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Modified 'pascal_triangle.py' program (#7901)
* Added pascals_triangle.py program to maths directory * Deleted 'pascals_triangle.py' because of duplication. Added a optimized function to generate pascal's triangle to 'pascal_triangle.py' program. Added some aadditional doctests to the existing function. Added some type check functionality to the existing function. * Modified type check hints in 'generate_pascal_triangle_optimized' function' q * Modified 'pascal_triangle' prgram * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update pascal_triangle.py Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
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@ -1,13 +1,10 @@
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"""
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This implementation demonstrates how to generate the
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elements of a Pascal's triangle. The element having
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a row index of r and column index of c can be derived
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as follows:
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This implementation demonstrates how to generate the elements of a Pascal's triangle.
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The element havingva row index of r and column index of c can be derivedvas follows:
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triangle[r][c] = triangle[r-1][c-1]+triangle[r-1][c]
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What is Pascal's triangle?
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- It is a triangular array containing binomial coefficients.
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Refer to (https://en.wikipedia.org/wiki/Pascal%27s_triangle)
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for more info about this triangle.
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A Pascal's triangle is a triangular array containing binomial coefficients.
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https://en.wikipedia.org/wiki/Pascal%27s_triangle
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"""
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@ -38,6 +35,8 @@ def print_pascal_triangle(num_rows: int) -> None:
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def generate_pascal_triangle(num_rows: int) -> list[list[int]]:
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"""
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Create Pascal's triangle for different number of rows
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>>> generate_pascal_triangle(0)
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[]
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>>> generate_pascal_triangle(1)
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[[1]]
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>>> generate_pascal_triangle(2)
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@ -48,7 +47,26 @@ def generate_pascal_triangle(num_rows: int) -> list[list[int]]:
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[[1], [1, 1], [1, 2, 1], [1, 3, 3, 1]]
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>>> generate_pascal_triangle(5)
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[[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1]]
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>>> generate_pascal_triangle(-5)
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Traceback (most recent call last):
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...
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ValueError: The input value of 'num_rows' should be greater than or equal to 0
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>>> generate_pascal_triangle(7.89)
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Traceback (most recent call last):
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...
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TypeError: The input value of 'num_rows' should be 'int'
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"""
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if not isinstance(num_rows, int):
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raise TypeError("The input value of 'num_rows' should be 'int'")
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if num_rows == 0:
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return []
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elif num_rows < 0:
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raise ValueError(
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"The input value of 'num_rows' should be greater than or equal to 0"
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)
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triangle: list[list[int]] = []
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for current_row_idx in range(num_rows):
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current_row = populate_current_row(triangle, current_row_idx)
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@ -90,7 +108,82 @@ def calculate_current_element(
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current_row[current_col_idx] = above_to_left_elt + above_to_right_elt
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def generate_pascal_triangle_optimized(num_rows: int) -> list[list[int]]:
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"""
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This function returns a matrix representing the corresponding pascal's triangle
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according to the given input of number of rows of Pascal's triangle to be generated.
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It reduces the operations done to generate a row by half
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by eliminating redundant calculations.
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:param num_rows: Integer specifying the number of rows in the Pascal's triangle
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:return: 2-D List (matrix) representing the Pascal's triangle
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Return the Pascal's triangle of given rows
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>>> generate_pascal_triangle_optimized(3)
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[[1], [1, 1], [1, 2, 1]]
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>>> generate_pascal_triangle_optimized(1)
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[[1]]
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>>> generate_pascal_triangle_optimized(0)
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[]
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>>> generate_pascal_triangle_optimized(-5)
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Traceback (most recent call last):
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...
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ValueError: The input value of 'num_rows' should be greater than or equal to 0
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>>> generate_pascal_triangle_optimized(7.89)
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Traceback (most recent call last):
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...
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TypeError: The input value of 'num_rows' should be 'int'
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"""
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if not isinstance(num_rows, int):
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raise TypeError("The input value of 'num_rows' should be 'int'")
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if num_rows == 0:
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return []
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elif num_rows < 0:
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raise ValueError(
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"The input value of 'num_rows' should be greater than or equal to 0"
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)
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result: list[list[int]] = [[1]]
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for row_index in range(1, num_rows):
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temp_row = [0] + result[-1] + [0]
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row_length = row_index + 1
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# Calculate the number of distinct elements in a row
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distinct_elements = sum(divmod(row_length, 2))
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row_first_half = [
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temp_row[i - 1] + temp_row[i] for i in range(1, distinct_elements + 1)
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]
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row_second_half = row_first_half[: (row_index + 1) // 2]
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row_second_half.reverse()
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row = row_first_half + row_second_half
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result.append(row)
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return result
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def benchmark() -> None:
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"""
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Benchmark multiple functions, with three different length int values.
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"""
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from collections.abc import Callable
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from timeit import timeit
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def benchmark_a_function(func: Callable, value: int) -> None:
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call = f"{func.__name__}({value})"
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timing = timeit(f"__main__.{call}", setup="import __main__")
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# print(f"{call:38} = {func(value)} -- {timing:.4f} seconds")
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print(f"{call:38} -- {timing:.4f} seconds")
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for value in range(15): # (1, 7, 14):
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for func in (generate_pascal_triangle, generate_pascal_triangle_optimized):
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benchmark_a_function(func, value)
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print()
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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benchmark()
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