How does a Red-Black Tree ensure balance after insertion?

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Question: How does a Red-Black Tree ensure balance after insertion?

Options:

Correct Answer: By performing rotations and recoloring

Solution:

Red-Black Trees maintain balance after insertion by performing rotations and recoloring nodes to satisfy the properties of the tree.

How does a Red-Black Tree ensure balance after insertion?

How does a Red-Black Tree ensure balance after insertion?

Step 1: Insert the new node as you would in a regular binary search tree. Color the new node red.
Step 2: Check if the parent of the new node is red. If the parent is black, the tree is still balanced, and you are done.
Step 3: If the parent is red, you have a violation of the Red-Black Tree properties. Find the uncle of the new node (the sibling of the parent).
Step 4: If the uncle is red, recolor the parent and the uncle to black, and the grandparent to red. Then, move up to the grandparent and repeat from Step 2.
Step 5: If the uncle is black (or null), you will need to perform rotations. Depending on the position of the new node (left or right), perform a left or right rotation on the parent or grandparent to fix the tree.
Step 6: After rotation, recolor the nodes as necessary to maintain the Red-Black Tree properties.

Red-Black Tree Properties – Red-Black Trees maintain specific properties (such as node color and balance) to ensure efficient operations.
Rotations – Rotations are tree restructuring operations that help maintain the balance of the tree after insertions.
Recoloring – Recoloring nodes is a technique used to adjust the colors of nodes to restore the properties of the Red-Black Tree.