1. Recursion When performing a repetitive task either: a loop recursion
n! = n*(n-1)*...*1 with a loop
int fact(int n) {
int result = 1;
int i;
/* n! = 1*n*(n-1)*...*2 */
for(i=n; i>1; i--)
result = result*i;
return result; }
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2. n! with a recursive function
int fact(int n) {
int result = 1;
/* n = n * (n-1)! for n>1*/
if (n>1) result = n*fact(n-1);
return result; }
What is going on?
Recall that when calling a function,
arguments are passed BY VALUE
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3. An Example: Fact(4) fact(4) 24 (=4!) 4 n 4 * fact(3) result 6 3
n (different memory location)
result 6 3
3 * fact(2) n
result 2 2
2 * fact(1) 1 n
result 1 1
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4. Loop vs Recursion Any iterative algorithm (=Loop) can be
reworked to use recursion instead
Some algorithms are more naturally
written in terms of recursion
However, recursion is generally more time
consuming (overhead time)
The computer needs to store the location
in the program where the function is called {
... }
int fact(int n)
x = fact(n);
Store the address of this statement to
be able to come back here (store on the
stack).
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5. The Towers of Hanoi Move the tower of disks from the left to
the right peg
You can't place a larger disk on top of a
smaller one
Very well suited to a recursion algorithm
We know how to move 1 disk
To move n disks, move n-1 and then 1
To move n-1 disks, move n-2 and then 1
...
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6. void move(int ndisks,int peginit, int pegfinal, int pegtemp) {
Write a function: move
void move(int ndisks,int peginit,
int pegfinal, int pegtemp) {
/* move ndisks from peginit to
pegfinal, using pegtemp as a
temporary holding area */
if (ndisks ==1)
{/* easy! */}
else
/*move ndisks -1 to pegtemp*/
move(ndisks-1,peginit,pegtemp,pegfinal);
/*move the remaining disk to pegfinal*/
move(1,peginit,pegfinal,pegtemp);
/*move ndisks -1 to pegfinal*/
move(ndisks-1,pegtemp,pegfinal,peginit); }
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7. Another example Getting 'y' or 'n' from the user: char yes_or_no(void){
char answer;
printf("Enter 'y' or 'n': ");
scanf("%c",&answer);
if (answer!='y' && answer!='n')
/* flush the buffer */
fflush(stdin);
/* ask again */
answer = yes_or_no(); }
return answer;
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