Let L be the doubly linked list with values [10, 20, 30, 40, 50], and let I be a…

Let \(L\) be the doubly linked list with values \([10, 20, 30, 40, 50]\), and let \(I\) be a bidirectional iterator currently at 30 (so `DEREF(I) = 30`). Iterators support `ADVANCE` (forward one), `RETREAT` (backward one), `DEREF`, and the list supports `INSERT-BEFORE(I, x)` and `DELETE-AT(I)`. Adopt the following validity rules: `INSERT-BEFORE` does not invalidate \(I\) and leaves \(I\) at the same element as before; `DELETE-AT(I)` invalidates \(I\) and no other iterator, and returns an iterator to the former successor (or past-the-end if \(I\) was last). Trace the following program. After each numbered line, write the list contents and the value of `DEREF` at each currently valid iterator named below, or write “invalid” or “past-the-end”. ``` I ← iterator at 30 J ← BEGIN(L) // at 10 K ← END(L) // past-the-end 1 INSERT-BEFORE(I, 25) 2 ADVANCE(I) 3 DELETE-AT(J) 4 RETREAT(I) 5 INSERT-BEFORE(K, 60) 6 M ← DELETE-AT(I) 7 ADVANCE(M) ```

`INSERT-BEFORE` never invalidates its argument iterator; `DELETE-AT` invalidates only its argument and hands back the successor.