1206. Design Skiplist

Description

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 is 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).

See more about Skiplist: https://en.wikipedia.org/wiki/Skip_list

Implement the Skiplist class:

• Skiplist() Initializes the object of the skiplist.
• bool search(int target) Returns true if the integer target exists in the Skiplist or false otherwise.
• void add(int num) Inserts the value num into the SkipList.
• bool erase(int num) Removes the value num from the Skiplist and returns true. If num does not exist in the Skiplist, do nothing and return false. If there exist multiple num values, removing any one of them is fine.

Note that duplicates may exist in the Skiplist, your code needs to handle this situation.

 

Example 1:

Input
["Skiplist", "add", "add", "add", "search", "add", "search", "erase", "erase", "search"]
[[], [1], [2], [3], [0], [4], [1], [0], [1], [1]]
Output
[null, null, null, null, false, null, true, false, true, false]

Explanation
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 <= 2 * 104
• At most 5 * 104 calls will be made to search, add, and erase.

Solutions

Solution 1

Python3JavaC++Go

class Node:
    __slots__ = ['val', 'next']

    def __init__(self, val: int, level: int):
        self.val = val
        self.next = [None] * level


class Skiplist:
    max_level = 32
    p = 0.25

    def __init__(self):
        self.head = Node(-1, self.max_level)
        self.level = 0

    def search(self, target: int) -> bool:
        curr = self.head
        for i in range(self.level - 1, -1, -1):
            curr = self.find_closest(curr, i, target)
            if curr.next[i] and curr.next[i].val == target:
                return True
        return False

    def add(self, num: int) -> None:
        curr = self.head
        level = self.random_level()
        node = Node(num, level)
        self.level = max(self.level, level)
        for i in range(self.level - 1, -1, -1):
            curr = self.find_closest(curr, i, num)
            if i < level:
                node.next[i] = curr.next[i]
                curr.next[i] = node

    def erase(self, num: int) -> bool:
        curr = self.head
        ok = False
        for i in range(self.level - 1, -1, -1):
            curr = self.find_closest(curr, i, num)
            if curr.next[i] and curr.next[i].val == num:
                curr.next[i] = curr.next[i].next[i]
                ok = True
        while self.level > 1 and self.head.next[self.level - 1] is None:
            self.level -= 1
        return ok

    def find_closest(self, curr: Node, level: int, target: int) -> Node:
        while curr.next[level] and curr.next[level].val < target:
            curr = curr.next[level]
        return curr

    def random_level(self) -> int:
        level = 1
        while level < self.max_level and random.random() < self.p:
            level += 1
        return level


# 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)

class Skiplist {
    private static final int MAX_LEVEL = 32;
    private static final double P = 0.25;
    private static final Random RANDOM = new Random();
    private final Node head = new Node(-1, MAX_LEVEL);
    private int level = 0;

    public Skiplist() {
    }

    public boolean search(int target) {
        Node curr = head;
        for (int i = level - 1; i >= 0; --i) {
            curr = findClosest(curr, i, target);
            if (curr.next[i] != null && curr.next[i].val == target) {
                return true;
            }
        }
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