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skiplist.pyx
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skiplist.pyx
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# Cython version of IndexableSkiplist, for implementing moving median
# with O(log n) updates
# Original author: Raymond Hettinger
# Original license: MIT
# Link: http://code.activestate.com/recipes/576930/
# Cython version: Wes McKinney
from random import random
from libc.math cimport log
import numpy as np
# MSVC does not have log2!
cdef double Log2(double x):
return log(x) / log(2.)
# TODO: optimize this, make less messy
cdef class Node:
# cdef public:
# double value
# list next
# list width
def __init__(self, double value, list next, list width):
self.value = value
self.next = next
self.width = width
# Singleton terminator node
NIL = Node(np.inf, [], [])
cdef class IndexableSkiplist:
"""
Sorted collection supporting O(lg n) insertion, removal, and
lookup by rank.
"""
# cdef:
# Py_ssize_t size, maxlevels
# Node head
def __init__(self, expected_size=100):
self.size = 0
self.maxlevels = int(1 + Log2(expected_size))
self.head = Node(np.NaN, [NIL] * self.maxlevels, [1] * self.maxlevels)
def __len__(self):
return self.size
def __getitem__(self, i):
return self.get(i)
cpdef get(self, Py_ssize_t i):
cdef:
Py_ssize_t level
Node node
node = self.head
i += 1
for level in range(self.maxlevels - 1, -1, -1):
while node.width[level] <= i:
i -= node.width[level]
node = node.next[level]
return node.value
cpdef insert(self, double value):
cdef:
Py_ssize_t level, steps, d
Node node, prevnode, newnode, next_at_level, tmp
list chain, steps_at_level
# find first node on each level where node.next[levels].value > value
chain = [None] * self.maxlevels
steps_at_level = [0] * self.maxlevels
node = self.head
for level in range(self.maxlevels - 1, -1, -1):
next_at_level = node.next[level]
while next_at_level.value <= value:
steps_at_level[level] = (steps_at_level[level] +
node.width[level])
node = next_at_level
next_at_level = node.next[level]
chain[level] = node
# insert a link to the newnode at each level
d = min(self.maxlevels, 1 - int(Log2(random())))
newnode = Node(value, [None] * d, [None] * d)
steps = 0
for level in range(d):
prevnode = chain[level]
newnode.next[level] = prevnode.next[level]
prevnode.next[level] = newnode
newnode.width[level] = (prevnode.width[level] - steps)
prevnode.width[level] = steps + 1
steps += steps_at_level[level]
for level in range(d, self.maxlevels):
(<Node>chain[level]).width[level] += 1
self.size += 1
cpdef remove(self, double value):
cdef:
Py_ssize_t level, d
Node node, prevnode, tmpnode, next_at_level
list chain
# find first node on each level where node.next[levels].value >= value
chain = [None] * self.maxlevels
node = self.head
for level in range(self.maxlevels - 1, -1, -1):
next_at_level = node.next[level]
while next_at_level.value < value:
node = next_at_level
next_at_level = node.next[level]
chain[level] = node
if value != (<Node>(<Node>(<Node>chain[0]).next)[0]).value:
raise KeyError('Not Found')
# remove one link at each level
d = len((<Node>(<Node>(<Node>chain[0]).next)[0]).next)
for level in range(d):
prevnode = chain[level]
tmpnode = prevnode.next[level]
prevnode.width[level] += tmpnode.width[level] - 1
prevnode.next[level] = tmpnode.next[level]
for level in range(d, self.maxlevels):
tmpnode = chain[level]
tmpnode.width[level] -= 1
self.size -= 1