Umstellen der Auswertungslogik
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@@ -1,58 +1,63 @@
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from utils.memory_manager import MemoryManager
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from utils.memory_array import MemoryArray
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from utils.literal import Literal
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from utils.algo_context import AlgoContext
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from utils.algo_array import Array
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from b_tree import BTree
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from b_tree_node import BTreeNode
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class MemoryManagerBTree(MemoryManager):
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"""
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Diese Klasse erweitert den MemoryManager, um spezifische Statistiken für B-Bäume zu speichern.
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"""
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@staticmethod
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def count_loads():
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return sum([cell.loaded_count for cell in MemoryManager().cells if isinstance(cell, BTreeNode)])
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@staticmethod
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def count_saves():
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return sum([cell.saved_count for cell in MemoryManager().cells if isinstance(cell, BTreeNode)])
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@staticmethod
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def save_stats(count):
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data = { "cells": MemoryManager.count_cells(),
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"reads": MemoryManager.count_reads(),
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"writes": MemoryManager.count_writes(),
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"compares": MemoryManager.count_compares(),
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"adds": MemoryManager.count_adds(),
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"subs": MemoryManager.count_subs(),
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"muls": MemoryManager.count_muls(),
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"divs": MemoryManager.count_divs(),
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"bitops": MemoryManager.count_bitops(),
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"loads": MemoryManagerBTree.count_loads(),
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"saves": MemoryManagerBTree.count_saves() }
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MemoryManager.stats[count] = data
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def count_loads(root: BTreeNode) -> int:
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"""Summiert load()-Aufrufe über alle Knoten des Baums."""
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if root is None:
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return 0
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total = root.loaded_count
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for child in root.children:
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if child is not None:
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total += count_loads(child)
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return total
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def count_saves(root: BTreeNode) -> int:
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"""Summiert save()-Aufrufe über alle Knoten des Baums."""
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if root is None:
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return 0
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total = root.saved_count
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for child in root.children:
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if child is not None:
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total += count_saves(child)
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return total
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def analyze_complexity(sizes):
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"""
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Analysiert die Komplexität
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ctx = AlgoContext()
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stats: dict[int, dict] = {}
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:param sizes: Eine Liste von Eingabegrößen für die Analyse.
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"""
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for size in sizes:
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MemoryManager.purge() # Speicher zurücksetzen
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tree = BTree(5)
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random_array = MemoryArray.create_random_array(size, -100, 100)
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for i in range(size-1):
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tree.insert(int(random_array[Literal(i)]))
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MemoryManager.reset()
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tree.insert(int(random_array[Literal(size-1)]))
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MemoryManagerBTree.save_stats(size)
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ctx.reset()
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z = Array.random(size, -100, 100, ctx)
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tree = BTree(5, ctx)
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for i in range(size - 1):
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tree.insert(z[i])
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ctx.reset()
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tree.insert(z[size - 1])
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stats[size] = {
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"comparisons": ctx.comparisons,
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"writes": ctx.writes,
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"loads": count_loads(tree.root),
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"saves": count_saves(tree.root),
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}
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# Einfaches Liniendiagramm über alle gespeicherten Metriken
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import matplotlib.pyplot as plt
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x = list(stats.keys())
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fig, axes = plt.subplots(len(stats[x[0]]), 1, figsize=(8, 12), sharex=True)
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for ax, label in zip(axes, stats[x[0]].keys()):
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ax.plot(x, [stats[k][label] for k in x], label=label)
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ax.set_ylabel(label)
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ax.legend()
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plt.xlabel("n")
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plt.tight_layout()
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plt.show()
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MemoryManager.plot_stats(["cells", "compares", "loads", "saves"])
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if __name__ == "__main__":
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sizes = range(1, 1001, 2)
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analyze_complexity(sizes)
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analyze_complexity(sizes)
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@@ -1,23 +1,29 @@
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from utils.literal import Literal
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from utils.memory_cell import MemoryCell
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from utils.memory_array import MemoryArray
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from utils.algo_context import AlgoContext
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from utils.algo_array import Array
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from utils.algo_int import Int
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from b_tree_node import BTreeNode
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class BTree:
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def __init__(self, m: int):
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def __init__(self, m: int, ctx: AlgoContext):
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self.m = m
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self.root = BTreeNode(m)
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self.ctx = ctx
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self.root = BTreeNode(m, ctx)
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def _new_node(self):
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return BTreeNode(self.m, self.ctx)
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def search(self, value, start: BTreeNode = None) -> BTreeNode | None:
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if not start:
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start = self.root
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start.load()
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if not isinstance(value, Int):
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value = Int(value, self.ctx)
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i = 0
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if not isinstance(value, MemoryCell):
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value = MemoryCell(value)
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while i < start.n and value > start.value[Literal(i)]:
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while i < start.n and value > start.value[i]:
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i += 1
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if i < start.n and value == start.value[Literal(i)]:
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if i < start.n and value == start.value[i]:
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return start
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if start.leaf:
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return None
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@@ -26,11 +32,11 @@ class BTree:
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def split_child(self, parent: BTreeNode, i: int):
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child = parent.children[i]
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child.load()
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h = BTreeNode(self.m)
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h = self._new_node()
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h.leaf = child.leaf
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h.n = self.m - 1
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for j in range(self.m - 1):
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h.value[Literal(j)] = child.value[Literal(j + self.m)]
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h.value[j] = child.value[j + self.m]
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if not h.leaf:
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for j in range(self.m):
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h.children[j] = child.children[j + self.m]
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@@ -41,18 +47,18 @@ class BTree:
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h.save()
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for j in range(parent.n, i, -1):
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parent.children[j + 1] = parent.children[j]
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parent.value[Literal(j)] = parent.value[Literal(j - 1)]
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parent.value[j] = parent.value[j - 1]
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parent.children[i + 1] = h
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parent.value[Literal(i)] = child.value[Literal(self.m - 1)]
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parent.value[i] = child.value[self.m - 1]
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parent.n += 1
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parent.save()
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def insert(self, value):
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if not isinstance(value, MemoryCell):
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value = MemoryCell(value)
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if not isinstance(value, Int):
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value = Int(value, self.ctx)
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r = self.root
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if r.n == 2 * self.m - 1:
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h = BTreeNode(self.m)
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h = self._new_node()
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self.root = h
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h.leaf = False
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h.n = 0
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@@ -62,44 +68,40 @@ class BTree:
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else:
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self.insert_in_node(r, value)
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def insert_in_node(self, start: BTreeNode, value):
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def insert_in_node(self, start: BTreeNode, value: Int):
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start.load()
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i = start.n
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if start.leaf:
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while i >= 1 and value < start.value[Literal(i-1)]:
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start.value[Literal(i)] = start.value[Literal(i-1)]
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while i >= 1 and value < start.value[i - 1]:
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start.value[i] = start.value[i - 1]
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i -= 1
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start.value[Literal(i)].set(value)
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start.value[i] = value
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start.n += 1
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start.save()
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else:
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j = 0
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while j < start.n and value > start.value[Literal(j)]:
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while j < start.n and value > start.value[j]:
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j += 1
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if start.children[j].n == 2 * self.m - 1:
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self.split_child(start, j)
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if value > start.value[Literal(j)]:
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if value > start.value[j]:
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j += 1
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self.insert_in_node(start.children[j], value)
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def traversal(self, callback):
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def traversal_recursive(node, callback):
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def _rec(node, callback):
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i = 0
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while i < node.n:
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if not node.leaf:
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traversal_recursive(node.children[i], callback)
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callback(node.value[Literal(i)])
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_rec(node.children[i], callback)
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callback(node.value[i])
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i += 1
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if not node.leaf:
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traversal_recursive(node.children[i], callback)
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traversal_recursive(self.root, callback)
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_rec(node.children[i], callback)
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_rec(self.root, callback)
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def walk(self):
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def print_key(key):
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print(key, end=" ")
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self.traversal(print_key)
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self.traversal(lambda key: print(key, end=" "))
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def height(self, start: BTreeNode = None):
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if not start:
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@@ -110,8 +112,9 @@ class BTree:
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if __name__ == "__main__":
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a = MemoryArray.create_array_from_file("data/seq3.txt")
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tree = BTree(3)
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ctx = AlgoContext()
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a = Array.from_file("data/seq3.txt", ctx)
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tree = BTree(3, ctx)
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for cell in a:
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tree.insert(cell)
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print(f"Height: {tree.height()}")
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@@ -1,24 +1,27 @@
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from utils.literal import Literal
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from utils.memory_cell import MemoryCell
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from utils.memory_array import MemoryArray
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from utils.algo_context import AlgoContext
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from utils.algo_array import Array
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class BTreeNode(MemoryCell):
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def __init__(self, m: int):
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super().__init__()
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class BTreeNode:
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"""
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Knoten eines B-Baums.
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value – Array der Schlüssel (Kapazität: 2m-1)
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n – Anzahl aktuell gespeicherter Schlüssel
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leaf – True wenn Blattknoten
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loaded_count / saved_count – Disk-I/O-Zähler für externe Komplexitätsanalyse
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"""
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def __init__(self, m: int, ctx: AlgoContext):
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self.m = m
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self.ctx = ctx
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self.n = 0
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self.leaf = True
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self.value = MemoryArray(Literal(2 * m - 1))
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self.value = Array([0] * (2 * m - 1), ctx)
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self.children = [None] * (2 * m)
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self.loaded_count = 0
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self.saved_count = 0
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def reset_counters(self):
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super().reset_counters()
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self.loaded_count = 0
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self.saved_count = 0
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def load(self):
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self.loaded_count += 1
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@@ -26,4 +29,4 @@ class BTreeNode(MemoryCell):
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self.saved_count += 1
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def __str__(self):
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return "(" + " ".join([str(self.value[Literal(i)]) for i in range(self.n)]) + ")"
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return "(" + " ".join([str(self.value[i]) for i in range(self.n)]) + ")"
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