Suppose that, instead of promoting an element from Li-1 into Li based on a coin toss, we promote it with some probability p, 0 < p < 1.
1. Show that, with this modification, the expected length of a search path is at most (1/p) log1/p n + O(1).
2. What is the value of p that minimizes the preceding expression?
3. What is the expected height of the skiplist?
4. What is the expected number of nodes in the skiplist?