Question

I am facing a problem on creating pascal triangle. The code is given below. Here sumLstElts will sum the elements on a row, putBetween will put the sum at the right side of the [1]. pascal n will give us the series of pascal sequences in a row.

    sumLstElts (x:[])=[x]
    sumLstElts []=[]
    sumLstElts xs=[head xs+head(tail xs)]++sumLstElts (tail xs)

    putBetween xs'= [1]++xs''
            where xs''=sumLstElts xs'

    pascal 0=[1]
    pascal n= putBetween(pascal (n-1)) ++ pascal(n-1)

Would u pls help me to identify my error?
thnx in advance.

saugata

Answer 1

If you want just the n-th row,

pascal n= putBetween(pascal (n-1))

is the right way, putBetween already constructs the complete next row from a given. If you want to create the triangle as a list of rows, something like

pascal :: Int -> [[Integer]]
pascal n = take (n+1) $ iterate putBetween [1]

would construct the triangle starting with row 0. If you want the part of the triangle in reverse order, longer rows first,

pascal :: Int -> [[Integer]]
pascal 0 = [[1]]
pascal n = putBetween top : previous
  where
    previous = pascal (n-1)
    top = head previous

does that.

The problem with your attempt is that putBetween is applied to the entire result of pascal (n-1), which is intended to contain not only the n-1-st row, but also the previous rows. So pascal 1 gave the concatenation of the first row [1,1] with the zeroth [1], and when pascal 2 applies putBetween to that, it’s not a row of Pascal’s triangle, so the result isn’t one either. You could also get the concatenation of the rows by

pascal 0 = [1]
pascal n = putBetween (take n previous) ++ previous
  where
    previous = pascal (n-1)

but in my opinion it’s better to have the triangle as a list of rows.