In a Binary Search Tree (BST), the Lowest Common Ancestor (LCA) of two nodes is defined as the lowest (i.e., deepest) node in the tree that has both of the given nodes as descendants.
Here are a few key points about the LCA in a BST:
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Binary Search Tree Property: In a BST, all nodes in the left subtree of a node have values less than the node's value, and all nodes in the right subtree have values greater than the node's value.
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LCA Characteristics: The LCA of two nodes in a BST is the node at which the paths from the root to the two nodes diverge. It's the node with the smallest value that is greater than or equal to the value of one node and less than or equal to the value of the other node.
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Path Comparison: One way to identify the LCA is to compare the values of the two nodes with the current node's value while traversing the tree from the root downward. Based on the comparison, you can determine whether to move to the left or right subtree to search for the LCA.
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Recursive Approach: A common approach to finding the LCA in a BST is to use recursion. Starting from the root, recursively search for the LCA by comparing the values of the current node with the values of the two target nodes. Based on the comparison, navigate to the left or right subtree accordingly until the LCA is found.
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Iterative Approach: Alternatively, you can use an iterative approach without recursion. Start from the root and traverse down the tree iteratively, comparing the values of the current node with the values of the two target nodes to determine the direction of traversal.
Overall, the LCA in a Binary Search Tree is the node with the smallest value that is greater than or equal to one node's value and less than or equal to the other node's value. It's a fundamental concept in BSTs and is commonly used in various tree-related algorithms and problem-solving tasks.
