Factorial

ALGORITHM $1$ A Recursive Algorithm for Computing $n!.$

procedure factorial $(n$ : nonnegative integer$)$

if $n=0$ then return $1$

else return $n*$ factorial $(n-1)$

$\{$output is $n!\}$

Trace the function call: int result $=$ factorial$(5)$; trace all of the recursive calls and return values

$\backslash$table$[[$Argument$($s$),\backslash$table$[[$Return statement$],[($base case OR recursive$],[$call$)]],$Return value$],[,,],[,,],[,,],[,,],[,,],[,,],[,,]]$

GCD

ALGORITHM $3$ A Recursive Algorithm for Computing ged$(a,b).$

procedure : nonnegative integers with $a=0bgcd(bmoda,a)gcd(a,b)=gcd(21,49)a$