B-Tree

vorlesung/L06_b_baeume/b_tree.py

@@ -0,0 +1,120 @@
+from utils.literal import Literal
+from utils.memory_cell import MemoryCell
+from utils.memory_array import MemoryArray
+from b_tree_node import BTreeNode
+
+class BTree:
+    def __init__(self, m: int):
+        self.m = m
+        self.root = BTreeNode(m)
+
+    def search(self, value, start: BTreeNode = None) -> BTreeNode | None:
+        if not start:
+            start = self.root
+        start.load()
+        i = 0
+        if not isinstance(value, MemoryCell):
+            value = MemoryCell(value)
+        while i < start.n and value > start.value[Literal(i)]:
+            i += 1
+        if i < start.n and value == start.value[Literal(i)]:
+            return start
+        if start.leaf:
+            return None
+        return self.search(value, start.children[i])
+
+    def split_child(self, parent: BTreeNode, i: int):
+        child = parent.children[i]
+        child.load()
+        h = BTreeNode(self.m)
+        h.leaf = child.leaf
+        h.n = self.m - 1
+        for j in range(self.m - 1):
+            h.value[Literal(j)] = child.value[Literal(j + self.m)]
+        if not h.leaf:
+            for j in range(self.m):
+                h.children[j] = child.children[j + self.m]
+            for j in range(self.m, child.n + 1):
+                child.children[j] = None
+        child.n = self.m - 1
+        child.save()
+        h.save()
+        for j in range(parent.n, i, -1):
+            parent.children[j + 1] = parent.children[j]
+            parent.value[Literal(j)] = parent.value[Literal(j - 1)]
+        parent.children[i + 1] = h
+        parent.value[Literal(i)] = child.value[Literal(self.m - 1)]
+        parent.n += 1
+        parent.save()
+
+    def insert(self, value):
+        if not isinstance(value, MemoryCell):
+            value = MemoryCell(value)
+        r = self.root
+        if r.n == 2 * self.m - 1:
+            h = BTreeNode(self.m)
+            self.root = h
+            h.leaf = False
+            h.n = 0
+            h.children[0] = r
+            self.split_child(h, 0)
+            self.insert_in_node(h, value)
+        else:
+            self.insert_in_node(r, value)
+
+    def insert_in_node(self, start: BTreeNode, value):
+        start.load()
+        i = start.n
+        if start.leaf:
+            while i >= 1 and value < start.value[Literal(i-1)]:
+                start.value[Literal(i)] = start.value[Literal(i-1)]
+                i -= 1
+            start.value[Literal(i)].set(value)
+            start.n += 1
+            start.save()
+        else:
+            j = 0
+            while j < start.n and value > start.value[Literal(j)]:
+                j += 1
+            if start.children[j].n == 2 * self.m - 1:
+                self.split_child(start, j)
+                if value > start.value[Literal(j)]:
+                    j += 1
+            self.insert_in_node(start.children[j], value)
+
+    def traversal(self, callback):
+        def traversal_recursive(node, callback):
+            i = 0
+            while i < node.n:
+                if not node.leaf:
+                    traversal_recursive(node.children[i], callback)
+                callback(node.value[Literal(i)])
+                i += 1
+            if not node.leaf:
+                traversal_recursive(node.children[i], callback)
+
+        traversal_recursive(self.root, callback)
+
+    def walk(self):
+        def print_key(key):
+            print(key, end=" ")
+
+        self.traversal(print_key)
+
+    def height(self, start: BTreeNode = None):
+        if not start:
+            start = self.root
+        if start.leaf:
+            return 0
+        return 1 + self.height(start.children[0])
+
+
+if __name__ == "__main__":
+    a = MemoryArray.create_array_from_file("data/seq3.txt")
+    tree = BTree(3)
+    for cell in a:
+        tree.insert(cell)
+    print(f"Height: {tree.height()}")
+    tree.walk()
+    s = tree.search(0)
+    print(f"\nKnoten mit 0: {str(s)}")

vorlesung/L06_b_baeume/b_tree_node.py

@@ -0,0 +1,29 @@
+from utils.literal import Literal
+from utils.memory_cell import MemoryCell
+from utils.memory_array import MemoryArray
+
+class BTreeNode(MemoryCell):
+
+    def __init__(self, m: int):
+        super().__init__()
+        self.m = m
+        self.n = 0
+        self.leaf = True
+        self.value = MemoryArray(Literal(2 * m - 1))
+        self.children = [None] * (2 * m)
+        self.loaded_count = 0
+        self.saved_count = 0
+
+    def reset_counters(self):
+        super().reset_counters()
+        self.loaded_count = 0
+        self.saved_count = 0
+
+    def load(self):
+        self.loaded_count += 1
+
+    def save(self):
+        self.saved_count += 1
+
+    def __str__(self):
+        return "(" + " ".join([str(self.value[Literal(i)]) for i in range(self.n)]) + ")"