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SkipList.cs
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SkipList.cs
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using System;
using System.Collections.Generic;
using System.Linq;
namespace Algorithms.Sources.SkipLists
{
public class SkipList
{
private const int MAX_LEVELS = 32;
private readonly Node _head;
private readonly Random _random;
private int _currentMaxLevels;
private readonly int _maxLevels;
public SkipList(int maxLevels = MAX_LEVELS)
{
_maxLevels = maxLevels >= 1 && maxLevels <= MAX_LEVELS ? maxLevels : MAX_LEVELS;
_head = new Node(int.MinValue + 1, maxLevels);
_head.LevelNodes[0] = new LevelNode(_head);
_random = new Random();
_currentMaxLevels = 0;
}
public void Insert(int value)
{
var map = new Dictionary<int, int> { { 1, 1 }, { 2, 2 }, { 7, 1 }, { 9, 2 }, { 10, 3 } };
// logN operation
int nodeLevels = generateRandomLevelCount(); //map[value];
// avoid going beyond the current max levels
if (nodeLevels > _currentMaxLevels)
{
_head.LevelNodes[_currentMaxLevels] = new LevelNode(_head);
// increase the current max level
_currentMaxLevels++;
nodeLevels = _currentMaxLevels;
}
var node = new Node(value, nodeLevels);
// start scanning from the highest level accessible to this node
// need to update later on the skipped nodes for each level
// and the next for each node on each level
// we cannot do that unless we know how many level 0 nodes were actually skipped
var skippedNodesMap = new Dictionary<int, dynamic>();
var countSkippedPerLevel = new int[_currentMaxLevels];
LevelNode pointer = _head.LevelNodes[_currentMaxLevels - 1];
for (var level = _currentMaxLevels - 1; level >= 0; level--)
{
pointer = pointer.ParentNode.LevelNodes[level];
countSkippedPerLevel[level] = 0;
while (pointer.Next != null)
{
if (pointer.Next.Value > value)
{
// no need to step away, found our node
break;
}
pointer = pointer.Next;
// if we are on the highest level and moving, it means we haven't found the anchor point
if (level != _currentMaxLevels - 1)
{
countSkippedPerLevel[level] += pointer.SkippedNodes + 1;
}
}
if (level < nodeLevels)
{
// create node if needed
var levelNode = new LevelNode(node);
levelNode.Next = pointer.Next;
node.LevelNodes[level] = levelNode;
pointer.Next = levelNode;
// will have to update the skipped nodes for this node
skippedNodesMap[level] = new {
IsNew = true,
Node = levelNode
};
if (level > 0)
{
// we'll update this value later
levelNode.SkippedNodes = 0;
}
else
{
// update values for upper levels
for (int i = 1; i < _currentMaxLevels; i++)
{
dynamic toUpdate = skippedNodesMap[i];
LevelNode nodeToUpdate = toUpdate.Node;
if (toUpdate.IsNew)
{
nodeToUpdate.SkippedNodes = nodeToUpdate.ParentNode.LevelNodes[i - 1].SkippedNodes +
countSkippedPerLevel[i - 1];
if (nodeToUpdate.Next != null)
{
nodeToUpdate.Next.SkippedNodes = nodeToUpdate.Next.SkippedNodes -
nodeToUpdate.SkippedNodes;
}
}
else
{
if (nodeToUpdate.Next != null)
{
nodeToUpdate.Next.SkippedNodes += 1;
}
}
}
}
}
else
{
skippedNodesMap[level] = new
{
IsNew = false,
Node = pointer
};
}
}
}
public IEnumerable<int> GetElements()
{
// O(N) operation
LevelNode tmp = _head.LevelNodes[0].Next;
while (tmp != null)
{
yield return tmp.Value;
tmp = tmp.Next;
}
}
public bool Exists(int value)
{
// start scanning from the highest level
Node tmp = _head;
for (var level = _currentMaxLevels - 1; level >= 0; level--)
{
LevelNode pointer = tmp.LevelNodes[level];
while (pointer.Next != null)
{
if (pointer.Next.Value == value)
{
return true;
}
if (pointer.Next.Value > value)
{
// no need to step away, found our node
break;
}
pointer = pointer.Next;
}
tmp = pointer.ParentNode;
}
return false;
}
public void Remove(int value)
{
// logN operation
// find the node in the list and remove it from every level
Node tmp = _head;
for (var level = _currentMaxLevels - 1; level >= 0; level--)
{
LevelNode pointer = tmp.LevelNodes[level];
while (pointer.Next != null)
{
if (pointer.Next.Value == value)
{
pointer.Next = pointer.Next.Next;
if (pointer.Next != null
&& pointer.Next.SkippedNodes > 0)
{
pointer.Next.SkippedNodes--;
}
break;
}
if (pointer.Next.Value > value)
{
break;
}
pointer = pointer.Next;
}
tmp = pointer.ParentNode;
}
}
public int? FindClosestElement(int value)
{
if (isEmpty())
{
return null;
}
// logN operation
// start scanning from the highest level
Node tmp = _head;
for (var level = _currentMaxLevels - 1; level >= 0; level--)
{
LevelNode pointer = tmp.LevelNodes[level];
while (pointer.Next != null)
{
if (pointer.Next.Value == value)
{
return value;
}
if (pointer.Next.Value > value)
{
// no need to step away, found our node
break;
}
pointer = pointer.Next;
}
tmp = pointer.ParentNode;
if (level == 0)
{
// check whether the left or right is closer
if (pointer.Next == null)
{
return pointer.Value;
}
int left = Math.Abs(pointer.Value - value);
int right = Math.Abs(value - pointer.Next.Value);
return left <= right ?
(pointer.ParentNode == _head ? _head.LevelNodes[0].Value : pointer.Value) : pointer.Next.Value;
}
}
return _head.Value;
}
public int? FindKLargestElement(int k)
{
if (k <= 0)
{
return null;
}
// logN operation
// start scanning from the highest level
int count = 0;
Node tmp = _head;
for (var level = _currentMaxLevels - 1; level >= 0; level--)
{
LevelNode pointer = tmp.LevelNodes[level];
while (pointer.Next != null)
{
if (count + pointer.Next.SkippedNodes + 1 == k)
{
return pointer.Next.ParentNode.Value;
}
if (count + pointer.Next.SkippedNodes + 1 > k)
{
// no need to step away, found our node
break;
}
pointer = pointer.Next;
count = count + pointer.SkippedNodes + 1;
}
tmp = pointer.ParentNode;
}
return null;
}
public int CountElementsInRange(int left, int right)
{
// logN operation
if (left > right || isEmpty())
{
return 0;
}
// find the left edge (not necessarily equal to left)
// then the right edge
// can do it in one step, but when left is found, we have to go the highest level again
// it's more clear with two distinct iterations
bool leftFound = false;
Node edge = _head;
int levelFound = 0;
for (var level = _currentMaxLevels - 1; !leftFound && level >= 0; level--)
{
LevelNode pointer = edge.LevelNodes[level];
while (!leftFound && pointer.Next != null)
{
// exactly on the left edge
if (pointer.Next.Value == left)
{
levelFound = level;
leftFound = true;
}
else if (pointer.Next.Value > left)
{
if (level == 0)
{
// ok, no value equal to left in this list
// will have to settle to the closest higher value if not higher than right
if (pointer.Next.Value > right)
{
return 0;
}
leftFound = true;
}
else
{
// go down a level
break;
}
}
pointer = pointer.Next;
}
edge = pointer.ParentNode;
}
if (!leftFound)
{
return 0;
}
int count = 1;
// look for the right edge
for (var level = levelFound; level >= 0; level--)
{
LevelNode pointer = edge.LevelNodes[level];
while (pointer.Next != null)
{
// exactly on the right edge
if (pointer.Next.Value == right)
{
return count + pointer.Next.ParentNode.LevelNodes[level].SkippedNodes + 1;
}
if (pointer.Next.Value > right)
{
// try on lower levels
break;
}
count += pointer.Next.ParentNode.LevelNodes[level].SkippedNodes + 1;
pointer = pointer.Next;
}
edge = pointer.ParentNode;
}
return count;
}
public void PrintConfiguration()
{
Console.WriteLine("List configuration");
var tmp = _head.LevelNodes[0];
while (tmp.Next != null)
{
Console.WriteLine(string.Format("Value: {0}, Levels with skipped: {1}",
tmp.Next.ParentNode.Value,
string.Join(", ",
tmp.Next.ParentNode.LevelNodes.Select(x => string.Format("{0}", x.SkippedNodes)))));
tmp = tmp.Next;
}
}
private int generateRandomLevelCount()
{
// the limit for the number of levels is MAX_LEVELS
// the probability of having more than one level is 1/2
// having more than two levels is 1/4 and so on
// generate a random number to cover the probability for MAX_LEVELS
// but we should have at least one level
// so let's generate a number with at most MAX_LEVELS bits
// and choose the probability as the succession of bits of 1
// don't go beyond the limits of int
// max positive int 2^31-1
int randLimit = 2 ^ (_maxLevels > 30 ? 30 : _maxLevels);
int random = _random.Next(0, randLimit);
// count the number of 1 bits in succession
int level = 0;
for (; (random & 1) == 1; random >>= 1)
{
level++;
}
return level + 1;
}
private bool isEmpty()
{
return _currentMaxLevels == 0 || _head.LevelNodes[0] == null || _head.LevelNodes[0].Next == null;
}
}
}