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.
Here I just wanted to have something that could be used for more matrix operations.
I thus created a Matrix with the goal of having a saddle_points method as
simple as possible with the algorithm as clear as possible:
def saddle_points(self):
is_max_in_row = self.is_cell(condition=max, within=Axis.ROW)
is_min_in_col = self.is_cell(condition=min, within=Axis.COLUMN)
is_saddle = is_max_in_row & is_min_in_col
saddle_indexes = set(self.index_where(is_saddle))
return saddle_indexesFor an input matrix self:
Matrix(
[9, 8, 7],
[5, 3, 2],
[6, 6, 7]
)The first matrix I compute, is_row_max is such that if is_row_max[i,j] is True
then self[i,j] is (one of) the maximum(s) within its row.
Matrix(
[True, False, False],
[True, False, False],
[False, False, True]
)The second matrix, is_col_min represents the same thing min values within columns:
Matrix(
[False, False, False],
[True, True, True],
[False, False, False]
)Finally is_saddle[i, j] will be true if both is_row_max[i,j]
and is_col_min[i,j] are true (notice that you need to implement the magic method __and__
for is_row_max & is_col_min to work). The matrix is_saddle is the following:
Matrix(
[False, False, False],
[True, False, False],
[False, False, False]
)Here you can notice that the only index at which a saddle point has been found is
(1, 0) (5 > 3 > 2 and 5 < 6 < 9 which make it a valid saddle point).
Matrix(
[9, 8, 7],
[5, 3, 2],
[6, 6, 7]
)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
-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.