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    Lab 12: Fruitful Recursion
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# Lab 12: Fruitful Recursion


## [Worksheet Solutions](https://docs.google.com/document/d/1mdtdx5uTbnt1SF181y_Tm_vxm2vy5PEkZ3n7u_i4KvU/edit?usp=sharing)
## [Python Solutions](/content/labs/lab12/solutions) 


## Summary
+ Part 0: Worksheet warm-up
+ Part 1: Simple Fruitful Recursion 
+ Part 2: Branching Recursion
+ Part 3: Extra Exercises


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- Note that 


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## Big Questions {.bigqs}

- **In a fruitful recursive function, which function frames contribute to the
  value returned by the original function frame?**
  <details class="answer">
    <summary>Show Answer</summary>
    The answer here is "all of them." Although only the original function frame
    directly returns the result value, it will typically use information
    returned by other function frames to construct that value, so all of the
    function frames end up contributing to the eventual result somehow.
  </details>

- **When writing a loop, we often need to initialize a counter or result
  variable before the loop starts. How can we do that in a recursive
  function?**
  <details class="answer">
    <summary>Show Answer</summary>
    You can't really do the same thing, since each function call frame
    gets its own variables. However, you can initialize something in the
    base case of your recursive function and then return it, making it
    available for the next-higher function call frame to modify and
    return, which ends up achieving the same effect.
  </details>

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