############################################################################
#
#       File:     pascltri.icn
#
#       Subject:  Procedure to compute a row of Pascal's Triangle
#
#       Author:   Erik Eid
#
#       Date:     August 7, 1997
#
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#
#   This file is in the public domain.
#
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#
#     The procedure, when invoked by a call to PascalsTriangle(n), returns
# the nth row of Pascal's Triangle in list form.  Pascal's Triangle is a
# mathematical structure in which each element of a row is the sum of the
# two elements directly above it.  The first few levels are:
# 
#    Row 1:          1           Triangle stored as: [[1],
#        2:        1   1                              [1, 1],
#        3:      1   2   1                            [1, 2, 1],
#        4:    1   3   3   1                          [1, 3, 3, 1],
#        5:  1   4   6   4   1                        [1, 4, 6, 4, 1]]
#
# For example, PascalsTriangle(4) would return the list [1, 3, 3, 1].
#
#     The procedure fails if n is not an integer or if it is less than one.
#
############################################################################

procedure PascalsTriangle(level)	#: Pascal triangle row
static tri
local row, elem, temp
initial tri := [[1], [1, 1]]               # Start with first two rows stored
  if not (level = integer(level)) then fail
  if level < 1 then fail
  if level > *tri then                     # If we haven't calculated this
                                           # row before, then do so and keep
                                           # it statically to prevent having
                                           # to do so again.
    every row := *tri+1 to level do {
      temp := [1]                          # First element of any row is 1.
      every elem := 2 to row-1 do          # Each of the next elements is
        put (temp, tri[row-1][elem-1] +    # the sum of the two above it.
             tri[row-1][elem])
      put (temp, 1)                        # Last element of any row is 1.
      put (tri, temp)                      # Attach this row to the triangle.
    }
  return tri[level]                        # Return the chosen level.
end