I have a set of concrete steps. Each step has a height. I record the height of each stair, from first to last, bottom to top, as a list of heights: [1.3, 2, 3.5, 4.2]. There is an implicit first height, the height of the ground, which is zero.
The difference in height between any two steps may not be the same. This is a tripping hazard. I wish to adjust the steps so that the height increase between any two steps is uniform, within an acceptable tolerance, q (example: 0.2).
Adding concrete is time-consuming on a per-step basis, but concrete is cheap, so it doesn't matter how much height I add to any one step, only how many steps I raise. I can't subtract height from any steps. Neither the ground nor the the landing (the final listed height) may be raised.
What is the minimum number of steps that can be added to such that the height gain from any one step to the next is within the tolerance, q?