Given an n$-$sided die, we want to determine how many different ways one could repeatedly sum die rolls and

get to a given total.

For instance, given a $4-$sided die, we could obtain a total of $3$ in four different ways:

$1+1+1($rolling a $1$ three times$)$

$1+2($rolling a $1$ and then rolling a $2)$

$2+1($rolling a $2$ and then rolling a $1)$

$3($rolling a $3)$

We will write two different functions to solve this problem. Each functions takes $n($the number of sides on

the die$)$ and total $($the total to which we'll sum rolls$)$ as input. Each function must use its corresponding

dynamic programming methodology in order to solve the problem.

vays$\_$to$\_$sum$\_$memo$($n$,$ total$)$

must use memoization

vays$\_$to$\_$sum$\_$tab$($n$,$ total$)$

must use tabulation

$$ ways$\_$to$\_$sum$\_$memo $,$ total $=3$

$4$

$$ ways$\_$to$\_$sum$\_$tab$(n=4,$ total$=3)$

$4$

Imports

No imports allowed on this assignment, with the following exceptions:

Any modules you have written yourself

typing $-$ this is not required, but some students have requested it

For testing only $($do not use these for functionality in any other classes$/$algorithms$)$:

unittest

random