[UI] Icon arranging, sorting, lerping, moving, snapping like in iOS.

Hey developers,

I've recently got a game idea, but I got stuck at this part. I'm from Hungary, my vocabulary isn't the richest about this topic and probably that's why I couldn't find any solutions on the web.

Okay, so what's my problem. Because I can't really express my problem in words, I made a little gif about what I imagined. Basically, I want some UI image elements (icons) to arrange on only the x coordinate, lerp when changed position and snap the icons to the other icons' place. This explanation was pretty horrible, so if you can please take a look at the gif :P

I hope someone knows what script or other methods I should use to make my idea a reality.

Thank you! :)