 # paulfioravanti's solution

## to Saddle Points in the Ruby Track

Published at Jul 13 2018 · 0 comments
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.

The matrix can have a different number of rows and columns (Non square).

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 Ruby resources 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
end

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

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

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

def initialize(string)
@rows = generate_rows(string).freeze
@columns = rows.transpose.freeze
end

def saddle_points
rows
.each
.with_index
.with_object([], &method(:check_row_saddle_points))
end

private

def generate_rows(string)
string
.each_line
.map(&method(:row_to_integers))
end

def row_to_integers(row)
row
.split
.map(&:to_i)
end

def check_row_saddle_points((row, row_index), acc)
row
.each
.with_index
.with_object([row, row_index, acc], &method(:check_column_saddle_points))
end

def check_column_saddle_points((value, column_index), (row, row_index, acc))
return unless saddle_point?(value, row, columns[column_index])

acc << [row_index, column_index]
end

def saddle_point?(value, row, column)
value == row.max && value == column.min
end
end``````

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