$1.$ Write and test a C$++$ program to implement the following algorithms:

$$ GCD computation using iterative and recursive algorithms

$$ Tower of Hanoi displaying the order of moving disks using recursive algorithm.

The pseudocode for algorithms are given as below:

GCD$\_$Iterative$($a$,$ b$)$

While b $!=0$

temp $$ a mod b

a $$ b

b $$ temp

return a

GCD$\_$Recursive$($a$,$ b$)$

If b $=0$

Return a

Else

Return GCD$\_$Recursive$($b$,$ a mod b$)$

Tower$\_$Of$\_$Hanoi$($N$,$ From, To$,$ Via$)$

$//$ From, To$,$ Via are string variables, N is integer

If N $=0$

Return

Tower$\_$Of$\_$Hanoi$($N$-1,$ From, Via, To$)$

Print $$Move Disk $$ n $$from $$ From $$To $$ To

Tower$\_$Of$\_$Hanoi$($N$-1,$ Via, To$,$ From$)$

In all these functions, introduce a runtime for computations of runtime.

Initialize the runtime for each one to $0$ in the beginning of main.

Then increment by $1$ relevant runtime in each of the three functions

From the main, call each of the functions with suitable inputs.

For GCD$,$ a and b must be user inputs

For the Tower problem, send names of tower $($say A$,$ B$,$ C or tower$1,$ tower$2,$ tower$3)$ and number of disks as user inputs $($this must be done either at the time of calling the function or prior to it$.$