diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml index a2fcf12c9bbd..0abe647b017a 100644 --- a/.pre-commit-config.yaml +++ b/.pre-commit-config.yaml @@ -14,7 +14,7 @@ repos: - id: requirements-txt-fixer - repo: https://github.com/psf/black - rev: 22.8.0 + rev: 22.10.0 hooks: - id: black @@ -26,7 +26,7 @@ repos: - --profile=black - repo: https://github.com/asottile/pyupgrade - rev: v2.38.2 + rev: v3.0.0 hooks: - id: pyupgrade args: @@ -42,7 +42,7 @@ repos: - --max-line-length=88 - repo: https://github.com/pre-commit/mirrors-mypy - rev: v0.981 + rev: v0.982 hooks: - id: mypy args: diff --git a/DIRECTORY.md b/DIRECTORY.md index 668da4761f74..9ef72c403f32 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -927,6 +927,7 @@ ## Scheduling * [First Come First Served](scheduling/first_come_first_served.py) * [Highest Response Ratio Next](scheduling/highest_response_ratio_next.py) + * [Job Sequencing With Deadline](scheduling/job_sequencing_with_deadline.py) * [Multi Level Feedback Queue](scheduling/multi_level_feedback_queue.py) * [Non Preemptive Shortest Job First](scheduling/non_preemptive_shortest_job_first.py) * [Round Robin](scheduling/round_robin.py) diff --git a/matrix/inverse_of_matrix.py b/matrix/inverse_of_matrix.py index 92780e656ea1..8086b4bb5f17 100644 --- a/matrix/inverse_of_matrix.py +++ b/matrix/inverse_of_matrix.py @@ -6,13 +6,14 @@ def inverse_of_matrix(matrix: list[list[float]]) -> list[list[float]]: """ A matrix multiplied with its inverse gives the identity matrix. - This function finds the inverse of a 2x2 matrix. + This function finds the inverse of a 2x2 and 3x3 matrix. If the determinant of a matrix is 0, its inverse does not exist. Sources for fixing inaccurate float arithmetic: https://stackoverflow.com/questions/6563058/how-do-i-use-accurate-float-arithmetic-in-python https://docs.python.org/3/library/decimal.html + Demo for 2x2 >>> inverse_of_matrix([[2, 5], [2, 0]]) [[0.0, 0.5], [0.2, -0.2]] >>> inverse_of_matrix([[2.5, 5], [1, 2]]) @@ -25,24 +26,137 @@ def inverse_of_matrix(matrix: list[list[float]]) -> list[list[float]]: [[0.16666666666666666, -0.0625], [-0.3333333333333333, 0.25]] >>> inverse_of_matrix([[10, 5], [3, 2.5]]) [[0.25, -0.5], [-0.3, 1.0]] + + Demo for 3x3 + >>> inverse_of_matrix([[2, 5, 7], [2, 0, 1], [1, 2, 3]]) + [[2.0, 1.0, -5.0], [5.0, 1.0, -12.0], [-4.0, -1.0, 10.0]] + >>> inverse_of_matrix([[1, 2, 2], [1, 2, 2], [3, 2, -1]]) + Traceback (most recent call last): + ... + ValueError: This matrix has no inverse. + + More examples: + + >>> inverse_of_matrix([]) + Traceback (most recent call last): + ... + ValueError: Please provide a matrix of size 2x2 or 3x3. + + >>> inverse_of_matrix([[],[]]) + Traceback (most recent call last): + ... + ValueError: Please provide a matrix of size 2x2 or 3x3. + + >>> inverse_of_matrix([[1, 2], [3, 4], [5, 6]]) + Traceback (most recent call last): + ... + ValueError: Please provide a matrix of size 2x2 or 3x3. + + >>> inverse_of_matrix([[1, 2, 1], [0,3, 4]]) + Traceback (most recent call last): + ... + ValueError: Please provide a matrix of size 2x2 or 3x3. + + >>> inverse_of_matrix([[1, 2, 3], [7, 8, 9], [7, 8, 9]]) + Traceback (most recent call last): + ... + ValueError: This matrix has no inverse. + + >>> inverse_of_matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) + [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]] """ D = Decimal # An abbreviation for conciseness # Check if the provided matrix has 2 rows and 2 columns # since this implementation only works for 2x2 matrices - if len(matrix) != 2 or len(matrix[0]) != 2 or len(matrix[1]) != 2: - raise ValueError("Please provide a matrix of size 2x2.") + if len(matrix) == 2 and len(matrix[0]) == 2 and len(matrix[1]) == 2: + # Calculate the determinant of the matrix + determinant = D(matrix[0][0]) * D(matrix[1][1]) - D(matrix[1][0]) * D( + matrix[0][1] + ) + if determinant == 0: + raise ValueError("This matrix has no inverse.") + + # Creates a copy of the matrix with swapped positions of the elements + swapped_matrix = [[0.0, 0.0], [0.0, 0.0]] + swapped_matrix[0][0], swapped_matrix[1][1] = matrix[1][1], matrix[0][0] + swapped_matrix[1][0], swapped_matrix[0][1] = -matrix[1][0], -matrix[0][1] + + # Calculate the inverse of the matrix + return [ + [float(D(n) / determinant) or 0.0 for n in row] for row in swapped_matrix + ] + elif ( + len(matrix) == 3 + and len(matrix[0]) == 3 + and len(matrix[1]) == 3 + and len(matrix[2]) == 3 + ): + # Calculate the determinant of the matrix using Sarrus rule + determinant = ( + (D(matrix[0][0]) * D(matrix[1][1]) * D(matrix[2][2])) + + (D(matrix[0][1]) * D(matrix[1][2]) * D(matrix[2][0])) + + (D(matrix[0][2]) * D(matrix[1][0]) * D(matrix[2][1])) + ) - ( + (D(matrix[0][2]) * D(matrix[1][1]) * D(matrix[2][0])) + + (D(matrix[0][1]) * D(matrix[1][0]) * D(matrix[2][2])) + + (D(matrix[0][0]) * D(matrix[1][2]) * D(matrix[2][1])) + ) + if determinant == 0: + raise ValueError("This matrix has no inverse.") + + # Creating cofactor matrix + cofactor_matrix = [ + [D(0.0), D(0.0), D(0.0)], + [D(0.0), D(0.0), D(0.0)], + [D(0.0), D(0.0), D(0.0)], + ] + cofactor_matrix[0][0] = (D(matrix[1][1]) * D(matrix[2][2])) - ( + D(matrix[1][2]) * D(matrix[2][1]) + ) + cofactor_matrix[0][1] = -( + (D(matrix[1][0]) * D(matrix[2][2])) - (D(matrix[1][2]) * D(matrix[2][0])) + ) + cofactor_matrix[0][2] = (D(matrix[1][0]) * D(matrix[2][1])) - ( + D(matrix[1][1]) * D(matrix[2][0]) + ) + cofactor_matrix[1][0] = -( + (D(matrix[0][1]) * D(matrix[2][2])) - (D(matrix[0][2]) * D(matrix[2][1])) + ) + cofactor_matrix[1][1] = (D(matrix[0][0]) * D(matrix[2][2])) - ( + D(matrix[0][2]) * D(matrix[2][0]) + ) + cofactor_matrix[1][2] = -( + (D(matrix[0][0]) * D(matrix[2][1])) - (D(matrix[0][1]) * D(matrix[2][0])) + ) + cofactor_matrix[2][0] = (D(matrix[0][1]) * D(matrix[1][2])) - ( + D(matrix[0][2]) * D(matrix[1][1]) + ) + cofactor_matrix[2][1] = -( + (D(matrix[0][0]) * D(matrix[1][2])) - (D(matrix[0][2]) * D(matrix[1][0])) + ) + cofactor_matrix[2][2] = (D(matrix[0][0]) * D(matrix[1][1])) - ( + D(matrix[0][1]) * D(matrix[1][0]) + ) - # Calculate the determinant of the matrix - determinant = D(matrix[0][0]) * D(matrix[1][1]) - D(matrix[1][0]) * D(matrix[0][1]) - if determinant == 0: - raise ValueError("This matrix has no inverse.") + # Transpose the cofactor matrix (Adjoint matrix) + adjoint_matrix = [ + [D(0.0), D(0.0), D(0.0)], + [D(0.0), D(0.0), D(0.0)], + [D(0.0), D(0.0), D(0.0)], + ] + for i in range(3): + for j in range(3): + adjoint_matrix[i][j] = cofactor_matrix[j][i] - # Creates a copy of the matrix with swapped positions of the elements - swapped_matrix = [[0.0, 0.0], [0.0, 0.0]] - swapped_matrix[0][0], swapped_matrix[1][1] = matrix[1][1], matrix[0][0] - swapped_matrix[1][0], swapped_matrix[0][1] = -matrix[1][0], -matrix[0][1] + # Inverse of the matrix using the formula (1/determinant) * adjoint matrix + inverse_matrix = [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]] + for i in range(3): + for j in range(3): + inverse_matrix[i][j] = float(adjoint_matrix[i][j]) / float(determinant) - # Calculate the inverse of the matrix - return [[float(D(n) / determinant) or 0.0 for n in row] for row in swapped_matrix] + # Calculate the inverse of the matrix + return [[float(D(n)) or 0.0 for n in row] for row in inverse_matrix] + else: + raise ValueError("Please provide a matrix of size 2x2 or 3x3.")