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8
data/hoehle.txt
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"Höhleneingang" <> "Ost/West-Passage"
"Höhleneingang" <> "Nord/Süd-Passage"
"Nord/Süd-Passage" <> "Nebelraum"
"Steiniger Pfad" > "Ost/West-Passage"
"Ost/West-Passage" <> "Schwefelgewölbe"
"Schwefelgewölbe" > "Steiniger Pfad"
"Schatzkammer" > "Nebelraum"
"Steiniger Pfad" > "Schatzkammer"

124
praktika/07_hashtable/praktikum.py
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import math
import unittest
from utils.literal import Literal
from utils.memory_cell import MemoryCell
from utils.memory_array import MemoryArray
from vorlesung.L07_hashtable.hashtable import HashTableOpenAddressing
#Goldener Schnitt
a = Literal((math.sqrt(5) - 1) / 2)
# Hashfunktion nach multiplikativer Methode
def h(x: MemoryCell, m: Literal) -> Literal:
with MemoryCell(int(x * a)) as integer_part, MemoryCell(x * a) as full_product:
with MemoryCell(full_product - integer_part) as fractional_part:
return Literal(abs(int(fractional_part * m)))
# Quadratische Sondierung
def f(x: MemoryCell, i: Literal, m: Literal) -> Literal:
c1 = 1
c2 = 5
with MemoryCell(h(x, m)) as initial_hash, MemoryCell(c2 * int(i) * int(i)) as quadratic_offset:
with MemoryCell(initial_hash + quadratic_offset) as probe_position:
probe_position += Literal(c1 * int(i)) # Linear component
return probe_position % m
# Symmetrische quadratische Sondierung
def fs(x: MemoryCell, i: Literal, m: Literal) -> Literal:
with MemoryCell(h(x, m)) as base_hash, MemoryCell(int(i) * int(i)) as square:
if int(i) % 2 == 0: # gerades i: Vorwärtssondierung
with MemoryCell(base_hash + square) as position:
return position % m
else: # ungerades i: Rückwärtssondierung
with MemoryCell(base_hash - square) as position:
return position % m
class TestHashTableOpenAddressing(unittest.TestCase):
def test_hash_function(self):
x = MemoryCell(22)
m = Literal(20)
self.assertEqual(11, h(x, m).value)
def test_probe_function(self):
x = MemoryCell(22)
i = Literal(0)
m = Literal(20)
self.assertEqual(11, f(x, i, m).value)
i = Literal(1)
self.assertEqual(17, f(x, i, m).value)
i = Literal(2)
self.assertEqual(13, f(x, i, m).value)
if __name__ == "__main__":
#unittest.main()
print("*** Aufgabe 3 ***")
size = Literal(20)
print(f"Anlage einer Hash-Tabelle mit offener Adressierung mit Größe {size}")
ht = HashTableOpenAddressing(size, f)
print("Einfügen der Werte aus seq0.txt")
for cell in MemoryArray.create_array_from_file("data/seq0.txt"):
if not ht.insert(cell):
print(f"Einfügen von {cell} nicht möglich")
print(ht)
print(f"Belegungsfaktor: {ht.alpha()}")
with MemoryCell(52) as cell:
print(f"Suche nach {cell}")
if ht.search(cell):
print(f"{cell} gefunden, wird gelöscht.")
ht.delete(cell)
else:
print(f"{cell} nicht gefunden")
print(ht)
print(f"Belegungsfaktor: {ht.alpha()}")
print("Einfügen von 24")
with MemoryCell(24) as cell:
if not ht.insert(cell):
print(f"Einfügen von {cell} nicht möglich")
print(ht)
print(f"Belegungsfaktor: {ht.alpha()}")
print()
print("*** Aufgabe 4 ***")
size = Literal(90)
print(f"Anlage einer Hash-Tabelle mit offener Adressierung mit Größe {size}")
ht = HashTableOpenAddressing(size, f)
print("Einfügen der Werte aus seq1.txt")
for cell in MemoryArray.create_array_from_file("data/seq1.txt"):
if not ht.insert(cell):
print(f"Einfügen von {cell} nicht möglich")
print(ht)
print(f"Belegungsfaktor: {ht.alpha()}")
print()
print("*** Aufgabe 5 ***")
size = Literal(89)
print(f"Anlage einer Hash-Tabelle mit offener Adressierung mit Größe {size}")
ht = HashTableOpenAddressing(size, f)
print("Einfügen der Werte aus seq1.txt")
for cell in MemoryArray.create_array_from_file("data/seq1.txt"):
if not ht.insert(cell):
print(f"Einfügen von {cell} nicht möglich")
print(ht)
print(f"Belegungsfaktor: {ht.alpha()}")
print()
print("*** Aufgabe 6 ***")
size = Literal(90)
print(f"Anlage einer Hash-Tabelle mit offener Adressierung mit Größe {size}")
print("Verwendung der symmetrischen quadratischen Sondierung")
ht = HashTableOpenAddressing(size, fs)
print("Einfügen der Werte aus seq1.txt")
for cell in MemoryArray.create_array_from_file("data/seq1.txt"):
if not ht.insert(cell):
print(f"Einfügen von {cell} nicht möglich")
print(ht)
print(f"Belegungsfaktor: {ht.alpha()}")
print()

0
vorlesung/L07_hashtable/__init__.py
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60
vorlesung/L07_hashtable/analyze_hashtable.py
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import math
import random
from utils.literal import Literal
from utils.memory_cell import MemoryCell
from utils.memory_array import MemoryArray
from utils.memory_manager import MemoryManager
from vorlesung.L07_hashtable.hashtable import HashTableOpenAddressing
#Goldener Schnitt
a = Literal((math.sqrt(5) - 1) / 2)
# Hashfunktion nach multiplikativer Methode
def h(x: MemoryCell, m: Literal) -> Literal:
with MemoryCell(int(x * a)) as integer_part, MemoryCell(x * a) as full_product:
with MemoryCell(full_product - integer_part) as fractional_part:
return Literal(abs(int(fractional_part * m)))
# Quadratische Sondierung
def f(x: MemoryCell, i: Literal, m: Literal) -> Literal:
c1 = 1
c2 = 5
with MemoryCell(h(x, m)) as initial_hash, MemoryCell(c2 * int(i) * int(i)) as quadratic_offset:
with MemoryCell(initial_hash + quadratic_offset) as probe_position:
probe_position += Literal(c1 * int(i)) # Linear component
return probe_position % m
# Symmetrische quadratische Sondierung
def fs(x: MemoryCell, i: Literal, m: Literal) -> Literal:
with MemoryCell(h(x, m)) as base_hash, MemoryCell(int(i) * int(i)) as square:
if int(i) % 2 == 0: # gerades i: Vorwärtssondierung
with MemoryCell(base_hash + square) as position:
return position % m
else: # ungerades i: Rückwärtssondierung
with MemoryCell(base_hash - square) as position:
return position % m
def analyze_complexity(sizes):
"""
Analysiert die Komplexität
:param sizes: Eine Liste von Eingabegrößen für die Analyse.
"""
for size in sizes:
MemoryManager.purge() # Speicher zurücksetzen
ht = HashTableOpenAddressing(size, f)
random_array = MemoryArray.create_random_array(size, -100, 100)
for cell in random_array:
ht.insert(cell)
MemoryManager.reset()
cell = random.choice(random_array.cells)
ht.search(cell)
MemoryManager.save_stats(size)
MemoryManager.plot_stats(["cells", "compares"])
if __name__ == "__main__":
sizes = range(1, 1001, 10)
analyze_complexity(sizes)

76
vorlesung/L07_hashtable/hashtable.py
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from collections.abc import Callable
from utils.literal import Literal
from utils.memory_array import MemoryArray
from utils.memory_cell import MemoryCell
from utils.memory_range import mrange
UNUSED_MARK = "UNUSED"
DELETED_MARK = "DELETED"
class HashTableOpenAddressing:
def __init__(self, m: Literal, f: Callable[[MemoryCell, Literal, Literal], Literal]):
if not isinstance(m, Literal):
m = Literal(m)
self.m = m
self.f = f
self.table = MemoryArray(m)
for i in mrange(m):
self.table[i].value = UNUSED_MARK
def insert(self, x: MemoryCell):
with MemoryCell(0) as i:
while i < self.m:
j = self.f(x, i, self.m)
if self.is_free(j):
self.table[j].set(x)
return True
i.set(i.succ())
return False
def search(self, x: MemoryCell):
with MemoryCell(0) as i:
while i < self.m:
j = self.f(x, i, self.m)
if self.is_unused(j):
return False
if self.table[j] == x:
return True
i.set(i.succ())
return False
def delete(self, x: MemoryCell):
with MemoryCell(0) as i:
while i < self.m:
j = self.f(x, i, self.m)
if self.is_unused(j):
return False
if self.table[j] == x:
self.table[j].value = DELETED_MARK
return True
i.set(i.succ())
return False
def __str__(self):
return str(self.table)
def alpha(self):
with MemoryCell(0) as i:
used = 0
while i < self.m:
used += 0 if self.is_free(i) else 1
i.set(i.succ())
return used / int(self.m)
def is_unused(self, i: Literal):
if self.table[i].value == UNUSED_MARK:
return True
return False
def is_deleted(self, i: Literal):
if self.table[i].value == DELETED_MARK:
return True
return False
def is_free(self, i: Literal):
return self.is_unused(i) or self.is_deleted(i)