Skip List Level-Height & Search-Cost Distribution

A skip list balances itself purely by chance: every node's height comes from a run of biased coin flips, giving a geometric distribution that makes each express lane exponentially sparser than the one below it. This lab builds a real skip list over N sorted keys, draws every node's height from that coin-flip process, and renders the resulting lane-occupancy counts as a live 3D histogram next to the theoretical curve N·p^(k−1). A second Monte Carlo control runs genuine top-down searches against the built structure and reports the measured average comparison count against Pugh's theoretical estimate log(1/p)(N)/p, so you can see the probabilistic O(log n) guarantee hold up (or wobble) as you change p and N.