0x00-pascal_triangle

0x00. Pascal's Triangle

Algorithm Python

Pascal Triangle

Pascal's triangle is a triangular array of numbers where each number is the sum of the two numbers directly above it. The first and last numbers in each row are always 1.

Problem Statement

Create a function def pascal_triangle(n): that returns a list of lists of integers representing the Pascal’s triangle of n:

Returns an empty list if n <= 0
You can assume n will be always an integer

Solution Overview

The pascal_triangle function generates Pascal's triangle with n rows. This function takes an integer n as input and return a list of lists of integers representing Pascal's triangle.

Algorithm Explanation

1. Base Case Handling:

   • if n is less then or equal to 0, the function returns an empty list, as Pascal's triangle cannot have negative or zero rows.

2. Constructing the Triangle:

   • Initialize the triangle list with the top row [1].
   • For each row from the second row to the nth row:
     • Start building the row with [1].
     • Iterate over each element in the current row, expect the first and last elements.
       • Obtain the diagonal values from the row directly above.
       • Sum the diagonal values to get the current element.
       • Append the sum to the current row.
     • End the with 1.
     • Append the completed row to the triangle list.

Logic Breakdown:

• The inner loop iterates over each element in a row, except the first and last elements, to calculate the values based on the sum of the diagonal elements from the row above.
• The diagonal elements to the left (diagonal_left) and right (diagonal_right) of the current position are obtained from the previous row.
• These diagonal elements are summed to compute the value of the current position.
• The resulting row is then appended to the triangle list.

Example Usage

triangle = pascal_triangle(5)
print(triangle)

This will generate and Print Pascal's triangle with 5 rows [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1]]