// programming  iterative vs recursive


// use array
// use index to divide array
// an array has index [0..N], its size is N+1

ax = array 100
N = 10

// ------- sum of an array ----------

to suma x | s i =
  s = 0
  for i 0 N
    s = s + x[i]
  s

to sumrec x i =
  if i == N
    x[i]
  else
    x[i] + (sumrec x (i+1))

to testsum | i =
  for i 0 N
    ax[i] = i
  print suma ax nl
  print sumrec ax 0 nl

// -------- max of an array --------

to maxa x | i m =
  m = x[0]
  for i 1 N
    if m < x[i]
      m = x[i]
  m

to max2 a b =
  if a > b
    a
  else
    b

to maxrec x a b | c =
  if a == b              //  one item
    x[a]
  else
    c = (a + b)/2        // divide in the middle
    max2 (maxrec x a c) (maxrec x (c+1) b)

to testmax | i =
  for i 0 N
    ax[i] = i
  ax[5] = 88
  print maxa ax nl
  print maxrec ax 0 N nl

// ----- multiply by add repeat add -----------

to mul a b | i s =
  s = 0
  for i 1 b
    s = s + a
  s

to mulrec a b =
  if b == 0
    0
  else if b == 1
    a
  else 
    a + (mulrec a (b-1))

to mulreca2 a b c = {}

to mulreca a b = 
  mulreca2 a b 0

to mulreca2 a b c =
  if b == 0
    c
  else
    mulreca2 a (b-1) (c+a)

to testmul =
  print mul 5 4 nl
  print mulrec 5 4 nl
  print mulreca 5 4 nl

to main = testmul

// 19 Jan 2010