Functions for partial factorials, factorials, binomial coeffs., & rows of Pascale's Triangle., R

Language: Layout:

#R version 3.3.2 
#
# Functions to compute partial factorials, factorials, 
#   binomial coefficients, and rows of Pascale's Triangle.
#
partfact = function(n,k) { 
  # compute the partial factorial of n to k
  p=1
  for(c in 1:k-1) { p=p*(n-c) }
  return(p)
}

fact = function(k) {
  # compute the factorial of k
  m=1
  if(k>1) { for(i in 2:k) { m=m*i } }
  return(m)
}
cat("The factorial of 5 is:\n")
fact(5)

combin = function(n,k) {
  # Compute the binary coeff. C(n,k)
  # Requires functions partfact() and fact() to be defined
  c = partfact(n,k) / fact(k);
  print(c);
}
cat("\nThe number of ways to combine 6 things taken 3 at a time:", combin(6,3))

pascale.row = function(n) {
  # Compute the Nth row of Pascale's Triangle, where n >= 0
  # Requires functions partfact() and fact() to be defined
  row = seq(0,0,length.out=n+1)
  row[1]=1
  for(i in 1:n+1) { 
    row[i] = partfact(n,i-1) / fact(i-1)
    }
  ifelse(n>0,return(row),return(1))
}
cat("\n\nRows 2-7 of Pascale's Triangle: \n")
pascale.row(2)
pascale.row(3)
pascale.row(4)
pascale.row(5)
pascale.row(6)
pascale.row(7)

[ + ] Show input
Absolute running time: 0.68 sec, cpu time: 0.78 sec, memory peak: 30 Mb, absolute service time: 0,69 sec

Functions for partial factorials, factorials, binomial coeffs., & rows...