Binary search tree

Binary search tree

• 1.
  BINARY SEARCH TREE
• 2.
  DEFINITION:  Binary searchtree is node based binary tree data structure. Each node has a key and an associated value. 27 14 10 19 35 4231
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  Node: A node havingsome data, references to its left and right child nodes. struct nodes { int data; struct node *leftChild; struct node *rightChild; };
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  BASIC OPERATION: Search Insert Pre-ordetraversal In-order traversal Postordertraversal
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  OPERATION ON BINARYSEARCH TREE: Search − Searches an element in a tree. Insert − Inserts an element in a tree. Pre-order Traversal − Traverses a tree in a pre-order manner. In-order Traversal − Traverses a tree in an in-order manner. Post-order Traversal − Traverses a tree in a post-order manner.
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  SEARCH: Start searching fromthe root node. Then if the data is less than the key value, search for the element in the left subtree. search for the element in the rightsubtree. EG: search(ptnode root, int key) { if (!root) return NULL; if (key == root->key) return root; if (key < root->key) return search(root->left,key); return search(root->right,key); }
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  INSERT: A new keyis always inserted at leaf. We start searching a key from root till we hit a leaf node. EG: void insert(TreeNode<ItemType>*& tree, ItemType item) { if(tree == NULL) { tree = new TreeNode<ItemType>; tree->right = NULL; tree->left = NULL; tree->info = item; } else if(item < tree->info) Insert(tree->left, item); else Insert(tree->right, item); }
• 8.
  9 7 5 4 6 8 10 10 10>7 10>9 INSERTAN ELEMENT IN THE LEAF NODE
• 9.
  INORDER TRAVERSAL: Visit thenodes in the left subtree, then visit the root of the tree, then visit the nodes in the right subtree . Inorder(tree) If tree is not NULL Inorder(Left(tree)) Visit Info(tree) Inorder(Right(tree))
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  IN ORDER 10 ‘J’ ‘E’ ‘A ’ ‘H ’ ‘T ’ ‘M’ ‘Y ’ tre e Visit leftsubtree first Visit right subtree last Visit second
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  PREORDER: Visit the rootof the tree first, then visit the nodes in the left subtree, then visit the nodes in the right subtree Preorder(tree) If tree is not NULL Visit Info(tree) Preorder(Left(tree)) Preorder(Right(tree))
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  PREORDER 12 ‘J’ ‘E’ ‘A ’ ‘H ’ ‘T ’ ‘M’ ‘Y ’ tre e Visit left subtreesecond Visit right subtree last Visit first
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  POST ORDER: Visit thenodes in the left subtree first, then visit the nodes in the right subtree, then visit the root of the tree Postorder(tree) If tree is not NULL Postorder(Left(tree)) Postorder(Right(tree)) Visit Info(tree)
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  POST ORDER: POST ORDER 14 ‘J’ ‘E’ ‘A ’ ‘H ’ ‘T ’ ‘M’ ‘Y ’ tre e Visitleft subtree first Visit right subtree second
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  THANK YOU