Bi-increasing vector P99753

In this problem, we say that a vector with $n$ integer numbers @v[0..@$n-1$@]@ is bi-increasing if $n \ge 2$, @v[0]@ $>$ @v[@$n-1$@]@, and there exists an index $j$ between $0$ and $n-2$ such that:

• @v[0]@ $\le \ldots \le$ @v[@$j-1$@]@ $\le$ @v[@$j$@]@,

• @v[@$j+1$@]@ $\le$ @v[@$j+2$@]@ $\le \ldots \le$ @v[@$n-1$@]@.

For instance, the vector @[12, 12, 15, 20, 1, 3, 3, 5, 9]@ is bi-increasing (with $j = 3$).

Implement an efficient function

    bool search(int x, const vector<int>& v);

such that, given an integer number @x@ and a bi-increasing vector @v@, returns if @x@ is in @v@ or not. You can use and implement auxiliary functions if you need them.

Precondition

The vector @v@ is bi-increasing.

Observation

You only need to submit the required procedure; your main program will be ignored.