human
I found an interesting problem on https://leetcode.com/problems/design-skiplist/:
Design a Skiplist without using any built-in libraries.
A Skiplist is a data structure that takes O(log(n)) time to add, erase and search. Comparing with treap and red-black tree which has the same function and performance, the code length of Skiplist can be comparatively short and the idea behind Skiplists are just simple linked lists.
For example: we have a Skiplist containing [30,40,50,60,70,90] and we want to add 80 and 45 into it. The Skiplist works this way:

Artyom Kalinin [CC BY-SA 3.0], via Wikimedia Commons
You can see there are many layers in the Skiplist. Each layer is a sorted linked list. With the help of the top layers, add , erase and search can be faster than O(n). It can be proven that the average time complexity for each operation is O(log(n)) and space complexity is O(n).
To be specific, your design should include these functions:

bool search(int target) : Return whether the target exists in the Skiplist or not.
void add(int num): Insert a value into the SkipList. 
bool erase(int num): Remove a value in the Skiplist. If num does not exist in the Skiplist, do nothing and return false. If there exists multiple num values, removing any one of them is fine.

See more about Skiplist : https://en.wikipedia.org/wiki/Skip_list
Note that duplicates may exist in the Skiplist, your code needs to handle this situation.
 
Example:
Skiplist skiplist = new Skiplist();

skiplist.add(1);
skiplist.add(2);
skiplist.add(3);
skiplist.search(0).
  // return false.
skiplist.add(4);
skiplist.search(1).
  // return true.
skiplist.erase(0).
   // return false, 0 is not in skiplist.
skiplist.erase(1).
   // return true.
skiplist.search(1).
  // return false, 1 has already been erased.
 
Constraints:

0 <= num, target <= 20000
At most 50000 calls will be made to search, add, and erase.

I tried it in Python, but could not do it. Can you solve it?

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What is a the Python program you requested?
assistant
#Here is the Python program you requested.

class Node:
    def __init__(self, val):
        self.val = val
        self.right, self.down = None, None
        
class Skiplist:

    def __init__(self):
        self.head = [Node(float('-inf')) for _ in range(16)]
        self.tail = [Node(float('inf')) for _ in range(16)]
        
        for h, t in zip(self.head, self.tail):
            h.right = t
            
        for up, down in zip(self.head, self.head[1:]):
            up.down = down

    def search(self, target: int) -> bool:
        current = self.head[0]
        while current:
            if current.val < target <= current.right.val:
                if current.right.val == target: return True
                current = current.down
            else:
                current = current.right
        return False
        
    def add(self, num: int) -> None:
        stack = []
        current = self.head[0]
        while current:
            if current.val < num <= current.right.val:
                stack.append(current)
                current = current.down
            else:
                current = current.right
        prev = None
        while stack:
            current = stack.pop()
            node = Node(num)
            node.right, current.right = current.right, node
            if prev: node.down = prev
            prev = node
            
            if random.randint(0, 1): break
        

    def erase(self, num: int) -> bool:
        current = self.head[0]
        is_removed = False
        while current:
            if current.val < num <= current.right.val:
                if current.right.val == num: 
                    current.right = current.right.right
                    is_removed = True
                current = current.down
            else:
                current = current.right
        return is_removed