From 973e5c3c824bb6328619524da3e5f6ab3dfd42fd Mon Sep 17 00:00:00 2001 From: Arijit Ghosal <97433331+arijitghosal03@users.noreply.github.com> Date: Thu, 16 Mar 2023 16:04:07 +0530 Subject: [PATCH] Create B-Tree.py The code has created a Btree class to insert a new node, remove or search through the B-Tree data structure. --- pydatastructs/trees/B-Tree.py | 195 ++++++++++++++++++++++++++++++++++ 1 file changed, 195 insertions(+) create mode 100644 pydatastructs/trees/B-Tree.py diff --git a/pydatastructs/trees/B-Tree.py b/pydatastructs/trees/B-Tree.py new file mode 100644 index 000000000..0bd60c115 --- /dev/null +++ b/pydatastructs/trees/B-Tree.py @@ -0,0 +1,195 @@ +class Node: + def __init__(self, t, leaf): + self.t = t # minimum degree + self.leaf = leaf + self.keys = [] + self.children = [] + + def traverse(self): + i = 0 + n = len(self.keys) + while i < n: + if self.leaf == False: + self.children[i].traverse() + print(self.keys[i]) + i += 1 + if self.leaf == False: + self.children[i].traverse() + +class BTree: + def __init__(self, t): + self.t = t # minimum degree + self.root = None + + def traverse(self): + if self.root != None: + self.root.traverse() + + def search(self, k): + if self.root == None: + return None + else: + return self.root.search(k) + + def insert(self, k): + if self.root == None: + self.root = Node(self.t, True) + self.root.keys.append(k) + else: + if len(self.root.keys) == (2 * self.t) - 1: + new_root = Node(self.t, False) + new_root.children.append(self.root) + new_root.split_child(0, self.root) + i = 0 + if new_root.keys[0] < k: + i += 1 + new_root.children[i].insert_non_full(k) + self.root = new_root + else: + self.root.insert_non_full(k) + + def delete(self, k): + if not self.root: + print("The tree is empty") + return + + self.root.delete(k) + + if not self.root.keys: + self.root = self.root.children[0] + + +class Node: + def __init__(self, t, leaf): + self.t = t + self.leaf = leaf + self.keys = [] + self.children = [] + + def traverse(self): + i = 0 + n = len(self.keys) + while i < n: + if self.leaf == False: + self.children[i].traverse() + print(self.keys[i]) + i += 1 + if self.leaf == False: + self.children[i].traverse() + + def search(self, k): + i = 0 + n = len(self.keys) + while i < n and k > self.keys[i]: + i += 1 + if self.keys[i] == k: + return self + if self.leaf == True: + return None + return self.children[i].search(k) + + def insert_non_full(self, k): + i = len(self.keys) - 1 + if self.leaf == True: + self.keys.append(0) + while i >= 0 and self.keys[i] > k: + self.keys[i+1] = self.keys[i] + i -= 1 + self.keys[i+1] = k + else: + while i >= 0 and self.keys[i] > k: + i -= 1 + if len(self.children[i+1].keys) == (2 * self.t) - 1: + self.split_child(i+1, self.children[i+1]) + if self.keys[i+1] < k: + i += 1 + self.children[i+1].insert_non_full(k) + + def split_child(self, i, y): + z = Node(y.t, y.leaf) + self.children.insert(i+1, z) + self.keys.insert(i, y.keys[self.t-1]) + z.keys = y.keys[self.t:(2*self.t)-1] + y.keys = y.keys[0:self.t-1] + if y.leaf == False: + z.children = y.children[self.t:(2*self.t)] + y.children = y.children[0:self.t-1] + + def delete(self, k): + n = len(self.keys) + i = 0 + while i < n and k > self.keys[i]: + i += 1 + if self.leaf: + if i < n and self.keys[i] == k: + self.keys.pop(i) + else: + print("The key", k, "does not exist in the tree") + return + else: + if i < n and self.keys[i] == k: + if len(self.children[i].keys) >= self.t: + prev = self.get_predecessor(i) + self.keys[i] = prev + self.children[i].delete(prev) + elif len(self.children[i+1].keys) >= self.t: + succ = self.get_successor(i) + self.keys[i] = succ + self.children[i+1].delete(succ) + else: + self.merge_children(i) + self.children[i].delete(k) + else: + if len(self.children[i].keys) == self.t-1: + if i > 0 and len(self.children[i-1].keys) >= self.t: + self.move_key_to_left_child(i) + elif i < n and len(self.children[i+1].keys) >= self: + self.move_key_to_right_child(i) + else: + self.merge_children(i) + self.children[i].delete(k) + else: + self.children[i].delete(k) + + if len(self.keys) == 0: + if self.leaf: + del self + else: + self.children[0].delete(k) + + def get_predecessor(self, i): + curr = self.children[i] + while not curr.leaf: + curr = curr.children[-1] + return curr.keys[-1] + + def get_successor(self, i): + curr = self.children[i+1] + while not curr.leaf: + curr = curr.children[0] + return curr.keys[0] + + def merge_children(self, i): + child1 = self.children[i] + child2 = self.children[i+1] + child1.keys.append(self.keys[i]) + child1.keys += child2.keys + child1.children += child2.children + self.children.pop(i+1) + self.keys.pop(i) + + def move_key_to_left_child(self, i): + child1 = self.children[i-1] + child2 = self.children[i] + child2.keys.insert(0, self.keys[i-1]) + self.keys[i-1] = child1.keys.pop(-1) + if not child1.leaf: + child2.children.insert(0, child1.children.pop(-1)) + + def move_key_to_right_child(self, i): + child1 = self.children[i] + child2 = self.children[i+1] + child1.keys.append(self.keys[i]) + self.keys[i] = child2.keys.pop(0) + if not child2.leaf: + child1.children.append(child2.children.pop(0))