Published at Jul 21 2018
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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.

Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include a message.

To raise a message with an exception, just write it as an argument to the exception type. For example, instead of
`raise Exception`

, you should write:

```
raise Exception("Meaningful message indicating the source of the error")
```

To run the tests, run the appropriate command below (why they are different):

- Python 2.7:
`py.test saddle_points_test.py`

- Python 3.4+:
`pytest saddle_points_test.py`

Alternatively, you can tell Python to run the pytest module (allowing the same command to be used regardless of Python version):
`python -m pytest saddle_points_test.py`

`pytest`

options-
`-v`

: enable verbose output -
`-x`

: stop running tests on first failure -
`--ff`

: run failures from previous test before running other test cases

For other options, see `python -m pytest -h`

Note that, when trying to submit an exercise, make sure the solution is in the `$EXERCISM_WORKSPACE/python/saddle-points`

directory.

You can find your Exercism workspace by running `exercism debug`

and looking for the line that starts with `Workspace`

.

For more detailed information about running tests, code style and linting, please see Running the Tests.

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

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

```
"""Tests for the saddle-points exercise
Implementation note:
The saddle_points function must validate the input matrix and raise a
ValueError with a meaningful error message if the matrix turns out to be
irregular.
"""
import unittest
from saddle_points import saddle_points
# Tests adapted from `problem-specifications//canonical-data.json` @ v1.1.0
class SaddlePointsTest(unittest.TestCase):
def test_identify_single_saddle_point(self):
matrix = [[9, 8, 7], [5, 3, 2], [6, 6, 7]]
self.assertEqual(saddle_points(matrix), set([(1, 0)]))
def test_empty_matrix_has_no_saddle_points(self):
self.assertEqual(saddle_points([]), set())
def test_identify_lack_of_saddle_points_when_there_are_none(self):
matrix = [[1, 2, 3], [3, 1, 2], [2, 3, 1]]
self.assertEqual(saddle_points(matrix), set())
def test_identify_multiple_saddle_points(self):
matrix = [[4, 5, 4], [3, 5, 5], [1, 5, 4]]
expected = set([(0, 1), (1, 1), (2, 1)])
self.assertEqual(saddle_points(matrix), expected)
def test_identify_saddle_point_in_bottom_right_corner(self):
matrix = [[8, 7, 9], [6, 7, 6], [3, 2, 5]]
expected = set([(2, 2)])
self.assertEqual(saddle_points(matrix), expected)
# Additional tests for this track
def test_irregular_matrix(self):
matrix = [[3, 2, 1], [0, 1], [2, 1, 0]]
with self.assertRaisesWithMessage(ValueError):
saddle_points(matrix)
# Utility functions
def setUp(self):
try:
self.assertRaisesRegex
except AttributeError:
self.assertRaisesRegex = self.assertRaisesRegexp
def assertRaisesWithMessage(self, exception):
return self.assertRaisesRegex(exception, r".+")
if __name__ == '__main__':
unittest.main()
```

```
def filter_check(function, xs):
for x in xs:
if function(x):
pass
else:
return False
return True
def verify_matrix(matrix):
n_rows = len(matrix)
for row in matrix:
if len(row) != n_rows:
raise ValueError('irregular matrix')
def saddle_points(matrix):
verify_matrix(matrix)
size = len(matrix)
saddle_points = list()
points = []
for i in range(size):
for j in range(size):
points.append((i, j))
for (x, y) in points:
row_values = matrix[x]
col_values = [matrix[k][y] for k in range(0, size)]
pt_value = matrix[x][y]
good_row = filter_check(lambda p: p <= pt_value, row_values)
good_col = filter_check(lambda p: p >= pt_value, col_values)
if good_row and good_col:
saddle_points.append((x, y))
return set(saddle_points)
```

A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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