24. Module – 02
The chapter discusses memoization and dynamic programming as strategies to optimize recursive computations, particularly in the context of defining functions like Fibonacci. Memoization prevents redundant calculations by storing previously computed results, while dynamic programming eliminates recursion by systematically filling in values based on identified dependencies. Through these strategies, computational efficiency improves significantly, addressing the challenges of overlapping subproblems in recursive definitions.
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What we have learnt
- Memoization involves storing results of expensive function calls and reusing them when the same inputs occur again.
- Dynamic programming transforms recursive formulations into iterative processes to enhance efficiency.
- Understanding the structure of dependencies in problems is vital in effectively applying dynamic programming methods.
Key Concepts
- -- Memoization
- A technique where results of expensive function calls are stored to avoid repeating the same calculations.
- -- Dynamic Programming
- An optimization method that solves complex problems by breaking them down into simpler subproblems and solving these subproblems just once.
- -- Fibonacci Numbers
- A sequence where each number is the sum of the two preceding ones, typically starts with 0 and 1.
- -- Inductive Definition
- A way of defining functions or sequences where the function is defined in terms of itself with base cases.
- -- Computational Tree
- A representation of the recursive calls made during the evaluation of a function, displaying the relationships between different subproblems.
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