Finding the Predecessor and Successor Node of a Binary Search Tree
August 31, 2020 algorithms A Binary Search Tree (BST) is a commonly used data structure that can be used to search an item in O(LogN) time. A BST should have the following characteristics: its left nodes are smaller than the root and its right nodes are larger than the root. If we perform an inorder traversal: left nodes first, current node, and then right nodes – we will have a fully sorted
sequence. inorder-traversal-of-a-bst To find the Predecessor or Sucessor Node of a BST – we can perform the following algorithms: predecessor-and-successor-of-a-bst Find the Predecessor Node of a Binary Search TreeThe predecessor node is the largest node that is smaller than the root (current node) – thus it is on the left branch of the Binary Search Tree, and the rightmost leaf (largest on the left branch). The C++ function to find the predecessor node of a BST node:
TreeNode* predecessor(TreeNode* root) { if (!root) return nullptr; root = root->left; while (root->right) root = root->right; return root; } And below is the Java implementation to get the predecessor node of a Binary Search Tree:
public int predecessor(TreeNode root) { if (root == null) return null; root = root.left; while (root.right != null) root = root.right; return root; } Python function to get the predecessor of a BST:
def predecessor(root): if root is None: return None root = root.left while root.right: root = root.right return root Find the Successor Node of a Binary Search TreeOn the other hand, the successor node is the smallest node that is bigger than the root/current – thus it is on the right branch of the BST, and also on the leftmost leaf (smallest on the right branch). The C++ function to get the successor node of a Binary Search Tree.
TreeNode* successor(TreeNode* root) { if (!root) return nullptr; root = root->right; while (root->left) root = root->left; return root; } Java method to get the successor:
public int successor(TreeNode root) { if (root == null) return null; root = root.right; while (root.left != null) root = root.left; return root; } Finally, the below is the Python implementation of getting a sucessor node of a BST:
def successor(root): if root is None: return None root = root.right while root.left: root = root.left return root All implementation of finding successor or predecessor takes O(1) constant space and run O(N) time (when BST is just a degraded linked list) – however, on average, the complexity is O(LogN) where the binary tree is balanced. Finding successor or predecessor is very useful – for example, we can use this to delete a node in a binary search tree. See also: Compute the Inorder Successor of a Binary Tree –EOF (The Ultimate Computing & Technology Blog) — GD Star Rating 745 words The Permanent URL is: Finding the Predecessor and Successor Node of a Binary Search Tree (AMP Version) Where is the inorder predecessor of a node A in a binary search tree?The in-order predecessor of a node in a Binary Search Tree is the node that comes before our key node when we write the inorder traversal of the tree.
Where is the predecessor in a binary search tree?Where is the predecessor of a node in a tree, assuming all keys are distinct? If X has two children, its predecessor is the maximum value in its left subtree and its successor the minimum value in its right subtree. If it does not have a left child, a node's predecessor is its rst left ancestor.
Where is inorder successor?Inorder Successor of a node in binary tree is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inorder traversal. In the above diagram, inorder successor of node 4 is 2 and node 5 is 1.
What is successor in binary search tree?In Binary Search Tree, Inorder Successor of an input node can also be defined as the node with the smallest key greater than the key of the input node. So, it is sometimes important to find next node in sorted order.
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