Implemented a Pascal triangle generator (#7317)

* Added a Pascal triangle implementation to the other folder

* Added Pascal triangle implementation to the other folder.

* Added Pascal triangle implementation to the other folder.

* Added Pascal triangle implementation to the other folder.

* Implemented a Pascal triangle generator.

* Reversed Changes to DIRECTORY.md

* Reversed changed to .md files

* Update other/pascal_triangle.py

Removed personal info

Co-authored-by: Paul <56065602+ZeroDayOwl@users.noreply.github.com>

* Update pascal_triangle.py

Expanded the description of the algorithm

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

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

* Printed output in triangular form

* Update CONTRIBUTING.md

Co-authored-by: Paul <56065602+ZeroDayOwl@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

other/pascal_triangle.py

@@ -0,0 +1,96 @@
+"""
+This implementation demonstrates how to generate the
+elements of a Pascal's triangle. The element having
+a row index of r and column index of c can be derived
+as follows:
+triangle[r][c] = triangle[r-1][c-1]+triangle[r-1][c]
+What is Pascal's triangle?
+- It is a triangular array containing binomial coefficients.
+Refer to (https://en.wikipedia.org/wiki/Pascal%27s_triangle)
+for more info about this triangle.
+"""
+
+
+def 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
+    """
+    triangle = generate_pascal_triangle(num_rows)
+    for row_idx in range(num_rows):
+        # Print left spaces
+        for _ in range(num_rows - row_idx - 1):
+            print(end=" ")
+        # Print row values
+        for col_idx in range(row_idx + 1):
+            if col_idx != row_idx:
+                print(triangle[row_idx][col_idx], end=" ")
+            else:
+                print(triangle[row_idx][col_idx], end="")
+        print()
+
+
+def generate_pascal_triangle(num_rows: int) -> list[list[int]]:
+    """
+    Create Pascal's triangle for different number of rows
+    >>> 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]]
+    """
+    triangle: list[list[int]] = []
+    for current_row_idx in range(num_rows):
+        current_row = populate_current_row(triangle, current_row_idx)
+        triangle.append(current_row)
+    return triangle
+
+
+def populate_current_row(triangle: list[list[int]], current_row_idx: int) -> list[int]:
+    """
+    >>> triangle = [[1]]
+    >>> populate_current_row(triangle, 1)
+    [1, 1]
+    """
+    current_row = [-1] * (current_row_idx + 1)
+    # first and last elements of current row are equal to 1
+    current_row[0], current_row[-1] = 1, 1
+    for current_col_idx in range(1, current_row_idx):
+        calculate_current_element(
+            triangle, current_row, current_row_idx, current_col_idx
+        )
+    return current_row
+
+
+def 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]
+    """
+    above_to_left_elt = triangle[current_row_idx - 1][current_col_idx - 1]
+    above_to_right_elt = triangle[current_row_idx - 1][current_col_idx]
+    current_row[current_col_idx] = above_to_left_elt + above_to_right_elt
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()