Step by Step solution about How to resolve the algorithm 9 billion names of God the integer step by step in the Haskell programming language

Haskell Code Overview:

This Haskell code defines functions for generating a set of triangular matrix rows, accumulating them into a cumulative matrix (cumu), and calculating the sum of the elements along the main diagonal of the matrix.

Creating Triangular Matrix Rows (rows Function):

• The rows function uses the mapAccumL function to generate a list of triangular matrix rows.
• It accumulates the rows in the list, starting with an empty list.
• The accumulator function f takes two arguments: the current row (row) and the accumulated rows (r).
• It generates a new row new_row by taking the heads of the accumulated rows.
• It also generates a list rr by removing the heads from the accumulated rows.
• The tailKeepOne function is used to remove the first element from a list, or to keep the entire list if it has only one element.

Creating Cumulative Matrix (cumu Function):

• The cumu function creates a cumulative matrix by applying the scanl function to the rows matrix.
• scanl accumulates the elements of the rows matrix using the addition operator, starting with an initial value of 0.

Calculating Diagonal Sums (sums Function):

• The sums function calculates the sum of the elements along the main diagonal of the cumulative matrix.
• It accesses the appropriate element of the cumulative matrix using the index n.
• An alternative, but faster, implementation is provided as a comment.

Main Function:

• The main function:
  • Prints the first 10 rows of the triangular matrix.
  • Prints the sums of the main diagonal elements for specific values of n.

import Data.List (mapAccumL)

cumu :: [[Integer]]
cumu = [1] : map (scanl (+) 0) rows

rows :: [[Integer]]
rows = snd $ mapAccumL f [] cumu where
    f r row = (rr, new_row) where
        new_row = map head rr
        rr = map tailKeepOne (row:r)
    tailKeepOne [x] = [x]
    tailKeepOne (_:xs) = xs

sums n = cumu !! n !! n
--curiously, the following seems to be faster
--sums = sum . (rows!!)

main :: IO ()
main = do
    mapM_ print $ take 10 rows
    mapM_ (print.sums) [23, 123, 1234, 12345]