R Programming

Problem Set

Q1

Write an R function print_hollow_square() to print a square pattern with * characters, but make it hollow.

• Example
  • input: 5 (size of the square)
  • output:

  *****
  *   *
  *   *
  *   *
  *****

Q1 - Solution ver1

print_hollow_square = function(size) {
  for (i in 1:size) {
    cat ("*")
  }
  cat ("\n")
  
  for (i in 2:(size-1)) {
    for (j in 1:size) {
      if (j == 1 || j == size) {
        cat("*")
      } else {
        cat(" ")
      }
    }
    cat("\n")
  }
  
  for (i in 1:size) {
    cat ("*")
  }
  cat ("\n")  
}

print_hollow_square(5)

*****
*   *
*   *
*   *
*****

Q1 - Solution ver2

print_hollow_square = function(size) {
  cat (rep("*", size), "\n", sep = "")

  for (i in 2:(size-1)) {
    for (j in 1:size) {
      if (j == 1 || j == size) {
        cat("*")
      } else {
        cat(" ")
      }
    }
    cat("\n")
  }
  
  cat (rep("*", size), "\n", sep = "")
}

print_hollow_square(5)

*****
*   *
*   *
*   *
*****

Q1 - Solution ver3

print_hollow_square = function(size) {
  for (i in 1:size) {
    for (j in 1:size) {
      if (i == 1 || i == size || j == 1 || j == size) {
        cat("*")
      } else {
        cat(" ")
      }
    }
    cat("\n")
  }
}

print_hollow_square(5)

*****
*   *
*   *
*   *
*****

Q2

Write an R function roll_dice() that simulates rolling a fair six-sided die n times, and returns the count of each face value.

• Example
  • input: 100
  • output: A named vector with counts for each face value (e.g., c('1' = 14, '2' = 19, '3' = 15, '4' = 18, '5' = 17, '6' = 17))

Q2 - Solution

roll_dice = function(n) {
  rolls = sample(1:6, n, replace = TRUE)
  table(rolls)
}
roll_dice (100)

rolls
 1  2  3  4  5  6 
18 13 19 16 19 15 

Q3

Write an R function second_largest() to find the second largest number in a vector.

• Example
  • input: c(1, 3, 4, 5, 0, 2)
  • output: 4

Q3 - Solution

second_largest = function(numbers) {
  if (length(numbers) < 2) {
    return(NULL)
  }

  sorted_numbers = sort(numbers, decreasing = TRUE)
  return(sorted_numbers[2])
}

second_largest(c(1, 3, 4, 5, 0, 2))

[1] 4

Q4

Write an R function square_or_cube() that takes a numeric vector as input and returns a new vector with the square of each number if it is even and the cube of each number if it is odd.

• Example
  • input: c(1, 2, 3, 4, 5)
  • output: c(1, 4, 27, 16, 125)

Q4 - Solution ver1

square_or_cube = function(numbers) {
  result = c()
  for (num in numbers) {
    if (num %% 2 == 0) {
      result = c(result, num^2)
    } else {
      result = c(result, num^3)
    }
  }
  return (result)
}

square_or_cube(c(1, 2, 3, 4, 5))

[1]   1   4  27  16 125

Q4 - Solution ver2

square_or_cube = function(numbers) {
  result = ifelse (numbers %% 2 == 0, numbers^2, numbers^3)
  return (result)
}

square_or_cube(c(1, 2, 3, 4, 5))

[1]   1   4  27  16 125

Q5

Write an R function is_prime_number() that takes an integer n as input and returns TRUE if n is a prime number, and FALSE otherwise. A prime number is a natural number greater than \(1\) that has no positive divisors other than \(1\) and itself.

• Example:
  • input: 7
  • output: TRUE

• Example:
  • input: 10
  • output: FALSE

Q5 - Solution ver1

is_prime_number = function(n) {
  if (n <= 1) {
    return(FALSE)
  }
  if (n == 2) {
    return(TRUE)
  }
  for (i in 2:floor(sqrt(n))) {
    if (n %% i == 0) {
      print(i)
      return(FALSE)
    }
  }
  return(TRUE)
}
is_prime_number(7)

[1] TRUE

is_prime_number(10)

[1] 2

[1] FALSE

Q5 - Solution ver2

is_prime_number = function(n) {
  if (n <= 1) {
    return(FALSE)
  }
  if (n == 2) {
    return(TRUE)
  }
  return (all(ifelse (n %% 2:floor(sqrt(n)) == 0, FALSE, TRUE)))
}
is_prime_number(7)

[1] TRUE

is_prime_number(10)

[1] FALSE

Q5 - Solution ver3

is_prime_number = function(n) {
  if (n <= 1) {
    return(FALSE)
  }
  if (n == 2) {
    return(TRUE)
  }
  return (all(n %% 2:floor(sqrt(n)) != 0))
}
is_prime_number(7)

[1] TRUE

is_prime_number(10)

[1] FALSE