freeloading.

There is a common interview problem called the "Unique Paths" problem. You have a grid of rows and columns. Write a function that takes as arguments the number of rows and the number of columns. It should calculate the number of possible unique "shortest" paths from the upper$-$leftmost square to the lower$-$rightmost square. By shortest what we mean is that you can only move down or to the right, there are other unique paths that can imagine involving moving left or up$,$ but those would just have wasted moves to get to the destination.

Below is what the grid looks like with three rows and seven columns. You want to get from the $"$S$"($Start$)$ to the $"$F$"($Finish$).$ Remember that you do not need to come up with the paths taken, just the number of unique paths that can exist. Hint, this problem is VERY similar to one of the famous problems solved using recursion we discussed this week, Fibonacci.

In addition I want you and your team to come up with a more efficient solution using one of the two techniques used in dynamic programming. Either take a bottom up approach and avoid recursion altogether or utilize memoization. Your choice. $($I want you to beat out all of the other applicants for this fictional job.$)$ So use one of the "Dynamic Programming" techniques from this week.