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remcopeereboom's solution

to Saddle Points in the Ruby Track

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

Detect saddle points in a matrix.

So say you have a matrix like so:

    0  1  2
  |---------
0 | 9  8  7
1 | 5  3  2     <--- saddle point at (1,0)
2 | 6  6  7

It has a saddle point at (1, 0).

It's called a "saddle point" because it is greater than or equal to every element in its row and less than or equal to every element in its column.

A matrix may have zero or more saddle points.

Your code should be able to provide the (possibly empty) list of all the saddle points for any given matrix.

Note that you may find other definitions of matrix saddle points online, but the tests for this exercise follow the above unambiguous definition.


For installation and learning resources, refer to the exercism help page.

For running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:

gem install minitest

If you would like color output, you can require 'minitest/pride' in the test file, or note the alternative instruction, below, for running the test file.

Run the tests from the exercise directory using the following command:

ruby saddle_points_test.rb

To include color from the command line:

ruby -r minitest/pride saddle_points_test.rb

Source

J Dalbey's Programming Practice problems http://users.csc.calpoly.edu/~jdalbey/103/Projects/ProgrammingPractice.html

Submitting Incomplete Solutions

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

saddle_points_test.rb

require 'minitest/autorun'
require_relative 'saddle_points'

class MatrixTest < Minitest::Test
  def test_extract_a_row
    matrix = Matrix.new("1 2\n10 20")
    assert_equal [1, 2], matrix.rows[0]
  end

  def test_extract_same_row_again
    skip
    matrix = Matrix.new("9 7\n8 6")
    assert_equal [9, 7], matrix.rows[0]
  end

  def test_extract_other_row
    skip
    matrix = Matrix.new("9 8 7\n19 18 17")
    assert_equal [19, 18, 17], matrix.rows[1]
  end

  def test_extract_other_row_again
    skip
    matrix = Matrix.new("1 4 9\n16 25 36")
    assert_equal [16, 25, 36], matrix.rows[1]
  end

  def test_extract_a_column
    skip
    matrix = Matrix.new("1 2 3\n4 5 6\n7 8 9\n 8 7 6")
    assert_equal [1, 4, 7, 8], matrix.columns[0]
  end

  def test_extract_another_column
    skip
    matrix = Matrix.new("89 1903 3\n18 3 1\n9 4 800")
    assert_equal [1903, 3, 4], matrix.columns[1]
  end

  def test_no_saddle_point
    skip
    matrix = Matrix.new("2 1\n1 2")
    assert_equal [], matrix.saddle_points
  end

  def test_a_saddle_point
    skip
    matrix = Matrix.new("1 2\n3 4")
    assert_equal [[0, 1]], matrix.saddle_points
  end

  def test_another_saddle_point
    skip
    matrix = Matrix.new("18 3 39 19 91\n38 10 8 77 320\n3 4 8 6 7")
    assert_equal [[2, 2]], matrix.saddle_points
  end

  def test_multiple_saddle_points
    skip
    matrix = Matrix.new("4 5 4\n3 5 5\n1 5 4")
    assert_equal [[0, 1], [1, 1], [2, 1]], matrix.saddle_points
  end
end
class Matrix
  attr_reader :rows

  def initialize(string)
    @rows = []

    string.each_line do |line|
      @rows << line.split.map(&:to_i)
    end
  end

  def columns
    @cols ||= @rows.transpose
  end

  def [](row, col)
    return nil unless (0...rows.size).include?(row)
    @rows[row][col] # Returns nil if col out of range.
  end

  def saddle_points
    (0...rows.size).each_with_object([]) do |row, saddle_points|
      (0...columns.size).each do |col|
        saddle_points << [row, col] if saddle_point?(row, col)
      end
    end
  end

  private

  def row_maxima
    @row_maxima ||= rows.map(&:max)
  end

  def col_minima
    @col_minima ||= columns.map(&:min)
  end

  def saddle_point?(row, col)
    element = self[row, col]
    row_maxima[row] == element && col_minima[col] == element
  end
end

Community comments

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Avatar of remcopeereboom

This is okay for now, but at some point we will want to have an each method that yields the elements and probably also specific methods for dealing with valid rows and columns as well as a helper that just returns the coords instead of the values.

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