# Unit 4: Programming Fundamentals (MT234) ## Data Frames - A **data frame** is a table whose columns are vectors of equal length but possibly different types: `df <- data.frame(name = c("A","B"), marks = c(80, 75))`. - Access: `df$marks`, `df[, 2]`, `df[1, ]`, `df[df$marks > 76, ]`, `df[["marks"]]`. - Functions: `nrow()`, `ncol()`, `names()`, `str()`, `summary()`, `head()`, `tail()`, `rbind()` for new rows, `cbind()` or `df$new <- ...` for new columns, `subset()`, `merge()`, `order()` for sorting. - Import with `read.csv()`; `attach(df)` lets column names be used directly (use with care). - Column statistics: `mean(df$marks)`, `sapply(df, mean)`, `tapply(df$marks, df$group, mean)`. ## Creating Functions - Syntax: `name <- function(arg1, arg2 = default) { body; return(value) }`; the last evaluated expression is returned automatically. - Example: `area <- function(r) { pi * r^2 }`; call `area(3)`. - Arguments can have defaults and be matched by name or position. - Variables created inside a function are **local**; functions help avoid repeated code and can return a list for several results. - Example: `se <- function(x) sd(x)/sqrt(length(x))`. ## Logical Operators and Conditional Statements - **Logical operators**: `&`, `|`, `!` (vectorised) and `&&`, `||` (single, short-circuit); comparisons `==`, `!=`, `<`, `>`. - **if**: `if (cond) { ... }`. - **if ... else**: `if (cond) { ... } else { ... }` (the `else` must sit on the same line as the closing brace of `if`). - **else if** chain: `if (x > 0) {...} else if (x < 0) {...} else {...}`. - Vectorised version: `ifelse(test, yes, no)`. - Example: classify marks: `if (m >= 40) "Pass" else "Fail"`. ## Loops - **for** loop: `for (i in 1:5) { print(i^2) }`; loops over elements of any vector or list. - **while** loop: repeats while the condition is `TRUE`: `i <- 1; while (i <= 5) { print(i); i <- i + 1 }`. - **repeat** loop: infinite loop exited by `break`: `repeat { ...; if (cond) break }`. - Control: `break` terminates the loop; `next` skips to the next iteration. - Examples: sum of the first $n$ integers with `s <- 0; for (i in 1:n) s <- s + i`; factorial; Fibonacci numbers. - Where possible vectorised operations (`sum(1:n)`, `cumsum`) or `apply` family are faster than explicit loops. ## Likely Exam Questions 1. What is a data frame? How does it differ from a matrix? (2 marks) 2. Write the syntax for defining a function in R. (2 marks) 3. Write an `if ... else` statement to test if a number is even. (2 marks) 4. Explain how to create, access and modify a data frame. (long) 5. Write R code to compute the factorial of $n$ using a `for` loop and using a `while` loop. (long) 6. Explain `for`, `while` and `repeat` loops with `break` and `next`. (long)