({x, y}, rows) do
row = Enum.at(rows, x)
Enum.at(row, y) == Enum.max(row)
end
defp min_in_column?({x, y}, columns) do
column = Enum.at(columns, y)
Enum.at(column, x) == Enum.min(column)
end
defp generate_coordinates(rows) do
rows
|> Enum.with_index()
|> Enum.flat_map(&generate_coordinates_row/1)
end
defp generate_coordinates_row({row, row_index}) do
row
|> Enum.with_index()
|> Enum.map(fn {_, col_index} -> {row_index, col_index} end)
end
end
Version data entries
69 entries across 69 versions & 1 rubygems