Write a memoized version of the recursive factorial function.

with the code:

$/*$ This program prints out a Fibonacci series $*/$

#include

$//$ Function Declaration

long fib $($long num$)$;

void fib$2($long num$)$;

long fibMemoized$($int num, int result$\_$cache$[])$;

int cnt$=0$;

int main $($void$)$

$\{$

$//$ Local Declarations

int result$\_$cache $[50]$;

int seriessize;

printf $("$This program prints a Fibonacci series.

$")$;

printf $("$How many numbers do you want? $")$;

scanf $("\%$d$",$ &seriessize$)$;

int fibn$=0$;

printf$("$

$")$;

for$($int i $=0$; i $<$ seriessize; i$++)$

$\{$

fibn $=$ fib$($i$)$;

printf$("$fib$(\%$d$)=\%3$d number of times $\%$d

$",$ i$,$ fibn, cnt$)$;

cnt $=0$;

$\}$

if $($seriessize $<2)$

seriessize $=2$;

printf$("$

$\backslash$ITERATIVELY

$")$;

fib$2($seriessize$)$;

for $($int looper $=0$; looper $<=$ seriessize; looper$++)$

result$\_$cache$[$looper$]=-1$;

result$\_$cache$[0]=1$;

result$\_$cache$[1]=1$;

cnt $=0$;

printf$("$

Optimized Fibonacci calls: $\%$d

$",$ seriessize$)$;

for $($int looper $=0$; looper $<$ seriessize; looper$++)$

$\{$

long temp;

temp $=$ fibMemoized $($looper$,$ result$\_$cache$)$ ;

printf$("$fib$(\%$d$)$ is $\%$ld

$",$ looper, temp$)$;

cnt$=0$;

$\}$

return $0$;

$\}//$ main

long fibMemoized$($int num, int result$\_$cache$[])$

$\{$

$//$ If results already calculated

if $($result$\_$cache $[$num$]>=0)$

return result$\_$cache $[$num$]$ ;

else

$\{$

$//$ printf $("$calling fib$(\%$d$)$

$",$ num$)$;

result$\_$cache $[$num$]=$ fibMemoized$($num $-1,$ result$\_$cache$)+$

fibMemoized$($num $-2,$ result$\_$cache$)$;

return result$\_$cache $[$num$]$;

$\}//$ fibMemoized

$\}$

$/*$ Calculates the nth Fibonacci number.

Pre num identifies Fibonacci number.

Post returns nth Fibonaci number.

$*/$

long fib $($long num$)$

$\{$

cnt$++$;

$//$ Statements

$//$ Base Case

if $($num $==0||$ num $==1)$

return $1$;

return $($fib $($num $-1)+$ fib $($num $-2))$;

$\}//$ fib

void fib$2($long num$)$

$\{$

int f$1=0,$ f$2=1,$ t;

$//$ if $($num $<=2)$

printf$("\%8$ld$",1)$;

for $($int i $=2$; i $<=$ num; i$++)$

$\{$

t $=$ f$2$;

f$2=$ f$1+$ f$2$;

f$1=$ t;

if $($f$2\%4)$

printf$("\%8$ld$",$ f$2)$;

else

printf$("$

$\%8$ld $",$ f$2)$;

$\}$

return;

$\}$

code for Fibonacci in $3$ ways using the code above

$($a$)$ Write an iterative version of the factorial function. Use it in a loop in the main function to go from $1$ to $20.$ Display the output in a nicely formatted way. $(5$ points$)$

$($b$)$ Write an recursive version of the factorial function. Use it in a loop in the main function to go from $1$ to $20.$ Display the output in a nicely formatted way. $(5$ points$)$

$($c$)$ Write an MEMOIZED recursive version of the factorial function. Use it in a loop in the main function to go from $1$ to $20.$ Display the output in a nicely formatted way. $(5$ points$)$

$($d$)$ What is the number of steps that are done for factorial$(20)$ by each of the $3$ methods. $(3$ points$).$

Upload the source code. Upload the images of the execution run. $($use a 'clear' theme.$)$