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56 lines
1.7 KiB
Markdown
56 lines
1.7 KiB
Markdown
## dynamic programming
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<br>
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* dynamic programming is the process of taking a recursive algorithm and cache overlapping problems (repeated calls).
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* the runtime is given by the number of calls.
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* **top-down**: how can we divide the problem into sub-problems?
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* top-down dynamic programming is called **memoization**.
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* **bottom-up**: solve for a simple case, then figure out for more elements.
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<br>
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---
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### recursion
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<br>
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* recursion is an approach to solving problems using a function that calls itself as a subroutine. every time the function calls itself, it reduces the problem into subproblems. the recursion calls continue until it reaches a point where the subproblem can be solved without further recursion.
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* a recursive function should have the following properties so it does not result in an infinite loop:
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* one or more base cases (a terminating scenario that does not use recursion to produce an answer)
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* a set of rules, also known as recurrence relation, that reduces all other cases towards the base case.
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* there can be multiple places where the function may call itself.
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* any recursion problem can be solved iteratively and vice-versa.
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<br>
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#### vizualing the stack
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<br>
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* to visualize how the stack operates during recursion calls, check the example below where we reverse a string:
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```python
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def reverse(s):
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if len(s) == 0:
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return s
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else:
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return reverse(s[1:]) + s[0]
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```
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<br>
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---
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### memoization
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<br>
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* memoization is an optimization technique that avoids recursion's duplicate calculations.
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* it's primarily used to speed up code by storing the intermediate results in a cache so that it can be reused later.
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* for example, a hash table can be used as a cache and should be passed along each subroutine call.
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