minimum travel from point to point with incremental steps


It’s my first time to make a question here. I have a curious problem about algorithm, in the center of Cartesian plane (0,0) I need to go to another point (x,y) but I only can use horizontaly and verticaly steps and this steps increases one by one.

For example, I need to go to (1,1) point and steps are:

  • Go to (1,0), a step of 1 unit.
  • Go to (1,-2) a step of 2 units.
  • Finally, go to (1,1) a step of 3 units.

Obviously, there are several ways to go to a point from center but the problem needs the minimal.

Are there a formula or an algorithm to answer this question? Thanks for read this and for your questions.