You are asked to implement the $0/1$ Knapsack Problem using the ARM Cortex MO$+$ architecture. In this problem, each item has a weight $($W$)$ and a profit $($P$).$ Our knapsack has a limited weight capacity $($W$).$ The objective is to maximize the profit without exceeding the weight capacity of the knapsack.

a$)(50$ Points$)$ You are asked to implement the $0/1$ knapsack problem recursively as given below.

$```$

#define W$\_$Capacity $50$

#define SIZE $3$

int profit$[]=\{60,100,120\}$;

int weight$[]=\{10,20,30\}$;

int max$($int a$,$ int b$)\{$

return a$>$b$?$ a : b;

$\}$

int knapSack$($int W$,$ int n$)$

$\{$

if $($n $==0||$ w $==0)$

return $0$;

if $($weight$[$n $-1]>$ w$)$

return knapSack$($W$,$ n $-1)$;

else

return max$($knapSack$($w$,$ n $-1),$

profit$[$n $-1]+$ knapSack$($W $-$ weight$[$n $-1],$ n $-1))$;

$\}$

void main$()$

$\{$

int value $=$ knapSack$($w$\_$Capacity, SIZE$))$;

while$(1)$;

$\}$

$```$ b$)(50$ Points$)$ You are asked to implement the $0/1$ knapsack problem iteratively as given below.

$```$

#define w$\_$Capacity $50$

#define SIZE $3$

int profit$[]=\{60,100,120\}$;

int weight$[]=\{10,20,30\}$;

int dp$[$w$\_$Capacity$]=\{0\}$;

int max$($int a$,$ int b$)\{$

return a$>$b $?$ a : b;

$\}$

int knapSack$($int W$,$ int n$)$

$\{$

for $($int i $=1$; i $$ n $+1$; i$++)\{$

for $($int w $=$ w; w $>=0$; w$--)\{$

if $($weight$[$i w$)$

dp$[$w$]=$ max$($dp$[$w$],$

dp$[$w $-$ weight$[$i $-1]]+$ profit$[$i $-1])$;

$\}$

$\}$

return dp$[$W$]$;

$\}$

void main$()$

$\{$

int value $=$ knapSack$($w$\_$Capacity, SIZE$))$;

while$(1)$;

$\}$

$```$

Constraints:

$\backslash (\backslash$cdot $\backslash )$ Your main function name or label must be $"\_\_$main".

$-$ Your code should include a comment for each line. Otherwise, points will be deducted.

$-$ The program must be implemented with Arm Cortex M$0+$ assembly language.

$-$ Your assembly source file is expected to work with Keil $\backslash (\backslash$mu $\backslash )$ Vision IDE v$5.$

$-$ Default configuration must be sufficient to run your programs. If your program expects any different configuration parameter, please write this at the top of the code in comment lines.

$-$ If your program does not run with Keil $\backslash (\backslash$mu $\backslash )$ Vision IDE you will get zero point from this question.

$-$ At the end of the program, ensure that R$0$ stores the value variable from the main function, R$1$ stores the starting address of the profit array, R$2$ stores the starting address of the weight array, and R$3$ stores the address of the dp array $($if available$).$