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CS 61A Discussion 3
Recursion
Attendance: links.cs61a.org/albert-disc Slides: albertxu.xyz/teaching/cs61a/
CS 61A Discussion 3 Recursion Albert Xu Attendance: - - PowerPoint PPT Presentation
CS 61A Discussion 3 Recursion Albert Xu Attendance: - - PowerPoint PPT Presentation
CS 61A Discussion 3 Recursion Albert Xu Attendance: links.cs61a.org/albert-disc Slides: albertxu.xyz/teaching/cs61a/ Announcements Recursion: an example Recursion: an example Here are the two key parts of recursion: 1) Base case 2) Recursive
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Recursion: an example
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Recursion: an example
Here are the two key parts of recursion: 1) Base case 2) Recursive call Look for them in this example.
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Recursion: an example
Base case
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Recursion: an example
Base case Recursive call (and multiply it by n)
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Recursion: an example
Base case Recursive call (and multiply it by n)
This function works because n! = n * (n - 1)!, which is our recursive call.
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Recursion: dominoes
1 2 3 4 5 6 . . .
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Recursion: dominoes
1 2 3 4 5 6 . . .
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Recursion: dominoes
1 2 3 4 5 6 . . . Let’s calculate factorial(4)!
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Recursion: dominoes
1 2 3 4 5 6 . . . factorial(4) = 4 * factorial(3)
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Recursion: dominoes
1 2 3 4 5 6 . . . factorial(3) = 3 * factorial(2)
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Recursion: dominoes
1 2 3 4 5 6 . . . factorial(2) = 2 * factorial(1)
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Recursion: dominoes
1 2 3 4 5 6 . . . factorial(1) = 1 * factorial(0)
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Recursion: dominoes
1 2 3 4 5 6 . . . factorial(1) = 1 * 1
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Recursion: dominoes
1 2 3 4 5 6 . . . factorial(1) = 1 * 1
When you’re writing code, assume the recursive call works!
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Approaching Recursion
hard functions are hard to write.
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Approaching Recursion
hard functions are hard to write. the first step is often the most difficult
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Approaching Recursion
hard functions are hard to write. the first step is often the most difficult
Write triangular. This computes the nth triangular number, which is 0 + 1 + 2 + … + n
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Approaching Recursion
hard functions are hard to write. the first step is often the most difficult
Write triangular. This computes the nth triangular number, which is 0 + 1 + 2 + … + n
Steps: 1) Recursive call(s) - what is a convenient subproblem that our
- verall problem shrinks to?
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Approaching Recursion
hard functions are hard to write. the first step is often the most difficult
Write triangular. This computes the nth triangular number, which is 0 + 1 + 2 + … + n
Steps: 1) Recursive call(s) - what is a convenient subproblem that our
- verall problem shrinks to?
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Approaching Recursion
hard functions are hard to write. the first step is often the most difficult
Write triangular. This computes the nth triangular number, which is 0 + 1 + 2 + … + n
Steps: 1) Recursive call(s) - what is a convenient subproblem that our
- verall problem shrinks to?
2) Build on the recursive call - what do I have to add to the result of the recursive call to get the answer to our overall problem
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Approaching Recursion
hard functions are hard to write. the first step is often the most difficult
Write triangular. This computes the nth triangular number, which is 0 + 1 + 2 + … + n
Steps: 1) Recursive call(s) - what is a convenient subproblem that our
- verall problem shrinks to?
2) Build on the recursive call - what do I have to add to the result of the recursive call to get the answer to our overall problem
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Approaching Recursion
hard functions are hard to write. the first step is often the most difficult
Write triangular. This computes the nth triangular number, which is 0 + 1 + 2 + … + n
Steps: 1) Recursive call(s) - what is a convenient subproblem that our
- verall problem shrinks to?
2) Build on the recursive call - what do I have to add to the result of the recursive call to get the answer to our overall problem 3) Base case - when do I stop… i.e. what is the smallest case
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Approaching Recursion
hard functions are hard to write. the first step is often the most difficult
Write triangular. This computes the nth triangular number, which is 0 + 1 + 2 + … + n
Steps: 1) Recursive call(s) - what is a convenient subproblem that our
- verall problem shrinks to?
2) Build on the recursive call - what do I have to add to the result of the recursive call to get the answer to our overall problem 3) Base case - when do I stop… i.e. what is the smallest case
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Thanks for coming.
Have a great rest of your week! :)
Attendance: links.cs61a.org/albert-disc Slides: albertxu.xyz/teaching/cs61a/