Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Imperative programming (resit) / 2 / a / Solution

Track the length r of the trailing constant segment of an array, and the best length m anywhere in the processed prefix:The loop invariant is: $1\le i\le n$; r is the length of the longest constant suffix of $a[\mathrm{0..}i)$; and m is the length of the longest constant segment of an array within $a[\mathrm{0..}i)$. Initially all three lengths are one, using $n\ge 1$.

When the next entry equals its predecessor, the trailing constant segment extends by one; otherwise its new length is one. Every new plateau either was already in the old prefix or ends at the new entry, so taking the larger of the old m and the new r preserves the loop invariant. The loop variant is $n-i$, a nonnegative integer decreased by one. At termination $i=n$, soThe auxiliary space is $O(1)$, and $n=1$ correctly returns one without entering the loop.