SECTION 15 / 24

Unpack the other end: last and init

last returns one endpoint element; init returns all preceding elements as a list.

last(L) returns the last element. init(L) returns the list without its final position. For [3,13,23,25], last is 25 and init is [3,13,23]. These complement first and rest. On a singleton, init gives []; on an empty list the tutorial defines init as [], but last has no defined element.

For non-empty L, [first(L)] ++ rest(L) and init(L) ++ [last(L)] both rebuild L.

# For a NON-EMPTY list L:
L == [first(L)] ++ rest(L)
L == init(L) ++ [last(L)]

first and last may return complex elements too. If L is a list of pairs, first(L) is an entire pair. Wrapping it in [first(L)] makes a singleton OUTER list. Bracket levels carry meaning.

For a known non-decreasing list of numeric marks, first gives its minimum and last its maximum, so the range is last(L) − first(L). This shortcut is invalid on an arbitrary unsorted list. A short expression also does not guarantee constant-time execution: the tutorial implements last with a full foreach scan.

Try it yourself

What is init([3,13,3])?

Show explained answer

[3,13]. Only the last occurrence is dropped, even though its value also appears at the start.

Try it yourself

Can you use last(L) − first(L) to find the range of [68,42,97,62]?

Show explained answer

No. It gives 62 − 68, not the true range 97 − 42 = 55. The endpoint shortcut needs sorted order.

Try it yourself

Why are the brackets in [first(L)] needed?

Show explained answer

first(L) is an element. ++ requires list operands, so the element must be wrapped in a singleton list.

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