Tree Structures PDF

UNIT – IV TREE STRUCTURES 1. TREE ADT 2. BINARY TREE ADT 3. TREE TRAVERSALS 4. BINARY SEARCH TREES 5. AVL TREES 6. HEAPS 7. MULTIWAY SEARCH TREES. 1) TREE ADT: A tree data structure is a hierarchical structure that is used to represent and organize data in a wa...

UNIT – IV TREE STRUCTURES 1. TREE ADT 2. BINARY TREE ADT 3. TREE TRAVERSALS 4. BINARY SEARCH TREES 5. AVL TREES 6. HEAPS 7. MULTIWAY SEARCH TREES. 1) TREE ADT: A tree data structure is a hierarchical structure that is used to represent and organize data in a way that is easy to navigate and search. It is a collection of nodes that are connected by edges and has a hierarchical relationship between the nodes. It is a non-linear data structure. The topmost node of the tree is called the root, and the nodes below it are called the child nodes. Each node can have multiple child nodes, and these child nodes can also have their own child nodes, forming a recursive structure. 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The idea is to do an iterative level order traversal of the given tree using queue. If we find a node whose left child is empty, we make a new key as the left child of the node. Else if we find a node whose right child is empty, we make the new key as the right child. We keep traversing the tree until we find a node whose either left or right child is empty. def insert_node(root, key): if not root: return Node(key) else: queue = [root] while queue: temp = queue.pop(0) if not temp.left:  temp.left = Node(key) break else: queue.append(temp.left) if not temp.right: temp.right = Node(key) break else: queue.append(temp.right) return root iii) Deletion: Given a binary tree, delete a node from it by making sure that the tree shrinks from the bottom (i.e. the deleted node is replaced by the bottom-most and rightmost node). This is different from BST deletion. Here we do not have any order among elements, so we replace them with the last element. def delete_node(root, key): if not root: return root if root.val == key: if not root.left: return root.right elif not root.right: return root.left else: temp = root.right while temp.left: temp = temp.left root.val = temp.val root.right = delete_node(root.right, temp.val) root.left = delete_node(root.left, key) root.right = delete_node(root.right, key) return root iv) Searching: This operation find any particular key value is present in the tree or not. def search_node(root, key): if not root: return False if root.val == key: return True left = search_node(root.left, key) right = search_node(root.right, key) return left or right  k. hiermdn oloa Suttun0 ho is a a t teee.. inTy in aha in foom ol fom ol KOhn uhan O3gpmzeg epIient S Serhira hirg, hat fsTICient Syem be ud i t me OrC on Paaes Cgarnize ea dhe Cocip comp Ue Okanpus rtcte is C p pn nid t o Some nac Document Cbja /xnAL HTL The CocsuG 1U ihe fm obee ompb C o n p i l a i H o n t o ne o p NG TG40 nd pese i n d e ch c httahkoee s CIficicnil inde t US r c s Ceu orn drlma o ol Ches Narb d e - - i n t t - (solldata) Seyf loft- No Sels ight -None Get oata: daia we initiaira o the ede ho, cro e d d Bire nco niado Co) Orl hlccb (344) nco f t cC g t tbde  G a metlard fs 1/tim al ts P90e toen On. to ter ty Plooles n Jechiaues tomso 3types fhee he PoOnes T9xaehga e a arle malens Onokn hoeso tedanal S alGo calltd asyomeric bolea odon The n e omd GlG c ic o Thc CLOdi in o n Cicle PeCi Subrea n betuecn ho o1 O2d 2g h nada iS ocG Kmon a5 1S 1 B n. 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F,6 H,2 Post orctos balesSr Poslolon tolorje G, L, H,D, E, 516, 15 25/20 T,K,3 FC, A D,B, 4,I,6,F 35, 4Go,50 ho30 E, CA kefove tPO kefoe taltnies he 1s a l u n Te.Jo and 00E had 3 D O -h h oo 9ight Subbes Ceyo wo da Ood 1bt in pas acla rea TRA t EYE and 7ght Clb accesGed af knoun a s LRN kroun LRN as iS s aso Cuclon agoailhm pOs pos Nocu) (Lf1-eghi- vecu19h 1y aloitn penfosmetd cODendosmed Opoa ons Tho fotouig Ot cach rode Conse ho Pit b l e 19na pratonse Right Fiaty olct podoicla12naternsa (soaDot) Pastodasi)ma\derngci (onot- Ut) eg: Se e8-aprard (not-daa)  Program for Binary Search Tree: Operations: i) Creation ii) Insertion iii) Deletion iv) Searching i) Creation: class Node: def __init__(self, value): self.value = value self.left = None self.right = None class BinarySearchTree: def __init__(self): self.root = None ii) Insertion: def insert(self, value): if self.root is None: self.root = Node(value) else: self._insert_recursive(self.root, value) def _insert_recursive(self, node, value): if value < node.value: if node.left is None:  node.left = Node(value) else: self._insert_recursive(node.left, value) elif value > node.value: if node.right is None: node.right = Node(value) else: self._insert_recursive(node.right, value) iii) DELETION: def delete(self, value): self.root = self._delete_recursive(self.root, value) def _delete_recursive(self, node, value): if node is None: return node if value < node.value: node.left = self._delete_recursive(node.left, value) elif value > node.value: node.right = self._delete_recursive(node.right, value) else: if node.left is None: return node.right elif node.right is None:  return node.left min_node = self._find_min(node.right) node.value = min_node.value node.right = self._delete_recursive(node.right, min_node.value) return node IV) Searching: def search(self, value): return self._search_recursive(self.root, value) def _search_recursive(self, node, value): if node is None or node.value == value: return node if value < node.value: return self._search_recursive(node.left, value) else: return self._search_recursive(node.right, value)  Nulti-way Sanch tsootint Denitioni Santh as m-wy toeo. gonsnaliyd Vouen bnay M-way ear ch The g onsttan on on an )Each nodo n the eoo can as ocicle twith chldson and (m-13 key atde Esample m- ley chetzbeen ?2/? ?/? ’mme mchldren The oe Koys in an node the aDLanged Fxample : the poit k chi ldren dos than tre key thu node V) The koy un the Aaut Cm-) Chidon highey than + By ang tree, tho weanch and pdate opnatbns much MoO yaant  2030 36 20K