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| 1 | + |
| 2 | +# Generic tree node class |
| 3 | +class TreeNode(object): |
| 4 | + def __init__(self, val): |
| 5 | + self.val = val |
| 6 | + self.left = None |
| 7 | + self.right = None |
| 8 | + self.height = 1 |
| 9 | + |
| 10 | +# AVL tree class which supports the |
| 11 | +# Insert operation |
| 12 | +class AVL_Tree(object): |
| 13 | + |
| 14 | + # Recursive function to insert key in |
| 15 | + # subtree rooted with node and returns |
| 16 | + # new root of subtree. |
| 17 | + def insert(self, root, key): |
| 18 | + |
| 19 | + # Step 1 - Perform normal BST |
| 20 | + if not root: |
| 21 | + return TreeNode(key) |
| 22 | + elif key < root.val: |
| 23 | + root.left = self.insert(root.left, key) |
| 24 | + else: |
| 25 | + root.right = self.insert(root.right, key) |
| 26 | + |
| 27 | + # Step 2 - Update the height of the |
| 28 | + # ancestor node |
| 29 | + root.height = 1 + max(self.getHeight(root.left), |
| 30 | + self.getHeight(root.right)) |
| 31 | + |
| 32 | + # Step 3 - Get the balance factor |
| 33 | + balance = self.getBalance(root) |
| 34 | + |
| 35 | + # Step 4 - If the node is unbalanced, |
| 36 | + # then try out the 4 cases |
| 37 | + # Case 1 - Left Left |
| 38 | + if balance > 1 and key < root.left.val: |
| 39 | + return self.rightRotate(root) |
| 40 | + |
| 41 | + # Case 2 - Right Right |
| 42 | + if balance < -1 and key > root.right.val: |
| 43 | + return self.leftRotate(root) |
| 44 | + |
| 45 | + # Case 3 - Left Right |
| 46 | + if balance > 1 and key > root.left.val: |
| 47 | + root.left = self.leftRotate(root.left) |
| 48 | + return self.rightRotate(root) |
| 49 | + |
| 50 | + # Case 4 - Right Left |
| 51 | + if balance < -1 and key < root.right.val: |
| 52 | + root.right = self.rightRotate(root.right) |
| 53 | + return self.leftRotate(root) |
| 54 | + |
| 55 | + return root |
| 56 | + |
| 57 | + def leftRotate(self, z): |
| 58 | + |
| 59 | + y = z.right |
| 60 | + T2 = y.left |
| 61 | + |
| 62 | + # Perform rotation |
| 63 | + y.left = z |
| 64 | + z.right = T2 |
| 65 | + |
| 66 | + # Update heights |
| 67 | + z.height = 1 + max(self.getHeight(z.left), |
| 68 | + self.getHeight(z.right)) |
| 69 | + y.height = 1 + max(self.getHeight(y.left), |
| 70 | + self.getHeight(y.right)) |
| 71 | + |
| 72 | + # Return the new root |
| 73 | + return y |
| 74 | + |
| 75 | + def rightRotate(self, z): |
| 76 | + |
| 77 | + y = z.left |
| 78 | + T3 = y.right |
| 79 | + |
| 80 | + # Perform rotation |
| 81 | + y.right = z |
| 82 | + z.left = T3 |
| 83 | + |
| 84 | + # Update heights |
| 85 | + z.height = 1 + max(self.getHeight(z.left), |
| 86 | + self.getHeight(z.right)) |
| 87 | + y.height = 1 + max(self.getHeight(y.left), |
| 88 | + self.getHeight(y.right)) |
| 89 | + |
| 90 | + # Return the new root |
| 91 | + return y |
| 92 | + |
| 93 | + def getHeight(self, root): |
| 94 | + if not root: |
| 95 | + return 0 |
| 96 | + |
| 97 | + return root.height |
| 98 | + |
| 99 | + def getBalance(self, root): |
| 100 | + if not root: |
| 101 | + return 0 |
| 102 | + |
| 103 | + return self.getHeight(root.left) - self.getHeight(root.right) |
| 104 | + |
| 105 | + def preOrder(self, root): |
| 106 | + |
| 107 | + if not root: |
| 108 | + return |
| 109 | + |
| 110 | + print("{0} ".format(root.val), end="") |
| 111 | + self.preOrder(root.left) |
| 112 | + self.preOrder(root.right) |
| 113 | + |
| 114 | + |
| 115 | +# Driver program to test above function |
| 116 | +myTree = AVL_Tree() |
| 117 | +root = None |
| 118 | + |
| 119 | +root = myTree.insert(root, 10) |
| 120 | +root = myTree.insert(root, 20) |
| 121 | +root = myTree.insert(root, 30) |
| 122 | +root = myTree.insert(root, 40) |
| 123 | +root = myTree.insert(root, 50) |
| 124 | +root = myTree.insert(root, 25) |
| 125 | + |
| 126 | +"""The constructed AVL Tree would be |
| 127 | + 30 |
| 128 | + / \ |
| 129 | + 20 40 |
| 130 | + / \ \ |
| 131 | + 10 25 50""" |
| 132 | + |
| 133 | +# Preorder Traversal |
| 134 | +print("Preorder traversal of the", |
| 135 | + "constructed AVL tree is") |
| 136 | +myTree.preOrder(root) |
| 137 | +print() |
| 138 | + |
| 139 | +# This code is contributed by Ajitesh Pathak |
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