Threaded Mode | Linear Mode

Gerald H · (This post was last modified: 06-15-2017 01:40 PM by Gene.)

For stack

N
M

both positive integers the programme returns the number of partitions of N into at most M parts.

For more info see

https://en.wikipedia.org/wiki/Partition_(number_theory)

eg For input

30
19

the programme returns

5465

in 3.9 seconds.

Code:

::

  CK2&Dispatch

  2REAL

  ::

    COERCE2

    2DUP

    #*

    #0=

    case2drop

    BINT0

    '

    ::

      DUP#1=

      3PICK

      #1=

      OR

      case2drop

      BINT1

      2DUP

      #<

      casedrop

      ::

        DUP

        1GETLAM

        EVAL

      ;

      OVER

      #=casedrop

      ::

        DUP#1-

        1GETLAM

        EVAL

        #1+

      ;

      2DUP

      #-OVER

      1GETLAM

      EVAL

      3UNROLL

      #1-

      1GETLAM

      EVAL

      #+

    ;

    DUP1LAMBIND

    EVAL

    ABND

    FPTR2 ^#>Z

  ;

;