Question

1206. Design Skiplist

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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

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;
      }
    }
    return false;
  }

  public void add(int num) {
    Node curr = head;
    int lv = randomLevel();
    Node node = new Node(num, lv);
    level = Math.max(level, lv);
    for (int i = level - 1; i >= 0; --i) {
      curr = findClosest(curr, i, num);
      if (i < lv) {
        node.next[i] = curr.next[i];
        curr.next[i] = node;
      }
    }
  }

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

  private Node findClosest(Node curr, int level, int target) {
    while (curr.next[level] != null && curr.next[level].val < target) {
      curr = curr.next[level];
    }
    return curr;
  }

  private static int randomLevel() {
    int level = 1;
    while (level < MAX_LEVEL && RANDOM.nextDouble() < P) {
      ++level;
    }
    return level;
  }

  static class Node {
    int val;
    Node[] next;

    Node(int val, int level) {
      this.val = val;
      next = new Node[level];
    }
  }
}

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

struct Node {
  int val;
  vector<Node*> next;
  Node(int v, int level)
    : val(v)
    , next(level, nullptr) {}
};

class Skiplist {
public:
  const int p = RAND_MAX / 4;
  const int maxLevel = 32;
  Node* head;
  int level;

  Skiplist() {
    head = new Node(-1, maxLevel);
    level = 0;
  }

  bool search(int target) {
    Node* curr = head;
    for (int i = level - 1; ~i; --i) {
      curr = findClosest(curr, i, target);
      if (curr->next[i] && curr->next[i]->val == target) return true;
    }
    return false;
  }

  void add(int num) {
    Node* curr = head;
    int lv = randomLevel();
    Node* node = new Node(num, lv);
    level = max(level, lv);
    for (int i = level - 1; ~i; --i) {
      curr = findClosest(curr, i, num);
      if (i < lv) {
        node->next[i] = curr->next[i];
        curr->next[i] = node;
      }
    }
  }

  bool erase(int num) {
    Node* curr = head;
    bool ok = false;
    for (int i = level - 1; ~i; --i) {
      curr = findClosest(curr, i, num);
      if (curr->next[i] && curr->next[i]->val == num) {
        curr->next[i] = curr->next[i]->next[i];
        ok = true;
      }
    }
    while (level > 1 && !head->next[level - 1]) --level;
    return ok;
  }

  Node* findClosest(Node* curr, int level, int target) {
    while (curr->next[level] && curr->next[level]->val < target) curr = curr->next[level];
    return curr;
  }

  int randomLevel() {
    int lv = 1;
    while (lv < maxLevel && rand() < p) ++lv;
    return lv;
  }
};

/**
 * 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);
 */

func init() { rand.Seed(time.Now().UnixNano()) }

const (
  maxLevel = 16
  p    = 0.5
)

type node struct {
  val  int
  next []*node
}

func newNode(val, level int) *node {
  return &node{
    val:  val,
    next: make([]*node, level),
  }
}

type Skiplist struct {
  head  *node
  level int
}

func Constructor() Skiplist {
  return Skiplist{
    head:  newNode(-1, maxLevel),
    level: 1,
  }
}

func (this *Skiplist) Search(target int) bool {
  p := this.head
  for i := this.level - 1; i >= 0; i-- {
    p = findClosest(p, i, target)
    if p.next[i] != nil && p.next[i].val == target {
      return true
    }
  }
  return false
}

func (this *Skiplist) Add(num int) {
  level := randomLevel()
  if level > this.level {
    this.level = level
  }
  node := newNode(num, level)
  p := this.head
  for i := this.level - 1; i >= 0; i-- {
    p = findClosest(p, i, num)
    if i < level {
      node.next[i] = p.next[i]
      p.next[i] = node
    }
  }
}

func (this *Skiplist) Erase(num int) bool {
  ok := false
  p := this.head
  for i := this.level - 1; i >= 0; i-- {
    p = findClosest(p, i, num)
    if p.next[i] != nil && p.next[i].val == num {
      p.next[i] = p.next[i].next[i]
      ok = true
    }
  }
  for this.level > 1 && this.head.next[this.level-1] == nil {
    this.level--
  }
  return ok
}

func findClosest(p *node, level, target int) *node {
  for p.next[level] != nil && p.next[level].val < target {
    p = p.next[level]
  }
  return p
}

func randomLevel() int {
  level := 1
  for level < maxLevel && rand.Float64() < p {
    level++
  }
  return level
}

/**
 * Your Skiplist object will be instantiated and called as such:
 * obj := Constructor();
 * param_1 := obj.Search(target);
 * obj.Add(num);
 * param_3 := obj.Erase(num);
 */