7 Questions
What are the two requirements for dynamic programming?
Dynamic programming requires optimal substructure and overlapping sub-problems.
Define optimal substructure in the context of dynamic programming.
Optimal substructure means that the solution to a problem can be obtained by combining optimal solutions to its sub-problems.
What does overlapping sub-problems mean for recursive algorithms?
Overlapping sub-problems means that recursive algorithms should solve the same sub-problems over and over.
How many times does dynamic programming solve each sub-problem?
Dynamic programming solves each sub-problem only once.
What are the two approaches to achieving efficiency in dynamic programming?
The two approaches to achieving efficiency in dynamic programming are the top-down and bottom-up approach.
What is memoization and how is it used in dynamic programming?
Memoization involves storing solutions to sub-problems in a table. In dynamic programming, it is used in the top-down approach to avoid solving the same sub-problems repeatedly.
In what type of languages is memoization an easily accessible design pattern?
Memoization is an easily accessible design pattern in term-rewrite based languages.
Study Notes
- Dynamic programming requires optimal substructure and overlapping sub-problems.
- Optimal substructure means that the solution to a problem can be obtained by combining optimal solutions to its sub-problems.
- Overlapping sub-problems means that recursive algorithms should solve the same sub-problems over and over.
- Dynamic programming solves each sub-problem only once.
- This can be achieved through a top-down or bottom-up approach.
- Top-down approach involves memoizing solutions to sub-problems in a table.
- Bottom-up approach involves solving small sub-problems first and building up to bigger sub-problems.
- Some programming languages have built-in memoization.
- Memoization is only possible for referentially transparent functions.
- Memoization is an easily accessible design pattern in term-rewrite based languages.
Test your knowledge on dynamic programming with this quiz! Learn about the important concepts of optimal substructure and overlapping sub-problems, and how dynamic programming solves each sub-problem only once. Explore the top-down and bottom-up approaches for solving sub-problems, and discover how memoization can be used to optimize the process. Whether you're a beginner or an expert, this quiz is perfect for anyone looking to improve their understanding of dynamic programming.
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