Add missing type hints in matrix directory (#6612)

* Update count_islands_in_matrix.py

* Update matrix_class.py

* Update matrix_operation.py

* Update nth_fibonacci_using_matrix_exponentiation.py

* Update searching_in_sorted_matrix.py

* Update count_islands_in_matrix.py

* Update matrix_class.py

* Update matrix_operation.py

* Update rotate_matrix.py

* Update sherman_morrison.py

* Update spiral_print.py

* Update count_islands_in_matrix.py

* formatting

* formatting

* Update matrix_class.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

matrix/count_islands_in_matrix.py

@@ -4,12 +4,12 @@
 
 
 class matrix:  # Public class to implement a graph
-    def __init__(self, row: int, col: int, graph: list):
+    def __init__(self, row: int, col: int, graph: list[list[bool]]) -> None:
         self.ROW = row
         self.COL = col
         self.graph = graph
 
-    def is_safe(self, i, j, visited) -> bool:
+    def is_safe(self, i: int, j: int, visited: list[list[bool]]) -> bool:
         return (
             0 <= i < self.ROW
             and 0 <= j < self.COL
@@ -17,7 +17,8 @@ class matrix:  # Public class to implement a graph
             and self.graph[i][j]
         )
 
-    def diffs(self, i, j, visited):  # Checking all 8 elements surrounding nth element
+    def diffs(self, i: int, j: int, visited: list[list[bool]]) -> None:
+        # Checking all 8 elements surrounding nth element
         rowNbr = [-1, -1, -1, 0, 0, 1, 1, 1]  # Coordinate order
         colNbr = [-1, 0, 1, -1, 1, -1, 0, 1]
         visited[i][j] = True  # Make those cells visited

matrix/matrix_class.py

@@ -1,5 +1,7 @@
 # An OOP approach to representing and manipulating matrices
 
+from __future__ import annotations
+
 
 class Matrix:
     """
@@ -54,7 +56,9 @@ class Matrix:
      [6. -12. 6.]
      [-3. 6. -3.]]
     >>> print(matrix.inverse())
-    None
+    Traceback (most recent call last):
+        ...
+    TypeError: Only matrices with a non-zero determinant have an inverse
 
     Determinant is an int, float, or Nonetype
     >>> matrix.determinant()
@@ -101,10 +105,9 @@ class Matrix:
      [198. 243. 288. 304.]
      [306. 378. 450. 472.]
      [414. 513. 612. 640.]]
-
     """
 
-    def __init__(self, rows):
+    def __init__(self, rows: list[list[int]]):
         error = TypeError(
             "Matrices must be formed from a list of zero or more lists containing at "
             "least one and the same number of values, each of which must be of type "
@@ -125,42 +128,43 @@ class Matrix:
             self.rows = []
 
     # MATRIX INFORMATION
-    def columns(self):
+    def columns(self) -> list[list[int]]:
         return [[row[i] for row in self.rows] for i in range(len(self.rows[0]))]
 
     @property
-    def num_rows(self):
+    def num_rows(self) -> int:
         return len(self.rows)
 
     @property
-    def num_columns(self):
+    def num_columns(self) -> int:
         return len(self.rows[0])
 
     @property
-    def order(self):
+    def order(self) -> tuple[int, int]:
         return (self.num_rows, self.num_columns)
 
     @property
-    def is_square(self):
+    def is_square(self) -> bool:
         return self.order[0] == self.order[1]
 
-    def identity(self):
+    def identity(self) -> Matrix:
         values = [
             [0 if column_num != row_num else 1 for column_num in range(self.num_rows)]
             for row_num in range(self.num_rows)
         ]
         return Matrix(values)
 
-    def determinant(self):
+    def determinant(self) -> int:
         if not self.is_square:
-            return None
+            return 0
         if self.order == (0, 0):
             return 1
         if self.order == (1, 1):
-            return self.rows[0][0]
+            return int(self.rows[0][0])
         if self.order == (2, 2):
-            return (self.rows[0][0] * self.rows[1][1]) - (
+            return int(
-                self.rows[0][1] * self.rows[1][0]
+                (self.rows[0][0] * self.rows[1][1])
+                - (self.rows[0][1] * self.rows[1][0])
             )
         else:
             return sum(
@@ -168,10 +172,10 @@ class Matrix:
                 for column in range(self.num_columns)
             )
 
-    def is_invertable(self):
+    def is_invertable(self) -> bool:
         return bool(self.determinant())
 
-    def get_minor(self, row, column):
+    def get_minor(self, row: int, column: int) -> int:
         values = [
             [
                 self.rows[other_row][other_column]
@@ -183,12 +187,12 @@ class Matrix:
         ]
         return Matrix(values).determinant()
 
-    def get_cofactor(self, row, column):
+    def get_cofactor(self, row: int, column: int) -> int:
         if (row + column) % 2 == 0:
             return self.get_minor(row, column)
         return -1 * self.get_minor(row, column)
 
-    def minors(self):
+    def minors(self) -> Matrix:
         return Matrix(
             [
                 [self.get_minor(row, column) for column in range(self.num_columns)]
@@ -196,7 +200,7 @@ class Matrix:
             ]
         )
 
-    def cofactors(self):
+    def cofactors(self) -> Matrix:
         return Matrix(
             [
                 [
@@ -209,25 +213,27 @@ class Matrix:
             ]
         )
 
-    def adjugate(self):
+    def adjugate(self) -> Matrix:
         values = [
             [self.cofactors().rows[column][row] for column in range(self.num_columns)]
             for row in range(self.num_rows)
         ]
         return Matrix(values)
 
-    def inverse(self):
+    def inverse(self) -> Matrix:
         determinant = self.determinant()
-        return None if not determinant else self.adjugate() * (1 / determinant)
+        if not determinant:
+            raise TypeError("Only matrices with a non-zero determinant have an inverse")
+        return self.adjugate() * (1 / determinant)
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         return str(self.rows)
 
-    def __str__(self):
+    def __str__(self) -> str:
         if self.num_rows == 0:
             return "[]"
         if self.num_rows == 1:
-            return "[[" + ". ".join(self.rows[0]) + "]]"
+            return "[[" + ". ".join(str(self.rows[0])) + "]]"
         return (
             "["
             + "\n ".join(
@@ -240,7 +246,7 @@ class Matrix:
         )
 
     # MATRIX MANIPULATION
-    def add_row(self, row, position=None):
+    def add_row(self, row: list[int], position: int | None = None) -> None:
         type_error = TypeError("Row must be a list containing all ints and/or floats")
         if not isinstance(row, list):
             raise type_error
@@ -256,7 +262,7 @@ class Matrix:
         else:
             self.rows = self.rows[0:position] + [row] + self.rows[position:]
 
-    def add_column(self, column, position=None):
+    def add_column(self, column: list[int], position: int | None = None) -> None:
         type_error = TypeError(
             "Column must be a list containing all ints and/or floats"
         )
@@ -278,18 +284,18 @@ class Matrix:
             ]
 
     # MATRIX OPERATIONS
-    def __eq__(self, other):
+    def __eq__(self, other: object) -> bool:
         if not isinstance(other, Matrix):
             raise TypeError("A Matrix can only be compared with another Matrix")
         return self.rows == other.rows
 
-    def __ne__(self, other):
+    def __ne__(self, other: object) -> bool:
         return not self == other
 
-    def __neg__(self):
+    def __neg__(self) -> Matrix:
         return self * -1
 
-    def __add__(self, other):
+    def __add__(self, other: Matrix) -> Matrix:
         if self.order != other.order:
             raise ValueError("Addition requires matrices of the same order")
         return Matrix(
@@ -299,7 +305,7 @@ class Matrix:
             ]
         )
 
-    def __sub__(self, other):
+    def __sub__(self, other: Matrix) -> Matrix:
         if self.order != other.order:
             raise ValueError("Subtraction requires matrices of the same order")
         return Matrix(
@@ -309,9 +315,11 @@ class Matrix:
             ]
         )
 
-    def __mul__(self, other):
+    def __mul__(self, other: Matrix | int | float) -> Matrix:
         if isinstance(other, (int, float)):
-            return Matrix([[element * other for element in row] for row in self.rows])
+            return Matrix(
+                [[int(element * other) for element in row] for row in self.rows]
+            )
         elif isinstance(other, Matrix):
             if self.num_columns != other.num_rows:
                 raise ValueError(
@@ -329,7 +337,7 @@ class Matrix:
                 "A Matrix can only be multiplied by an int, float, or another matrix"
             )
 
-    def __pow__(self, other):
+    def __pow__(self, other: int) -> Matrix:
         if not isinstance(other, int):
             raise TypeError("A Matrix can only be raised to the power of an int")
         if not self.is_square:
@@ -348,7 +356,7 @@ class Matrix:
         return result
 
     @classmethod
-    def dot_product(cls, row, column):
+    def dot_product(cls, row: list[int], column: list[int]) -> int:
         return sum(row[i] * column[i] for i in range(len(row)))
 
 

matrix/matrix_operation.py

@@ -4,8 +4,10 @@ Functions for 2D matrix operations
 
 from __future__ import annotations
 
+from typing import Any
 
-def add(*matrix_s: list[list]) -> list[list]:
+
+def add(*matrix_s: list[list[int]]) -> list[list[int]]:
     """
     >>> add([[1,2],[3,4]],[[2,3],[4,5]])
     [[3, 5], [7, 9]]
@@ -25,7 +27,7 @@ def add(*matrix_s: list[list]) -> list[list]:
     raise TypeError("Expected a matrix, got int/list instead")
 
 
-def subtract(matrix_a: list[list], matrix_b: list[list]) -> list[list]:
+def subtract(matrix_a: list[list[int]], matrix_b: list[list[int]]) -> list[list[int]]:
     """
     >>> subtract([[1,2],[3,4]],[[2,3],[4,5]])
     [[-1, -1], [-1, -1]]
@@ -45,7 +47,7 @@ def subtract(matrix_a: list[list], matrix_b: list[list]) -> list[list]:
     raise TypeError("Expected a matrix, got int/list instead")
 
 
-def scalar_multiply(matrix: list[list], n: int | float) -> list[list]:
+def scalar_multiply(matrix: list[list[int]], n: int | float) -> list[list[float]]:
     """
     >>> scalar_multiply([[1,2],[3,4]],5)
     [[5, 10], [15, 20]]
@@ -55,7 +57,7 @@ def scalar_multiply(matrix: list[list], n: int | float) -> list[list]:
     return [[x * n for x in row] for row in matrix]
 
 
-def multiply(matrix_a: list[list], matrix_b: list[list]) -> list[list]:
+def multiply(matrix_a: list[list[int]], matrix_b: list[list[int]]) -> list[list[int]]:
     """
     >>> multiply([[1,2],[3,4]],[[5,5],[7,5]])
     [[19, 15], [43, 35]]
@@ -77,7 +79,7 @@ def multiply(matrix_a: list[list], matrix_b: list[list]) -> list[list]:
     ]
 
 
-def identity(n: int) -> list[list]:
+def identity(n: int) -> list[list[int]]:
     """
     :param n: dimension for nxn matrix
     :type n: int
@@ -89,7 +91,9 @@ def identity(n: int) -> list[list]:
     return [[int(row == column) for column in range(n)] for row in range(n)]
 
 
-def transpose(matrix: list[list], return_map: bool = True) -> list[list] | map[list]:
+def transpose(
+    matrix: list[list[int]], return_map: bool = True
+) -> list[list[int]] | map[list[int]]:
     """
     >>> transpose([[1,2],[3,4]]) # doctest: +ELLIPSIS
     <map object at ...
@@ -108,7 +112,7 @@ def transpose(matrix: list[list], return_map: bool = True) -> list[list] | map[l
     raise TypeError("Expected a matrix, got int/list instead")
 
 
-def minor(matrix: list[list], row: int, column: int) -> list[list]:
+def minor(matrix: list[list[int]], row: int, column: int) -> list[list[int]]:
     """
     >>> minor([[1, 2], [3, 4]], 1, 1)
     [[1]]
@@ -117,7 +121,7 @@ def minor(matrix: list[list], row: int, column: int) -> list[list]:
     return [row[:column] + row[column + 1 :] for row in minor]
 
 
-def determinant(matrix: list[list]) -> int:
+def determinant(matrix: list[list[int]]) -> Any:
     """
     >>> determinant([[1, 2], [3, 4]])
     -2
@@ -133,7 +137,7 @@ def determinant(matrix: list[list]) -> int:
     )
 
 
-def inverse(matrix: list[list]) -> list[list] | None:
+def inverse(matrix: list[list[int]]) -> list[list[float]] | None:
     """
     >>> inverse([[1, 2], [3, 4]])
     [[-2.0, 1.0], [1.5, -0.5]]
@@ -157,27 +161,27 @@ def inverse(matrix: list[list]) -> list[list] | None:
     return scalar_multiply(adjugate, 1 / det)
 
 
-def _check_not_integer(matrix: list[list]) -> bool:
+def _check_not_integer(matrix: list[list[int]]) -> bool:
     return not isinstance(matrix, int) and not isinstance(matrix[0], int)
 
 
-def _shape(matrix: list[list]) -> tuple[int, int]:
+def _shape(matrix: list[list[int]]) -> tuple[int, int]:
     return len(matrix), len(matrix[0])
 
 
 def _verify_matrix_sizes(
-    matrix_a: list[list], matrix_b: list[list]
+    matrix_a: list[list[int]], matrix_b: list[list[int]]
-) -> tuple[tuple, tuple]:
+) -> tuple[tuple[int, int], tuple[int, int]]:
     shape = _shape(matrix_a) + _shape(matrix_b)
     if shape[0] != shape[3] or shape[1] != shape[2]:
         raise ValueError(
-            "operands could not be broadcast together with shape "
+            f"operands could not be broadcast together with shape "
             f"({shape[0], shape[1]}), ({shape[2], shape[3]})"
         )
     return (shape[0], shape[2]), (shape[1], shape[3])
 
 
-def main():
+def main() -> None:
     matrix_a = [[12, 10], [3, 9]]
     matrix_b = [[3, 4], [7, 4]]
     matrix_c = [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]

matrix/nth_fibonacci_using_matrix_exponentiation.py

@@ -16,7 +16,7 @@ We can decrease the n times multiplication by following the divide and conquer a
 """
 
 
-def multiply(matrix_a, matrix_b):
+def multiply(matrix_a: list[list[int]], matrix_b: list[list[int]]) -> list[list[int]]:
     matrix_c = []
     n = len(matrix_a)
     for i in range(n):
@@ -30,11 +30,11 @@ def multiply(matrix_a, matrix_b):
     return matrix_c
 
 
-def identity(n):
+def identity(n: int) -> list[list[int]]:
     return [[int(row == column) for column in range(n)] for row in range(n)]
 
 
-def nth_fibonacci_matrix(n):
+def nth_fibonacci_matrix(n: int) -> int:
     """
     >>> nth_fibonacci_matrix(100)
     354224848179261915075
@@ -54,7 +54,7 @@ def nth_fibonacci_matrix(n):
     return res_matrix[0][0]
 
 
-def nth_fibonacci_bruteforce(n):
+def nth_fibonacci_bruteforce(n: int) -> int:
     """
     >>> nth_fibonacci_bruteforce(100)
     354224848179261915075
@@ -70,7 +70,7 @@ def nth_fibonacci_bruteforce(n):
     return fib1
 
 
-def main():
+def main() -> None:
     for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
         n = int("".join(c for c in ordinal if c in "0123456789"))  # 1000th --> 1000
         print(

matrix/rotate_matrix.py

@@ -8,7 +8,7 @@ https://stackoverflow.com/questions/42519/how-do-you-rotate-a-two-dimensional-ar
 from __future__ import annotations
 
 
-def make_matrix(row_size: int = 4) -> list[list]:
+def make_matrix(row_size: int = 4) -> list[list[int]]:
     """
     >>> make_matrix()
     [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]
@@ -25,7 +25,7 @@ def make_matrix(row_size: int = 4) -> list[list]:
     return [[1 + x + y * row_size for x in range(row_size)] for y in range(row_size)]
 
 
-def rotate_90(matrix: list[list]) -> list[list]:
+def rotate_90(matrix: list[list[int]]) -> list[list[int]]:
     """
     >>> rotate_90(make_matrix())
     [[4, 8, 12, 16], [3, 7, 11, 15], [2, 6, 10, 14], [1, 5, 9, 13]]
@@ -37,7 +37,7 @@ def rotate_90(matrix: list[list]) -> list[list]:
     # OR.. transpose(reverse_column(matrix))
 
 
-def rotate_180(matrix: list[list]) -> list[list]:
+def rotate_180(matrix: list[list[int]]) -> list[list[int]]:
     """
     >>> rotate_180(make_matrix())
     [[16, 15, 14, 13], [12, 11, 10, 9], [8, 7, 6, 5], [4, 3, 2, 1]]
@@ -49,7 +49,7 @@ def rotate_180(matrix: list[list]) -> list[list]:
     # OR.. reverse_column(reverse_row(matrix))
 
 
-def rotate_270(matrix: list[list]) -> list[list]:
+def rotate_270(matrix: list[list[int]]) -> list[list[int]]:
     """
     >>> rotate_270(make_matrix())
     [[13, 9, 5, 1], [14, 10, 6, 2], [15, 11, 7, 3], [16, 12, 8, 4]]
@@ -61,22 +61,22 @@ def rotate_270(matrix: list[list]) -> list[list]:
     # OR.. transpose(reverse_row(matrix))
 
 
-def transpose(matrix: list[list]) -> list[list]:
+def transpose(matrix: list[list[int]]) -> list[list[int]]:
     matrix[:] = [list(x) for x in zip(*matrix)]
     return matrix
 
 
-def reverse_row(matrix: list[list]) -> list[list]:
+def reverse_row(matrix: list[list[int]]) -> list[list[int]]:
     matrix[:] = matrix[::-1]
     return matrix
 
 
-def reverse_column(matrix: list[list]) -> list[list]:
+def reverse_column(matrix: list[list[int]]) -> list[list[int]]:
     matrix[:] = [x[::-1] for x in matrix]
     return matrix
 
 
-def print_matrix(matrix: list[list]) -> None:
+def print_matrix(matrix: list[list[int]]) -> None:
     for i in matrix:
         print(*i)
 

matrix/searching_in_sorted_matrix.py

@@ -2,7 +2,7 @@ from __future__ import annotations
 
 
 def search_in_a_sorted_matrix(
-    mat: list[list], m: int, n: int, key: int | float
+    mat: list[list[int]], m: int, n: int, key: int | float
 ) -> None:
     """
     >>> search_in_a_sorted_matrix(
@@ -30,7 +30,7 @@ def search_in_a_sorted_matrix(
     print(f"Key {key} not found")
 
 
-def main():
+def main() -> None:
     mat = [[2, 5, 7], [4, 8, 13], [9, 11, 15], [12, 17, 20]]
     x = int(input("Enter the element to be searched:"))
     print(mat)

matrix/sherman_morrison.py

@@ -1,14 +1,18 @@
+from __future__ import annotations
+
+from typing import Any
+
+
 class Matrix:
     """
     <class Matrix>
     Matrix structure.
     """
 
-    def __init__(self, row: int, column: int, default_value: float = 0):
+    def __init__(self, row: int, column: int, default_value: float = 0) -> None:
         """
         <method Matrix.__init__>
         Initialize matrix with given size and default value.
-
         Example:
         >>> a = Matrix(2, 3, 1)
         >>> a
@@ -20,7 +24,7 @@ class Matrix:
         self.row, self.column = row, column
         self.array = [[default_value for c in range(column)] for r in range(row)]
 
-    def __str__(self):
+    def __str__(self) -> str:
         """
         <method Matrix.__str__>
         Return string representation of this matrix.
@@ -37,7 +41,7 @@ class Matrix:
         string_format_identifier = "%%%ds" % (max_element_length,)
 
         # Make string and return
-        def single_line(row_vector):
+        def single_line(row_vector: list[float]) -> str:
             nonlocal string_format_identifier
             line = "["
             line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)
@@ -47,14 +51,13 @@ class Matrix:
         s += "\n".join(single_line(row_vector) for row_vector in self.array)
         return s
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         return str(self)
 
-    def validateIndices(self, loc: tuple):
+    def validateIndices(self, loc: tuple[int, int]) -> bool:
         """
         <method Matrix.validateIndices>
         Check if given indices are valid to pick element from matrix.
-
         Example:
         >>> a = Matrix(2, 6, 0)
         >>> a.validateIndices((2, 7))
@@ -69,11 +72,10 @@ class Matrix:
         else:
             return True
 
-    def __getitem__(self, loc: tuple):
+    def __getitem__(self, loc: tuple[int, int]) -> Any:
         """
         <method Matrix.__getitem__>
         Return array[row][column] where loc = (row, column).
-
         Example:
         >>> a = Matrix(3, 2, 7)
         >>> a[1, 0]
@@ -82,11 +84,10 @@ class Matrix:
         assert self.validateIndices(loc)
         return self.array[loc[0]][loc[1]]
 
-    def __setitem__(self, loc: tuple, value: float):
+    def __setitem__(self, loc: tuple[int, int], value: float) -> None:
         """
         <method Matrix.__setitem__>
         Set array[row][column] = value where loc = (row, column).
-
         Example:
         >>> a = Matrix(2, 3, 1)
         >>> a[1, 2] = 51
@@ -98,11 +99,10 @@ class Matrix:
         assert self.validateIndices(loc)
         self.array[loc[0]][loc[1]] = value
 
-    def __add__(self, another):
+    def __add__(self, another: Matrix) -> Matrix:
         """
         <method Matrix.__add__>
         Return self + another.
-
         Example:
         >>> a = Matrix(2, 1, -4)
         >>> b = Matrix(2, 1, 3)
@@ -123,11 +123,10 @@ class Matrix:
                 result[r, c] = self[r, c] + another[r, c]
         return result
 
-    def __neg__(self):
+    def __neg__(self) -> Matrix:
         """
         <method Matrix.__neg__>
         Return -self.
-
         Example:
         >>> a = Matrix(2, 2, 3)
         >>> a[0, 1] = a[1, 0] = -2
@@ -143,14 +142,13 @@ class Matrix:
                 result[r, c] = -self[r, c]
         return result
 
-    def __sub__(self, another):
+    def __sub__(self, another: Matrix) -> Matrix:
         return self + (-another)
 
-    def __mul__(self, another):
+    def __mul__(self, another: int | float | Matrix) -> Matrix:
         """
         <method Matrix.__mul__>
         Return self * another.
-
         Example:
         >>> a = Matrix(2, 3, 1)
         >>> a[0,2] = a[1,2] = 3
@@ -177,11 +175,10 @@ class Matrix:
         else:
             raise TypeError(f"Unsupported type given for another ({type(another)})")
 
-    def transpose(self):
+    def transpose(self) -> Matrix:
         """
         <method Matrix.transpose>
         Return self^T.
-
         Example:
         >>> a = Matrix(2, 3)
         >>> for r in range(2):
@@ -201,7 +198,7 @@ class Matrix:
                 result[c, r] = self[r, c]
         return result
 
-    def ShermanMorrison(self, u, v):
+    def ShermanMorrison(self, u: Matrix, v: Matrix) -> Any:
         """
         <method Matrix.ShermanMorrison>
         Apply Sherman-Morrison formula in O(n^2).
@@ -211,7 +208,6 @@ class Matrix:
         impossible to calculate.
         Warning: This method doesn't check if self is invertible.
             Make sure self is invertible before execute this method.
-
         Example:
         >>> ainv = Matrix(3, 3, 0)
         >>> for i in range(3): ainv[i,i] = 1
@@ -243,7 +239,7 @@ class Matrix:
 # Testing
 if __name__ == "__main__":
 
-    def test1():
+    def test1() -> None:
         # a^(-1)
         ainv = Matrix(3, 3, 0)
         for i in range(3):
@@ -256,11 +252,11 @@ if __name__ == "__main__":
         v[0, 0], v[1, 0], v[2, 0] = 4, -2, 5
         print(f"u is {u}")
         print(f"v is {v}")
-        print(f"uv^T is {u * v.transpose()}")
+        print("uv^T is %s" % (u * v.transpose()))
         # Sherman Morrison
         print(f"(a + uv^T)^(-1) is {ainv.ShermanMorrison(u, v)}")
 
-    def test2():
+    def test2() -> None:
         import doctest
 
         doctest.testmod()

matrix/spiral_print.py

@@ -1,19 +1,17 @@
 """
 This program print the matrix in spiral form.
 This problem has been solved through recursive way.
-
       Matrix must satisfy below conditions
         i) matrix should be only one or two dimensional
         ii) number of column of all rows should be equal
 """
 
-from collections.abc import Iterable
 
-
+def check_matrix(matrix: list[list[int]]) -> bool:
-def check_matrix(matrix):
     # must be
-    if matrix and isinstance(matrix, Iterable):
+    matrix = list(list(row) for row in matrix)
-        if isinstance(matrix[0], Iterable):
+    if matrix and isinstance(matrix, list):
+        if isinstance(matrix[0], list):
             prev_len = 0
             for row in matrix:
                 if prev_len == 0:
@@ -29,32 +27,48 @@ def check_matrix(matrix):
     return result
 
 
-def spiralPrint(a):
+def spiral_print_clockwise(a: list[list[int]]) -> None:
+    """
+    >>> spiral_print_clockwise([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])
+    1
+    2
+    3
+    4
+    8
+    12
+    11
+    10
+    9
+    5
+    6
+    7
+    """
     if check_matrix(a) and len(a) > 0:
-        matRow = len(a)
+        a = list(list(row) for row in a)
-        if isinstance(a[0], Iterable):
+        mat_row = len(a)
-            matCol = len(a[0])
+        if isinstance(a[0], list):
+            mat_col = len(a[0])
         else:
             for dat in a:
-                print(dat),
+                print(dat)
             return
 
         # horizotal printing increasing
-        for i in range(0, matCol):
+        for i in range(0, mat_col):
-            print(a[0][i]),
+            print(a[0][i])
         # vertical printing down
-        for i in range(1, matRow):
+        for i in range(1, mat_row):
-            print(a[i][matCol - 1]),
+            print(a[i][mat_col - 1])
         # horizotal printing decreasing
-        if matRow > 1:
+        if mat_row > 1:
-            for i in range(matCol - 2, -1, -1):
+            for i in range(mat_col - 2, -1, -1):
-                print(a[matRow - 1][i]),
+                print(a[mat_row - 1][i])
         # vertical printing up
-        for i in range(matRow - 2, 0, -1):
+        for i in range(mat_row - 2, 0, -1):
-            print(a[i][0]),
+            print(a[i][0])
-        remainMat = [row[1 : matCol - 1] for row in a[1 : matRow - 1]]
+        remain_mat = [row[1 : mat_col - 1] for row in a[1 : mat_row - 1]]
-        if len(remainMat) > 0:
+        if len(remain_mat) > 0:
-            spiralPrint(remainMat)
+            spiral_print_clockwise(remain_mat)
         else:
             return
     else:
@@ -64,5 +78,5 @@ def spiralPrint(a):
 
 # driver code
 if __name__ == "__main__":
-    a = ([1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12])
+    a = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
-    spiralPrint(a)
+    spiral_print_clockwise(a)