# 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.

``````require 'minitest/autorun'

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

skip
matrix = Matrix.new("2 1\n1 2")
end

skip
matrix = Matrix.new("1 2\n3 4")
end

skip
matrix = Matrix.new("18 3 39 19 91\n38 10 8 77 320\n3 4 8 6 7")
end

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

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

(0...columns.size).each do |col|
end
end
end

private

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

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

element = self[row, col]
row_maxima[row] == element && col_minima[col] == element
end
end``````