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In a Red-Black tree, what property ensures that the tree remains balanced?

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Question: In a Red-Black tree, what property ensures that the tree remains balanced?

Options:

  1. Every node has two children
  2. The root is always black
  3. No two red nodes can be adjacent
  4. All leaves are at the same level

Correct Answer: No two red nodes can be adjacent

Solution: 

In a Red-Black tree, no two red nodes can be adjacent, which helps maintain balance and ensures that the longest path from the root to a leaf is no more than twice as long as the shortest path.

In a Red-Black tree, what property ensures that the tree remains balanced?

Practice Questions

Q1
In a Red-Black tree, what property ensures that the tree remains balanced?
  1. Every node has two children
  2. The root is always black
  3. No two red nodes can be adjacent
  4. All leaves are at the same level

Questions & Step-by-Step Solutions

In a Red-Black tree, what property ensures that the tree remains balanced?
  • Step 1: Understand what a Red-Black tree is. It is a type of binary search tree that has specific properties to keep it balanced.
  • Step 2: Learn about the color of the nodes. In a Red-Black tree, each node is either red or black.
  • Step 3: Know the key property: No two red nodes can be adjacent. This means that if a node is red, its children must be black.
  • Step 4: Understand how this property helps balance the tree. By preventing two red nodes from being next to each other, the tree avoids long chains of red nodes that could make it unbalanced.
  • Step 5: Recognize the result of this property: The longest path from the root to a leaf (the longest chain of nodes) is no more than twice as long as the shortest path. This keeps the tree balanced.
  • Red-Black Tree Properties – A Red-Black tree is a type of self-balancing binary search tree that maintains balance through specific properties, including the rule that no two red nodes can be adjacent.
  • Tree Height and Balance – The property that ensures the longest path from the root to a leaf is no more than twice as long as the shortest path is crucial for maintaining the balance of the tree.
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