matrix.pascal_triangle
======================

.. py:module:: matrix.pascal_triangle

.. autoapi-nested-parse::

   This implementation demonstrates how to generate the elements of a Pascal's triangle.
   The element havingva row index of r and column index of c can be derivedvas follows:
   triangle[r][c] = triangle[r-1][c-1]+triangle[r-1][c]

   A Pascal's triangle is a triangular array containing binomial coefficients.
   https://en.wikipedia.org/wiki/Pascal%27s_triangle



Functions
---------

.. autoapisummary::

   matrix.pascal_triangle.benchmark
   matrix.pascal_triangle.calculate_current_element
   matrix.pascal_triangle.generate_pascal_triangle
   matrix.pascal_triangle.generate_pascal_triangle_optimized
   matrix.pascal_triangle.populate_current_row
   matrix.pascal_triangle.print_pascal_triangle


Module Contents
---------------

.. py:function:: benchmark() -> None

   Benchmark multiple functions, with three different length int values.


.. py:function:: calculate_current_element(triangle: list[list[int]], current_row: list[int], current_row_idx: int, current_col_idx: int) -> None

   >>> triangle = [[1], [1, 1]]
   >>> current_row = [1, -1, 1]
   >>> calculate_current_element(triangle, current_row, 2, 1)
   >>> current_row
   [1, 2, 1]


.. py:function:: generate_pascal_triangle(num_rows: int) -> list[list[int]]

   Create Pascal's triangle for different number of rows
   >>> generate_pascal_triangle(0)
   []
   >>> generate_pascal_triangle(1)
   [[1]]
   >>> generate_pascal_triangle(2)
   [[1], [1, 1]]
   >>> generate_pascal_triangle(3)
   [[1], [1, 1], [1, 2, 1]]
   >>> generate_pascal_triangle(4)
   [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1]]
   >>> generate_pascal_triangle(5)
   [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1]]
   >>> generate_pascal_triangle(-5)
   Traceback (most recent call last):
       ...
   ValueError: The input value of 'num_rows' should be greater than or equal to 0
   >>> generate_pascal_triangle(7.89)
   Traceback (most recent call last):
       ...
   TypeError: The input value of 'num_rows' should be 'int'


.. py:function:: generate_pascal_triangle_optimized(num_rows: int) -> list[list[int]]

   This function returns a matrix representing the corresponding pascal's triangle
   according to the given input of number of rows of Pascal's triangle to be generated.
   It reduces the operations done to generate a row by half
   by eliminating redundant calculations.

   :param num_rows: Integer specifying the number of rows in the Pascal's triangle
   :return: 2-D List (matrix) representing the Pascal's triangle

   Return the Pascal's triangle of given rows
   >>> generate_pascal_triangle_optimized(3)
   [[1], [1, 1], [1, 2, 1]]
   >>> generate_pascal_triangle_optimized(1)
   [[1]]
   >>> generate_pascal_triangle_optimized(0)
   []
   >>> generate_pascal_triangle_optimized(-5)
   Traceback (most recent call last):
       ...
   ValueError: The input value of 'num_rows' should be greater than or equal to 0
   >>> generate_pascal_triangle_optimized(7.89)
   Traceback (most recent call last):
       ...
   TypeError: The input value of 'num_rows' should be 'int'


.. py:function:: populate_current_row(triangle: list[list[int]], current_row_idx: int) -> list[int]

   >>> triangle = [[1]]
   >>> populate_current_row(triangle, 1)
   [1, 1]


.. py:function:: print_pascal_triangle(num_rows: int) -> None

   Print Pascal's triangle for different number of rows
   >>> print_pascal_triangle(5)
       1
      1 1
     1 2 1
    1 3 3 1
   1 4 6 4 1