18. Recursion
Recursive functions utilize inductive definitions, as seen in the factorial function and Fibonacci series. This chapter explores how inductive reasoning leads to recursive implementations in Python, examining list structures and sorting algorithms like insertion sort. The relationship between recursion and efficiency is also discussed, highlighting practical challenges such as the recursion limit in Python and the need for robust algorithms for larger datasets.
Sections
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What we have learnt
- Recursive functions are defined based on inductive definitions.
- Inductive definitions allow for the creation of recursive computations that accurately reflect mathematical structures.
- Python imposes a recursion depth limit, which can be adjusted but requires careful management.
Key Concepts
- -- Recursion
- A method of solving problems where the solution depends on solutions to smaller instances of the same problem.
- -- Inductive Definition
- A way to define objects in terms of simpler or smaller objects, leading to recursive functions.
- -- Recursion Limit
- A constraint in Python that limits the depth of recursion to prevent infinite loops and stack overflow.
- -- Fibonacci Series
- A sequence where each number is the sum of the two preceding ones, usually starting with 0 and 1.
- -- Insertion Sort
- A simple sorting algorithm that builds a sorted list one element at a time by repeatedly picking the next element from the unsorted portion.
Additional Learning Materials
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