Dynamic Programming: Memoization

Dynamic Programming: Memoization

What is Memoization?

• Memoization is a technique used in dynamic programming to optimize performance by storing and reusing previously computed results.
• It is a form of caching that avoids redundant computations by remembering the results of expensive function calls.

How Memoization Works

1. Create a cache: Store the results of function calls in a cache data structure (e.g., array, dictionary, or hash table).
2. Check the cache: Before computing a result, check if it's already in the cache.
3. Return cached result: If the result is in the cache, return it immediately.
4. Compute and cache result: If not in the cache, compute the result, store it in the cache, and return it.

Benefits of Memoization

• Reduced computation time: Avoids redundant computations by reusing previously computed results.
• Improved performance: Can significantly speed up complex computations.

Example

Consider a function fib(n) that computes the n-th Fibonacci number. Without memoization, the function would recursively compute the same sub-problems multiple times. With memoization, the function stores the results of sub-problems in a cache, avoiding redundant computations.

Common Applications

• Dynamic programming algorithms: Memoization is often used in dynamic programming to optimize performance.
• Caching: Used in web development to cache frequently accessed data.
• Database query optimization: Memoization can be used to cache query results to improve database performance.