SLIDE 1
CS 61A Discussion 10
Tail Recursion
Slides: albertxu.xyz/teaching/cs61a/
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3)
CS 61A Discussion 10 Tail Recursion Albert Xu Slides: - - PowerPoint PPT Presentation
CS 61A Discussion 10 Tail Recursion Albert Xu Slides: - - PowerPoint PPT Presentation
CS 61A Discussion 10 Tail Recursion Albert Xu Slides: albertxu.xyz/teaching/cs61a/ The Cost of Recursion aint no free lunch (define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1))))) scm> (factorial 3) The Cost of Recursion
SLIDE 2
SLIDE 3
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3)
SLIDE 4
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3)
SLIDE 5
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3)
SLIDE 6
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3)
SLIDE 7
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3)
SLIDE 8
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3)
SLIDE 9
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3)
SLIDE 10
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3)
SLIDE 11
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3) scm> (factorial 10)
SLIDE 12
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3) scm> (factorial 10)
SLIDE 13
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3) scm> (factorial 10)
…11 frames!
SLIDE 14
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3) scm> (factorial 10)
How much memory does factorial take? Use big-theta notation! …11 frames!
SLIDE 15
The Cost of Recursion
ain’t no free lunch
(define (factorial n) (if (= n 0) 1 (* n (factorial (- n 1)))))
scm> (factorial 3) scm> (factorial 10)
How much memory does factorial take? Use big-theta notation! θ(n) …11 frames!
SLIDE 16
Tail Call Optimization
ain’t no free lunch
(define (factorial n sofar) (if (= n 0) sofar (factorial (- n 1) (* sofar n)))))
SLIDE 17
Tail Call Optimization
ain’t no free lunch
(define (factorial n sofar) (if (= n 0) sofar (factorial (- n 1) (* sofar n)))))
scm> (factorial 3 1)
SLIDE 18
Tail Call Optimization
ain’t no free lunch
(define (factorial n sofar) (if (= n 0) sofar (factorial (- n 1) (* sofar n)))))
scm> (factorial 3 1)
SLIDE 19
Tail Call Optimization
ain’t no free lunch
(define (factorial n sofar) (if (= n 0) sofar (factorial (- n 1) (* sofar n)))))
scm> (factorial 3 1)
SLIDE 20
Tail Call Optimization
ain’t no free lunch
(define (factorial n sofar) (if (= n 0) sofar (factorial (- n 1) (* sofar n)))))
scm> (factorial 3 1)
SLIDE 21
Tail Call Optimization
ain’t no free lunch
(define (factorial n sofar) (if (= n 0) sofar (factorial (- n 1) (* sofar n)))))
scm> (factorial 3 1)
SLIDE 22
Tail Call Optimization
ain’t no free lunch
How much memory does factorial take now? Use big-theta notation! (define (factorial n sofar) (if (= n 0) sofar (factorial (- n 1) (* sofar n)))))
scm> (factorial 3 1)
θ(1)
SLIDE 23
Is Tail Call Optimization Worth it?
Discuss: what are the benefits and what are the drawbacks of tail-call optimization?
SLIDE 24
Is Tail Call Optimization Worth it?
Discuss: what are the benefits and what are the drawbacks of tail-call optimization?
More memory efficient! Constant, instead of linear space.
+
SLIDE 25
Is Tail Call Optimization Worth it?
Discuss: what are the benefits and what are the drawbacks of tail-call optimization?
More memory efficient! Constant, instead of linear space.
+
- Impossible to trace errors back.
SLIDE 26
Is Tail Call Optimization Worth it?
Discuss: what are the benefits and what are the drawbacks of tail-call optimization?
More memory efficient! Constant, instead of linear space.
+
- Impossible to trace errors back.
Because of this drawback, Python does not perform tail-call optimization.
SLIDE 27
Tail Contexts
Tail contexts are locations in Scheme expressions where recursive calls would be the last operation performed in a frame! Why is this important?
Question: What makes a Scheme function tail recursive - in the context of tail calls? Check
- ut this example if you’re not sure…
…recursive calls in tail contexts are called tail calls! (define (factorial n sofar) (if (= n 0) sofar (factorial (- n 1) (* sofar n)))))
SLIDE 28
Identifying Tail Contexts
How can you tell what is a tail context?
SLIDE 29
Identifying Tail Contexts
How can you tell what is a tail context? …some examples