tail recursion in c - mitweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfcan we do the same...
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![Page 1: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/1.jpg)
Tail recursion in C
![Page 2: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/2.jpg)
Take this C code:
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
![Page 3: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/3.jpg)
Stack
main()
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
![Page 4: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/4.jpg)
Stack
main()always_zero(5)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
![Page 5: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/5.jpg)
Stack
main()always_zero(5)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
![Page 6: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/6.jpg)
Stack
main()always_zero(5)
always_zero(4)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
![Page 7: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/7.jpg)
Stack
always_zero(3)
main()always_zero(5)
always_zero(4)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
![Page 8: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/8.jpg)
Stack
always_zero(3)
main()always_zero(5)
always_zero(4)
always_zero(2)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
![Page 9: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/9.jpg)
Stack
always_zero(3)
main()always_zero(5)
always_zero(4)
always_zero(2)always_zero(1)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
![Page 10: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/10.jpg)
Stack
always_zero(3)
main()always_zero(5)
always_zero(4)
always_zero(2)
always_zero(0)
always_zero(1)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
![Page 11: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/11.jpg)
Stack
always_zero(3)
main()always_zero(5)
always_zero(4)
always_zero(2)always_zero(1)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
0
![Page 12: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/12.jpg)
Stack
always_zero(3)
main()always_zero(5)
always_zero(4)
always_zero(2)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
0
![Page 13: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/13.jpg)
Stack
always_zero(3)
main()always_zero(5)
always_zero(4)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
0
![Page 14: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/14.jpg)
Stack
main()always_zero(5)
always_zero(4)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
0
![Page 15: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/15.jpg)
Stack
main()always_zero(5)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
0
![Page 16: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/16.jpg)
Stack
main()
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
0
![Page 17: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/17.jpg)
A lot of unnecessary work and storage! Can we do better?
![Page 18: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/18.jpg)
Tail recursion
main()always_zero(5)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
![Page 19: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/19.jpg)
Tail recursion
main()always_zero(4)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
always_zero(5)
![Page 20: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/20.jpg)
Tail recursion
main()always_zero(3)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
always_zero(4)
![Page 21: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/21.jpg)
Tail recursion
main()always_zero(2)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
always_zero(3)
![Page 22: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/22.jpg)
Tail recursion
main()always_zero(1)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
always_zero(2)
![Page 23: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/23.jpg)
Tail recursion
main()always_zero(0)
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
always_zero(1)
![Page 24: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/24.jpg)
Tail recursion
main()
int always_zero(i){
if(i==0)return 0;
return always_zero(i-1);}
void main(){
always_zero(5);}
0
![Page 25: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/25.jpg)
Tail recursion
● Just discard unnecessary functions from the stack
● Same results● O(1) space instead of O(n) space● Faster too!
● Can we do this for all recursive algorithms?
![Page 26: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/26.jpg)
Take this C code:
int always_zero(i){
if(i==0)return 0;
return 5*always_zero(i-1);}
void main(){
always_zero(5);}
![Page 27: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/27.jpg)
Can we do the same trick?
● No! Results returned by always_zero(0) need to be further processed by always_zero(1)
● Results from always_zero(0) cannot be returned directly to main()
● Need to pass through always_zero(1), always_zero(2), always_zero(3), ...
![Page 28: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/28.jpg)
Tail recursion only works when we need no further processing.
![Page 29: Tail recursion in C - MITweb.mit.edu/pmitros/www/ceti/tail-recursion-in-c.pdfCan we do the same trick? No! Results returned by always_zero(0) need to be further processed by always_zero(1)](https://reader034.vdocuments.us/reader034/viewer/2022042401/5f100e617e708231d4473a64/html5/thumbnails/29.jpg)
Terminology
Scheme
Cfor(i=0; i<100; i++) {}
int f(int i){ if(i==0) return 0; return f(i-1);}
int f(int i){ if(i==0) return 1; else return i*f(i);}
Iteration Recursion
Iteration Normal recursionTail recursion