CUNY MSDA R Bridge - Week 1 Assignment

Exercise 1

Write a loop that calculates 12-factorial.

Note: Although the problem asks specifically only for the value of 12-factorial, I’ve decided to write a slightly more generic loop in a function to pratice my R skills.

get_factorial <- function(n = 0) {
  # Ideally the code to confirm that n is an integer would go here.
  # Since it is not directly requested by the problem, assuming n is integer. 
  
  # Check that n is non-negative
  if (n < 0) return(-1)
  
  # Return 1 if n is zero
  if (n == 0) return(1)
  
  # Loop to calculate factorial
  my_factorial <- 1
  for (i in 1:n) {
    my_factorial <- my_factorial * i
  }
  return(my_factorial)
}

get_factorial(12)

## [1] 479001600

Exercise 2

Show how to create a numeric vector that contains the sequence from 20 to 50 by 5.

five_vector <- c(seq.int(20, 50, by = 5))

five_vector

## [1] 20 25 30 35 40 45 50

Note: I believe c() is unnecessary, but I do not have a feel for how explicit does one need to be in R yet.

Exercise 3

Create the function “factorial” that takes a trio of input numbers a, b, and c and solve the quadratic equation. The function should print as output the two solutions.

Quadratic equation: \(ax^2 + bx + c = 0\)

Solution: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

quadratic <- function(a, b, c) {
  # Check that the equation is quadratic.
  if (a == 0) {
    return("Equation is not quadratic")
  }
  
  delta <- (b^2 - 4 * a * c)
  if (delta > 0) {
    # Two real solutions
    solution1 <- (-b + sqrt(delta)) / (2 * a)
    solution2 <- (-b - sqrt(delta)) / (2 * a)
    return(sprintf("Equation has two real solutions: %s and %s", solution1, solution2))
  } else if (delta == 0) {
    # One real solution
    solution1 <- -b / (2 * a)
    return(sprintf("Equation has only one solution: %s", solution1))
  } else {
    # Two complex solutions
    solution1 <- complex(real = -b / (2 * a), imaginary = sqrt(-delta) / (2 * a))
    solution2 <- complex(real = -b / (2 * a), imaginary = - sqrt(-delta) / (2 * a))
    return(sprintf("Equation has two complex solutions: %s and %s", solution1, solution2))
  }
}

Example 1:

quadratic(1, -1, -2)

## [1] "Equation has two real solutions: 2 and -1"

Example 2:

quadratic(1, 2, 1)

## [1] "Equation has only one solution: -1"

Example 3:

quadratic(0, 1, 1)

## [1] "Equation is not quadratic"

Example 4:

quadratic(5, 7, -11)

## [1] "Equation has two real solutions: 0.940121946685673 and -2.34012194668567"

Example 5:

quadratic(1, 2, 2)

## [1] "Equation has two complex solutions: -1+1i and -1-1i"