Recursion

Hello!
I’m Esther
You can find me on Github at @mindplace

This sentence
has 26 letters in
it.

This sentence starts with
the word "this" and ends
with the word "word."

”
“Walking with me in the middle of town
he suddenly remarked to me, “Daddy,
not every boat has a lifeboat, has it?” I
said "How come?” “Well, the lifeboat
could have a smaller lifeboat, but then
that would be without one.”
- Edsger W. Dijkstra

In everyday life...
Cleaning the apartment:
◉ If this isn’t the last room in the apartment:
If this room is messy, clean it.
◉ Otherwise, move to next room.

“Robot, walk iteratively”
◉ Calculate the number of steps between
you and the specified wall
◉ Walk that many steps
◉ Stop

“Robot, walk
recursively”◉ If there is a wall in front of you, stop.
◉ Otherwise, take a step forward.
◉ Go to the beginning of the instructions.

Qualities of a
recursive function
◉ Solves a big problem by solving smaller parts in
the same way
◉ Has a base case
◉ Calls itself
◉ Executes itself by adding those calls to the stack

def factorial(n)
return 1 if n <= 1
n * factorial(n - 1)
end

Let’s see this
with a stack!

factorial(5)
● Is 5 <= 1?
5 * factorial(4) - waiting...

factorial(5)
● Is 5 <= 1? No.
● Return value of
5 * factorial(4)

factorial(5)
● Is 5 >= 1? No.
● Return value of
5 * factorial(4)
Is value of factorial(4)
known?

factorial(5)
● Is 5 >= 1? No.
● Return value of
5 * factorial(4)
Is value of factorial(4)
known? No.
Wait until value is found...

factorial(4)
● Is 4 <= 1?
4 * factorial(3) ...

factorial(4)
● Is 4 <= 1? No.
And so on, until...

factorial(1)
● Is 1 <= 1?
2 * fact(1)...
fact(1)...

factorial(1)
● Is 1 <= 1? Yes!
2 * fact(1)...
fact(1)...

factorial(1)
● Is 1 <= 1? Yes!
● Return 1
2 * fact(1)...
fact(1)...

Now we know value of
factorial(1), can return
2 * factorial(1)
2 * fact(1)...
fact(1)... => 1

Now we know value of
factorial(1), can return
2 * factorial(1)
This value gets returned to the
function that called it in the
first place...
2 * fact(1)...
fact(1)... => 1

That function was factorial(2)!
2 * fact(1)...
fact(1)... => 1

That function was factorial(2)!
Now that factorial(2) gets the
value of factorial(1), it can
return the value of
2 * factorial(1)...5 * factorial(4) - waiting...
2 * fact(1)...
fact(1)... => 1

Which gets returned to
factorial(3), the function that
called it.
2 * fact(1)...
fact(1)... => 1
=> 2

This bubbling back of values
continues until the original
general case function gets
back the value it’s waiting for,
value of factorial(4)...
2 * fact(1)...
fact(1)... => 1
=> 2

...and finally returns the
answer:
120
2 * fact(1)...
fact(1)... => 1
=> 2
=> 6
=> 24

◉ Sudoku board solver: having to make a guess, then
another guess inside that guess case…
◉ Tree problems
◉ “...the solution to a problem depends on solutions to
smaller instances of the same problem”
Lots of problems can
be solved
recursively...

◉ Stack overflow
◉ Web development: waiting on a stack of calls
to resolve can create a slow user experience
◉ Can ‘feel’ complicated
… but… recursion isn’t
always the best choice.

Classic problems:
Factorial
3! => 3 * 2! ...
Fibonacci sequence
Each item is the sum
of the previous two
items
Sorting algorithms
Merge sort, quicksort
Palindrome
rotor == rotor

Recap:
a recursive function...
◉ Solves the big problem by solving small parts
◉ Has a base case
◉ Calls itself
◉ Executes itself by adding those calls to the stack

Thanks!
Any questions?
You can find me at @mindplace

Credits
◉ Presentation template by SlidesCarnival
◉ Plant illustrations from Köhler's Medizinal-Pflanzen in naturgetreuen at BHL
◉ Quora, “How should I explain recursion to a 4-year-old?”
◉ StackOverflow!
◉ YouTube, Computerphile: “What on Earth is Recursion?”

Recursion

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