Questions on red-black trees are very frequently asked in interview questions.
Red-black trees are specialized binary search trees which are always balanced, and hence overcomes the short coming of binary search trees which can become unbalanced, resulting in degraded efficiency of search operations.
Similar to other data structures, it is important to be thorough with the concepts of red-black trees, the common operations performed on red-black trees and the efficiency of these operations. Below interview questions on red-black trees addresses some of these topics. Java programming language will be used for code snippets when applicable to depict these concepts of red-black trees.
What are red-black trees? What problem do they solve
Binary search trees work well when they are ordered and balanced. But when new items are inserted into an ordered binary search tree, the binary search tree becomes unbalanced. With unbalanced trees the efficiency of searches degrades.
Red-black trees are specialized binary search trees with additional features which ensures that the trees are balanced.
How are red-black trees maintained in a balanced state?
Red-black trees are balanced during insertion and deletion od items to the tree. The insertion and deletion routines of the red-black tree check that certain characteristics of the tree are not violated. If these characteristics are violated, the routines re-structure the tree so that the tree remains in a balanced state.
What are the characteristics of red-black trees?
Following are the two characteristics of red-black trees.
1. Colored nodes: The nodes in a red-black tree are colored. Each node can be either red or black.
2. Red-black rules: When a node is inserted or deleted in a red-black tree. certain rules have to be followed to ensure that the tree remains balanced after the node deletion or insertion.
What are the rules that have to be followed when an item is inserted or deleted from a tree?
Followed are the rules that must be followed when a node is inserted or deleted from a red-black tree.
1. Every node is either a red node or a black node
2. The root node of the red-black tree is always black.
3. If a node is red then is child nodes must be black. The converse is not true. I.e. if a node is black then its child nodes can either be red or black.
4. Every path from the root node to a leaf node, or to a null node, must contain the same number of black nodes.
How do you fix rule violations when a node is inserted or deleted from a red-black tree?
There are two ways to fix rule violations in red-black trees.
1. Fix rule violations by changing the color of nodes.
2. Fix rule violations by performing rotations. A rotation is rearrangement of nodes that makes the tree more balanced.
What is the time efficiency of insertion, deletion and search operations on red-black trees?
Insertions, deletions and searches are the common operations performed on red-black trees.
The time efficiency of these operation on binary search trees is O(logN).
Data Structures - Interview Questions
