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 ≥ 2, v[0] > v[n−1], and there exists an index j between 0 and n−2 such that:

• v[0] ≤ … ≤ v[j−1] ≤ v[j],
• v[j+1] ≤ v[j+2] ≤ … ≤ 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

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.