|
| 1 | +''' |
| 2 | + Binary Search Tree |
| 3 | +A binary tree is a tree data structure in which each node can have a maximum of 2 children. It means that each node in a binary tree can have either one, or two or no children. Each node in a binary tree contains data and references to its children. Both the children are named as left child and the right child according to their position. |
| 4 | + |
| 5 | +Time Complexity - O(logn) |
| 6 | +''' |
| 7 | +class BinaryTreeNode: |
| 8 | + def __init__(self, data): |
| 9 | + self.data = data |
| 10 | + self.leftChild = None |
| 11 | + self.rightChild = None |
| 12 | + |
| 13 | + |
| 14 | +def insert(root, newValue): |
| 15 | + # if binary search tree is empty, make a new node and declare it as root |
| 16 | + if root is None: |
| 17 | + root = BinaryTreeNode(newValue) |
| 18 | + return root |
| 19 | + # binary search tree is not empty, so we will insert it into the tree |
| 20 | + # if newValue is less than value of data in root, add it to left subtree and proceed recursively |
| 21 | + if newValue < root.data: |
| 22 | + root.leftChild = insert(root.leftChild, newValue) |
| 23 | + else: |
| 24 | + # if newValue is greater than value of data in root, add it to right subtree and proceed recursively |
| 25 | + root.rightChild = insert(root.rightChild, newValue) |
| 26 | + return root |
| 27 | + |
| 28 | + |
| 29 | +def search(root, value): |
| 30 | + # Condition 1 |
| 31 | + if root == None: |
| 32 | + return False |
| 33 | + # Condition 2 |
| 34 | + elif root.data == value: |
| 35 | + return True |
| 36 | + # Condition 3 |
| 37 | + elif root.data < value: |
| 38 | + return search(root.rightChild, value) |
| 39 | + # Condition 4 |
| 40 | + else: |
| 41 | + return search(root.leftChild, value) |
| 42 | + |
| 43 | + |
| 44 | +def findLargestElement(root): |
| 45 | + # check if binary search tree is empty |
| 46 | + if root == None: |
| 47 | + return False |
| 48 | + # check if current node is rightmost node |
| 49 | + elif root.rightChild == None: |
| 50 | + return root.data |
| 51 | + # check right subtree of current node |
| 52 | + else: |
| 53 | + return findLargestElement(root.rightChild) |
| 54 | + |
| 55 | + |
| 56 | +root = insert(None, 15) |
| 57 | + |
| 58 | + |
| 59 | +def findSmallestElement(root): |
| 60 | + # check if binary search tree is empty |
| 61 | + if root == None: |
| 62 | + return False |
| 63 | + # check if current node is leftmost node |
| 64 | + elif root.leftChild == None: |
| 65 | + return root.data |
| 66 | + # check right subtree of current node |
| 67 | + else: |
| 68 | + return findSmallestElement(root.leftChild) |
| 69 | + |
| 70 | + |
| 71 | +insert(root, 10) |
| 72 | +insert(root, 25) |
| 73 | +insert(root, 6) |
| 74 | +insert(root, 14) |
| 75 | +insert(root, 20) |
| 76 | +insert(root, 60) |
| 77 | +print(search(root, 14)) # True |
| 78 | +print(findLargestElement(root)) # 60 |
| 79 | +print(findSmallestElement(root)) # 6 |
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