Python program to print Aitken’s array

Given a number n. The task is to print the Aikten’s array upto n.

Examples:

Input: 5
Output:
[1]
[1, 2]
[2, 3, 5]
[5, 7, 10, 15]
[15, 20, 27, 37, 52]


Input: 7
Output:
[1]
[1, 2]
[2, 3, 5]
[5, 7, 10, 15]
[15, 20, 27, 37, 52]
[52, 67, 87, 114, 151, 203]
[203, 255, 322, 409, 523, 674, 877]

To print it first we follow the following steps:

• We write 1 in the first row.
• Next, we fill the leftmost value of each row by the rightmost value of the previous row.
• The next elements of each row are filled by the simple rule i.e. each element of a particular row is the sum of values to the left of that row with the values of the upper row at the same position.
  For better understanding, let’s consider the third row of the above example consisting of the elements 2, 3, 5. The leftmost value of this row is the rightmost value of the above row i.e. 2. The next value 3 is the sum of value to the left if that row (2) and the value at same position of the above row (1). Similarly, 5 is the sum of 3 and 2.

Below is the implementation.

# Python program to print
# Aitken's array


from queue import Queue
from functools import reduce, lru_cache


# for dynamic programming
# Recursive function to print the
# Aitken's array.
@lru_cache()
def rec(n):

    # Base case
    if n == 1:
        print([1])
        return [1]

    array =  [rec(n-1)[-1]]

    for k in range(n-1):
        array.append(array[k] + rec(n-1)[k])

    print(array)

    return array

# Driver's code
rec(7)

Output:

[1]
[1, 2]
[2, 3, 5]
[5, 7, 10, 15]
[15, 20, 27, 37, 52]
[52, 67, 87, 114, 151, 203]
[203, 255, 322, 409, 523, 674, 877]