Compare the following three algorithms. When is the algorithm of part la correct.?

a$.$ INPUT $n,x_1,x_2,$dots,$x_n.$

OUTPUT PRODUCT.

Step $1$ Set PRODUCT $=0.$

Step $2$ For $i=1,2,$dots,$n$ do

Set PRODUCT $=$ PRODUCT $**x_i.$

Step $3$ OUTPUT PRODUCT; STOP.

b$.$ INPUT $n,x_1,x_2,$dots,$x_n.$

OUTPUT PRODUCT.

Step $1$ Set PRODUCT $=1.$

Step $2$ For $i=1,2,$dots,$n$ do

Set PRODUCT $=$ PRODUCT $**x_i.$

Step $3$ OUTPUT PRODUCT; STOP.

c$.$ INPUT $n,x_1,x_2,$dots,$x_n.$

OUTPUT PRODUCT.

Step $1$ Set PRODUCT $=1.$

Step $2$ For $i=1,2,$dots,$n$ do

if $x_i=0$ then set PRODUCT $=0$;

OUTPUT PRODUCT;

STOP

else set PRODUCT $=$ PRODUCT $**x_i.$

Step $3$ OUTPUT PRODUCT; STOP.