Disorder Test X41326

In a strictly increasing ordered sequence of integers $x_0,\ldots,x_r$ (such as 5, 8, 12, 20 for example) each element is strictly larger than the previous one: $x_i > x_{i-1}$ for all $i > 0$, that is, $x_{i-1} - x_i < 0$.

A $k$-ordered sequence is a sequence where $x_{i-1}-x_i < k$ for all $i > 0$. Thus, a strictly increasing sequence is 0-ordered, and a sequence that is increasing but maybe not strictly (like -3, -1 -1, 4, 4, 7 for example) is 1-ordered.

Larger values of $k$ represent bounded disorder: $k$ bounds how smaller than its predecessor each element can be.

Write a function $disorder\_test(k, ls)$ that receives a nonnegative integer $k$ and a list $ls$ of integers and checks whether $ls$ is $k$-ordered, that is, returns True if $ls$ is $k$-ordered, and False otherwise.

Observation

Only the function will be evaluated. If your submission includes a main program (e.g. with testmod), it must be either commented out or inside a condition "if __name__ == ’__main__’"