Pascal's Triangle

Creates a jagged 2d list of Pascal's Triangle.

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let pascal rows = // Create pascal's triangle as a jagged 2d list
  let pascalRow row = //Calculates a row of the triangle
    List.init (row + 1) (fun i -> i) //Create list of which the element values are the index
    |> List.scan (fun prev index -> //prev = previous element of this row, index=current element number of row
      if index = 0 then //Special case for the 1st element
        1
      else //Calculate the element at this index based on the previous value
        prev * (row + 1 - index)/index) 1
    |> List.tail //Remove the collected value to obtain the row
  List.init rows pascalRow // Create a new array of pascal row

pascal 3 //Four rows of Pascal's triangle, including row 0,1,2
// [[1]; [1; 1]; [1; 2; 1]]

val pascal : rows:int -> int list list

Full name: Script.pascal

val rows : int

val pascalRow : (int -> int list)

val row : int

Multiple items
module List

from Microsoft.FSharp.Collections

--------------------
type List<'T> =
  | ( [] )
  | ( :: ) of Head: 'T * Tail: 'T list
  interface IEnumerable
  interface IEnumerable<'T>
  member GetSlice : startIndex:int option * endIndex:int option -> 'T list
  member Head : 'T
  member IsEmpty : bool
  member Item : index:int -> 'T with get
  member Length : int
  member Tail : 'T list
  static member Cons : head:'T * tail:'T list -> 'T list
  static member Empty : 'T list

Full name: Microsoft.FSharp.Collections.List<_>

val init : length:int -> initializer:(int -> 'T) -> 'T list

Full name: Microsoft.FSharp.Collections.List.init

val i : int

val scan : folder:('State -> 'T -> 'State) -> state:'State -> list:'T list -> 'State list

Full name: Microsoft.FSharp.Collections.List.scan

val prev : int

val index : int

val tail : list:'T list -> 'T list

Full name: Microsoft.FSharp.Collections.List.tail

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More information

Link:	http://fssnip.net/7X5
Posted:	5 years ago
Author:	Kayden Tebau
Tags:	algebra , list , lists , math , pascal , triangle