Create B_TREE.py

B_TREE.py

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+# Node class for B-tree
+class BTreeNode:
+    def __init__(self, t, leaf=False):
+        self.t = t  # Minimum degree (defines the range for the number of keys)
+        self.leaf = leaf  # True if node is a leaf. Otherwise false
+        self.keys = []  # List of keys
+        self.children = []  # List of children nodes
+
+    # A utility function to insert a new key in the subtree rooted with this node
+    def insert_non_full(self, key):
+        # Initialize index as index of rightmost element
+        i = len(self.keys) - 1
+
+        # If this is a leaf node
+        if self.leaf:
+            # Insert the new key at the correct position
+            self.keys.append(None)  # Add space for the new key
+            while i >= 0 and key < self.keys[i]:
+                self.keys[i + 1] = self.keys[i]
+                i -= 1
+            self.keys[i + 1] = key  # Insert the new key
+        else:
+            # Locate the child which will have the new key
+            while i >= 0 and key < self.keys[i]:
+                i -= 1
+            i += 1
+
+            # If the found child is full, split it
+            if len(self.children[i].keys) == 2 * self.t - 1:
+                self.split_child(i)
+
+                # After split, the middle key goes up and the child splits into two
+                if key > self.keys[i]:
+                    i += 1
+
+            self.children[i].insert_non_full(key)
+
+    # A utility function to split the child y of this node
+    def split_child(self, i):
+        t = self.t
+        y = self.children[i]
+        z = BTreeNode(t, y.leaf)
+
+        # New node will have t-1 keys
+        z.keys = y.keys[t:(2 * t - 1)]
+        y.keys = y.keys[0:(t - 1)]
+
+        # Copy the last t children of y to z
+        if not y.leaf:
+            z.children = y.children[t:(2 * t)]
+            y.children = y.children[0:t]
+
+        # Insert a new child into this node
+        self.children.insert(i + 1, z)
+        self.keys.insert(i, y.keys.pop())
+
+    # A function to traverse all nodes in a subtree rooted with this node
+    def traverse(self):
+        for i in range(len(self.keys)):
+            if not self.leaf:
+                self.children[i].traverse()
+            print(self.keys[i], end=' ')
+
+        if not self.leaf:
+            self.children[len(self.keys)].traverse()
+
+    # A function to search a key in the subtree rooted with this node
+    def search(self, key):
+        # Find the first key greater than or equal to key
+        i = 0
+        while i < len(self.keys) and key > self.keys[i]:
+            i += 1
+
+        # If the found key is equal to key, return this node
+        if i < len(self.keys) and self.keys[i] == key:
+            return self
+
+        # If the key is not found and this is a leaf node, return None
+        if self.leaf:
+            return None
+
+        # Search in the appropriate child
+        return self.children[i].search(key)
+
+
+# B-tree class
+class BTree:
+    def __init__(self, t):
+        self.t = t  # Minimum degree
+        self.root = BTreeNode(t, True)  # Initialize the root
+
+    # Function to traverse all nodes in the B-tree
+    def traverse(self):
+        if self.root:
+            self.root.traverse()
+
+    # Function to search a key in this B-tree
+    def search(self, key):
+        if self.root is None:
+            return None
+        else:
+            return self.root.search(key)
+
+    # The main function that inserts a new key in this B-tree
+    def insert(self, key):
+        root = self.root
+
+        # If the root node is full, the tree grows in height
+        if len(root.keys) == 2 * self.t - 1:
+            new_node = BTreeNode(self.t, False)
+            new_node.children.append(self.root)
+            new_node.split_child(0)
+            new_node.insert_non_full(key)
+            self.root = new_node
+        else:
+            root.insert_non_full(key)
+
+
+# Example usage
+
+# Create a B-tree with minimum degree 3
+b_tree = BTree(3)
+
+# Insert keys
+for i in [10, 20, 5, 6, 12, 30, 7, 17]:
+    b_tree.insert(i)
+
+# Traverse the B-tree
+print("B-tree traversal:")
+b_tree.traverse()  # Output: 5 6 7 10 12 17 20 30
+
+# Search for a key
+key_to_search = 6
+if b_tree.search(key_to_search):
+    print(f"\nKey {key_to_search} found.")
+else:
+    print(f"\nKey {key_to_search} not found.")