Question

Build a left-leaning red-black tree by adding the following three elements in the order in which they are listed. Keep track of the left-rotations, rightrotations, and color-flips as you build the tree. 462 left-rotations: right-rotation color-flip:

Answer 1

To build a left-leaning red-black tree, we follow certain rules and perform rotations and color flips. In this example, the elements 4, 6, and 2 are added in that order, resulting in a tree with elements 4 (black), 2 (red), and 6 (black).

Step-by-step explanation:

A left-leaning red-black tree is a self-balancing binary search tree in which the nodes are colored red or black. The tree satisfies certain properties, such as the root being black and the leaves being black. When adding elements to a left-leaning red-black tree, we perform rotations and color flips to maintain the balance and properties of the tree.

In this particular example, we need to add three elements in the given order: 4, 6, and 2.

1. We start by inserting 4 as the root of the tree. Since it is the first element, it is colored black.
2. Next, we insert 6 as the right child of 4. Since it is the second element and the parent (4) is black, the new node (6) is colored red.
3. Finally, we insert 2 as the left child of 4. Since it is the third element, we need to perform rotations and color flips to satisfy the properties of a left-leaning red-black tree.

To add the element 2, we perform a left rotation on the root (4) and a color flip between the root (4) and the left child (2). This results in a left-leaning red-black tree with the elements 4 (black), 2 (red), and 6 (black).