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R is dynamic + interpreted, so loops are slow. Vectorized operations dispatch to compiled C/Fortran. The difference can be 100-1000x.

Slow:

result <- numeric(1000000)
for (i in 1:1000000) {
    result[i] <- i * i
}

Fast:

result <- (1:1000000) ^ 2

Both produce the same vector. The vectorized version is ~50x faster.

Vectorized arithmetic — element-wise:

x <- c(1, 2, 3, 4)
y <- c(10, 20, 30, 40)
x + y      # c(11, 22, 33, 44)
x * y      # c(10, 40, 90, 160)
x > 2      # c(FALSE, FALSE, TRUE, TRUE) — also vectorized

Vectorized indexing:

v <- c(10, 20, 30, 40, 50)
v[v > 20]                   # c(30, 40, 50)
v[c(1, 3, 5)]               # c(10, 30, 50)
v[-c(1, 2)]                 # exclude first two: c(30, 40, 50)

Logical operations propagate:

ages <- c(15, 30, 50, 70)
adults <- ages >= 18 & ages < 65    # c(FALSE, TRUE, TRUE, FALSE)
ages[adults]                          # c(30, 50)

Use ifelse for vectorized if:

x <- c(-3, -1, 0, 1, 3)
ifelse(x >= 0, "non-neg", "neg")
# c("neg", "neg", "non-neg", "non-neg", "non-neg")

Recycling rule — when vectors have different lengths, R recycles the shorter:

c(1, 2, 3, 4) + c(10, 20)    # 11 22 13 24 — c(10,20) recycled

Watch out — sometimes intended, sometimes a bug.

Reduce for fold:

Reduce(`+`, 1:10)            # 55
Reduce("+", 1:10, accumulate = TRUE)
# c(1, 3, 6, 10, 15, 21, 28, 36, 45, 55) — running totals

Vectorized string functions:

x <- c("apple", "banana", "cherry")
nchar(x)                     # c(5, 6, 6)
toupper(x)                   # c("APPLE", "BANANA", "CHERRY")
paste(x, collapse = ", ")    # "apple, banana, cherry"