$(10$ points$)$ Solve the instance $5,1,2,10,6$ of the coin$-$row problem.

a$.(8$ points$)$ Code implementation

b$.(2$ points$)$ Screenshot

$(10$ points$)$ Apply the dynamic programming algorithm to find all the solutions to the change$-$making

problem for the denominations $1,3,5$ and the amount n$=9.$

a$.(8$ points$)$ Code implementation

b$.(2$ points$)$ Screenshot

$(10$ points$)$ Find ALL LCSs of $($:$1,0,0,1,0,1,0,1$:$)$ and $($:$0,1,0,1,1,0,1,1,0$:$).$

a$.(8$ points$)$ Code implementation

b$.(2$ points$)$ Screenshot

$(15$ points$)$ How would you modify the dynamic programming algorithm for the coincollecting problem

if some cells on the board are inaccessible for the robot?

a$.(10$ points$)$ Code implementation.

b$.(5$ points$)$ Apply your algorithm to the board below, where the inaccessible cells are shown by X$\text{'}$s$.$ How

many optimal paths are there for this board?