Solutions to Week 4 Homework

Week4Solutions.Rmd

Core Solutions

First, core solutions are provided. Then some interesting student alternative solutions are examined.

1. Write a loop that calculates 12-factorial

i <- 1
fact <- 1
MAX_FACT = 12

while (i <= MAX_FACT)
{
  fact <- i * fact
  i <- i + 1
}
fact

## [1] 479001600

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

seq(20,50,5)

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

3. Show how to take a trio of input numbers a, b, and c and implement the quadratic equation.

a <- 1
b <- -4
c <- 4

x1 <- (-1 * b + (( b ^ 2 - (4 * a * c))^.5)) / (2 * a)
x2 <- (-1 * b - (( b ^ 2 - (4 * a * c))^.5)) / (2 * a)
print(c(x1, x2))

## [1] 2 2

Alternative Solutions

Here are some interesting alternative solutions proposed by students. Some of these were improvements to my provided solutions above.

Here is Mohamed’s solution to #1. I especially like that (1) he wraps the code in a function; and (2) he tests the function with a number of values. Also, he identifies a “base R” function that does the same job, then uses this to verify his results. Nice!

i=1
myfact=1
for  (i in 1:12)
{ myfact=myfact*i
  i<-i+1}
myfact

## [1] 479001600

# Testing using the built-in factorial function
factorial(12)

## [1] 479001600

# Or as function, it can be written a below for any integer that is greater than 0

myfactorial<- function(n) {
  
  if (n<0) { print("Please enter positive values")
             return()
           }
  i=1
  myfact=1
  if (n==0) { return(myfact)}
  for  (i in 1:n)
  { myfact=myfact*i
    i<-i+1}
  return(myfact)
}

#testing 
myfactorial(12)

## [1] 479001600

myfactorial(3)

## [1] 6

myfactorial(10)

## [1] 3628800

myfactorial(5)

## [1] 120

#Testing using the built-in factorial function
factorial(12)

## [1] 479001600

For #2, Vuthy provided the same solution that I did using the seq() function; he also provided this fun, mathy alternative approach:

vec1 <- c(4:10)

#Vectorize multiplication operation
vec2 <- vec1*5
vec2

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

Here is another cool and interesting alternative solution to #2, posted by Lalani:

nvect<-20:50
print(nvect[nvect %% 5 == 0])

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

For #3, Sreejaya wrapped the code into a function. Notice how Sreejaya handles the issue that a function can return only one thing and this function needs to return two values.

quadraticfunc <-function(a,b,c)
{
x1 <- ((-b) + sqrt(b^2-(4*a*c))/2*a)
x2 <- ((-b) - sqrt(b^2-(4*a*c))/2*a)

sqrtlist <- list(sqrtlistval = c(x1, x2))
sqrtlist$sqrtlistval
}

quadraticfunc(4,9,1)

## [1]   7.124515 -25.124515

The last executable statement in the function is returned, but I would have preferred using a return statement to make it explicit:

return(sqrtlist$sqrtlistval)

There is a bigger problem, that Sreejaya didn’t catch, and I didn’t catch when I graded it!
What happens when we pass the function instead quadraticfunc(1,-4,4). That is, (x-2)*(x-2)?

The lesson learned here is that its important to always test our code against known results.

Here is Yee’s solution to #3, where he adds support for complex roots.

a <- 1
b <- 6
c <- 87

x<-0
input<-c(a,b,c)

if ((input[2]^2-4*input[1]*input[3])>0) {
  x[1] <- (-input[2]+(input[2]^2-4*input[1]*input[3])^0.5)/(2*input[1])
  x[2] <- (-input[2]-(input[2]^2-4*input[1]*input[3])^0.5)/(2*input[1])
} else {
  x[1] <- complex(real=-input[2]/(2*input[1]),imaginary=(abs(input[2]^2-4*input[1]*input[3])^0.5)/(2*input[1]))
  x[2] <- complex(real=-input[2]/(2*input[1]),imaginary=-(abs(input[2]^2-4*input[1]*input[3])^0.5)/(2*input[1]))
}
  
print(paste0("First Root is ", x[1]))

## [1] "First Root is -3+8.83176086632785i"

print(paste0("Second Root is ", x[2]))

## [1] "Second Root is -3-8.83176086632785i"

To consider: how would you wrap Yee’s code in a function?

And finally, Vuthy’s answer to #3 doesn’t handle complex roots, but does provide graceful error handling:

quadratic_formula <- function(a,b,c) {
  
  if((b^2)-(4*a*c)>=0)
  {
    q_p_x <-((-1*b)+sqrt((b^2)-(4*a*c)))/(2*a)
    q_n_x <- ((-1*b)-sqrt((b^2)-(4*a*c)))/(2*a)
    quadratic <- c(q_p_x, q_n_x)
    quadratic
  }
  else cat("Can't Compute the Sqrt of a negative number")
}

quadratic_formula(1, -3, -4)

## [1]  4 -1

quadratic_formula(1, 3, 4)

## Can't Compute the Sqrt of a negative number