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Questions and Answers
What are the two requirements for dynamic programming?
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.
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?
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?
How many times does dynamic programming solve each sub-problem?
What are the two approaches to achieving efficiency in dynamic programming?
What are the two approaches to achieving efficiency in dynamic programming?
What is memoization and how is it used in dynamic programming?
What is memoization and how is it used in dynamic programming?
In what type of languages is memoization an easily accessible design pattern?
In what type of languages is memoization an easily accessible design pattern?
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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.
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