1206. Design Skiplist.md

1206. Design Skiplist.md Hard

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Share 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

# suppose theres n node, each node present for one number. each node has a list of l levels, the member is the next node in the same level

# node   1 2 3 4 5 6 7
# lv3 -inf 1   4
# lv2 -inf 1   4   8
# lv1	-inf 1 3 4 5 8 11
#  example: node2: [node4(next in lvl), node4(next in lv2), node3(next in lv3)]
class Node:
    __slots__ = 'val', 'nodes'
    def __init__(self, val, nLayer):
        self.val = val
        self.nodes = [None] * nLayer

class Skiplist:
    def __init__(self):
        self.nLayer = 16
        self.head = Node(-float('inf'), self.nLayer)
        
    def iterLvNode(self, target):
        pre = self.head
        for l in range(self.nLayer-1, -1, -1):
            cur = pre.nodes[l]
            while cur:
                if cur.val < target:
                    pre = cur
                    cur = cur.nodes[l]
                else:
                    break
            yield pre, l
                       
    def search(self, target: int) -> bool:
        for node, l in self.iterLvNode(target):
            if node.nodes[l] and node.nodes[l].val == target:
                return True
        return False

    def add(self, num: int) -> None:
        # finalLv = min(15, int(math.log2(1.0 / random.random())))
        finalLv = 0
        for i in range(self.nLayer):
            if random.random() < 0.5:
                break
            else:
                finalLv += 1
        new = Node(num, finalLv+1)
        for pre, l in self.iterLvNode(num):
            if l <= finalLv:
                cur = pre.nodes[l]
                pre.nodes[l] = new
                new.nodes[l] = cur

    def erase(self, num: int) -> bool:
        ret = False
        for pre, l in self.iterLvNode(num):
            cur = pre.nodes[l]
            if cur and cur.val == num:
                ret = True
                nxt = cur.nodes[l]
                pre.nodes[l] = nxt
                # del cur
        return ret


# Your Skiplist object will be instantiated and called as such:
# obj = Skiplist()
# param_1 = obj.search(target)
# obj.add(num)
# param_3 = obj.erase(num)