Lecture 321:- Red-Black Tree Deletion Examples

let's go through a few examples of Red-Black Tree deletion to illustrate the different cases and balancing operations involved. We will consider a Red-Black Tree before and after deletion for each example.

Example 1: Deleting a Red Node with 0 or 1 Children

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Initial Red-Black Tree:        8 (Black)       / \      4   10 (Red) Deleting node 10 (Red): Resulting Red-Black Tree:        8 (Black)       /      4

Example 2: Deleting a Black Node with 1 Red Child

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Initial Red-Black Tree:        8 (Black)       / \      4   10 (Black)            \             14 (Red) Deleting node 10 (Black) with a red child: Resulting Red-Black Tree:        8 (Black)       / \      4   14 (Black)

Example 3: Deleting a Black Node with 2 Black Children (Case 3)

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Initial Red-Black Tree:        8 (Black)       / \      4   14 (Black)         /  \        10   17 Deleting node 4 (Black) with two black children: Resulting Red-Black Tree:        14 (Black)       /   \      8     17 (Black)     /    10

Example 4: Deleting a Black Node with 2 Black Children (Case 3b and 3c)

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Initial Red-Black Tree:        10 (Black)       / \      5   15 (Black)         /  \        12   20 (Black) Deleting node 5 (Black) with two black children: Resulting Red-Black Tree:        15 (Black)       /   \      10    20 (Black)             /            12

In the above examples, we saw different scenarios of deleting nodes in a Red-Black Tree and how the tree is adjusted to maintain the Red-Black properties. The cases involved various recoloring and rotation operations to ensure that the tree remains balanced and satisfies the Red-Black properties after each deletion. Note that these are just simplified examples, and real-world Red-Black Tree deletions can involve more complex situations with multiple balancing operations.