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Binary Search Tree Element Deletion Strategies

Explore three cases of removing elements from a Binary Search Tree, including leaf, single child, and two children scenarios, with detailed implementation strategies and examples. Learn how to efficiently manage deletion operations.

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Binary Search Tree Element Deletion Strategies

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  1. Removing elements from a Binary Search Tree • Strategy: search for the target to be removed, and then delete it • There are three cases to consider, where the element to be removed • Is a leaf • Has a single child • Has two children CS-2851Dr. Mark L. Hornick

  2. Case 1: Removing a leaf element from a Binary Search Tree • Strategy: search for the target to be removed, and then delete it • Implementation similar to search() When target is found, current.equals(target) if current == parent.left parent.left = null if current ==parent.right parent.right = null • This effectively removes the target object • Must be a leaf! • And we need a way to access the parent! CS-2851Dr. Mark L. Hornick

  3. Case 1 (easy): Removing leaf elements from a Binary Search Tree Remove 30, 97, 110 CS-2851Dr. Mark L. Hornick

  4. Case 2: Removing an element with a single child from a Binary Search Tree First search() When target is found, current.equals(target) if current == parent.left parent.left = child; child.parent = parent; if current == parent.right parent.right = child; child.parent = parent; • For a single child • child = current.leftor • child = current.right CS-2851Dr. Mark L. Hornick

  5. Case 2 Example: Removing 92 CS-2851Dr. Mark L. Hornick

  6. Case 3: Removing an element with two children from a Binary Search Tree Consider removing element 92 CS-2851Dr. Mark L. Hornick

  7. Case 3: Removing an element with two children from a Binary Search Tree (1) To preserve ordering, replace the element to be removed with • It’s immediate predecessor • Right-most element in left subtree • It’s immediate successor • Left-most element in right sub-tree • We need a way (a method) to find the predecessor or successor Note: The left child of the left-most entry will be null, and the right child of the right-most entry will be null. CS-2851Dr. Mark L. Hornick

  8. Case 3: Removing an element with two children from a Binary Search Tree (2a) • First, copy successor element to target element • Assume target is 92 • 95 replaces 92 • Next, delete “old” 95 • Treat this as case of an element with a single child CS-2851Dr. Mark L. Hornick

  9. Case 3: Removing an element with two children from a Binary Search Tree(2b) • Alternately, copy predecessor element to target element • Assume target is 92 • 87 replaces 92 • Next, delete “old” 87 • Treat this as case of an element with no children CS-2851Dr. Mark L. Hornick

  10. Case 3: Removing an element with two children from a Binary Search Tree (3) Replace 92 with successor Replace 92 with predecessor CS-2851Dr. Mark L. Hornick

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