花花酱 LeetCode 1206. Design Skiplist

zxi — Fri, 06 Nov 2020 21:19:24 +0000

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.

Solution:

C++

// Author: Huahua
class Skiplist {
public:
  Skiplist() { head_ = make_shared(); }

  bool search(int target) {
    for (auto node = head_; node; node = node->down) {
      while (node->next && node->next->val < target)
        node = node->next;
      if (node->next && node->next->val == target)
        return true;
    }
    return false;
  }

  void add(int num) {
    stack> s;
    shared_ptr down;
    bool insert = true;
    
    for (auto node = head_; node; node = node->down) {
      while (node->next && node->next->val < num)
        node = node->next;
      s.push(node);
    }
    
    while (!s.empty() && insert) {
      auto cur = s.top(); s.pop();
      cur->next = make_shared(num, cur->next, down);
      down = cur->next;
      insert = rand() & 1; // 50% chance
    }
    
    if (insert) // create a new layer.
      head_ = make_shared(-1, nullptr, head_);
  }

  bool erase(int num) {
    bool found = false;
    for (auto node = head_; node; node = node->down) {
      while (node->next && node->next->val < num)
        node = node->next;
      if (node->next && node->next->val == num) {
        found = true;
        node->next = node->next->next;
      }
    }
    return found;
  }
private:
  struct Node {
    Node(int val = -1, 
         shared_ptr next = nullptr, 
         shared_ptr down = nullptr): 
          val(val), next(next), down(down) {}
    int val;
    shared_ptr next;
    shared_ptr down;
  };
  
  shared_ptr head_;
};

/**
 * Your Skiplist object will be instantiated and called as such:
 * Skiplist* obj = new Skiplist();
 * bool param_1 = obj->search(target);
 * obj->add(num);
 * bool param_3 = obj->erase(num);
 */

Python3

import random

class Node:
  def __init__(self, val=-1, right=None, down=None):
    self.val = val
    self.right = right
    self.down = down
    
class Skiplist:
  def __init__(self):
    self.head = Node() # Dummy head

  def search(self, target: int) -> bool:
    node = self.head
    while node:
      # Move to the right in the current level
      while node.right and node.right.val < target:
        node = node.right
      if node.right and node.right.val == target:
        return True
      # Move to the the next level
      node = node.down
    return False

  def add(self, num: int) -> None:
    nodes = []
    node = self.head
    while node:
      # Move to the right in the current level
      while node.right and node.right.val < num:
        node = node.right
      nodes.append(node)
      # Move to the next level
      node = node.down
    
    insert = True
    down = None
    while insert and nodes:
      node = nodes.pop()
      node.right = Node(num, node.right, down)
      down = node.right
      insert = (random.getrandbits(1) == 0)      
    
    # Create a new level with a dummy head.
    # right = None
    # down = current head
    if insert:
      self.head = Node(-1, None, self.head)

  def erase(self, num: int) -> bool:
    node = self.head
    found = False
    while node:
      # Move to the right in the current level
      while node.right and node.right.val < num:
        node = node.right
      # Find the target node
      if node.right and node.right.val == num:
        # Delete by skipping
        node.right = node.right.right
        found = True
      # Move to the next level
      node = node.down      
    return found
        
# 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)

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花花酱 LeetCode 1206. Design Skiplist

Solution:

C++

Python3