Coin$-$collecting Problem How would you modify the dynamic programming algorithm for the

coin$-$collecting problem if some cells on the board are inaccessible for the robot?

$($a$)$ Explain, in words, how this algorithm is different from the ordinary one in the book$/$lecture$.$

$($b$)$ Write pseudocode for this modified algorithm. The algorithm should have two inputs:

$C[1..n,1..m]$ that encodes the locations of the coins, and $B[1..n,1..m]$ that encodes the

locations of the inaccessible squares on the board. Your algorithm should return the

maximum number of coins that the robot can pick up$.$ Note that the robot has to start

in the upper$-$left, and finish in the lower$-$right $-$ so the location of the barriers might

make it impossible for the robot to solve the problem!.

$($c$)$ Use you algorithm to solve this problem instance $($O$\text{'}$s are coins, and X$\text{'}$s are inaccessible

places$).$

As part of your answer, fill out two grids like Figure $8\mathrm{.}3($b$)-($c$)$ in the textbook $($and

shown in lecture$),$ showing the maximum number of coins collectible up to each of the

squares on the board.