Question

how would you modify the dynamic programming algorithm for the coin- collecting problem if some cells on the board are inaccessible for the robot?

Answer 1

To consider inaccessible cells on the board, modify the algorithm by assigning a high cost or negative value to such cells.

Step-by-step explanation:

In the coin-collecting problem, the dynamic programming algorithm can be modified to account for inaccessible cells on the board. One way to do this is by assigning a high cost or negative value to the inaccessible cells, so that the robot will not consider them as viable options for collecting coins.

For example, if the original algorithm assigns a value of 0 to accessible cells and 1 to collecting a coin, the modified algorithm can assign a high cost (e.g., 9999) or a negative value (e.g., -1) to inaccessible cells. This way, the robot will avoid choosing those cells in its path.

By incorporating this modification, the dynamic programming algorithm can still optimize the collection of coins while avoiding inaccessible cells.

Answer 2

Step-by-step explanation:

To modify the dynamic programming algorithm for the coin-collecting problem when some cells on the board are inaccessible for the robot, we need to account for these inaccessible cells in our calculations. Here are the modifications:

Initialize the dynamic programming table: Set the value of inaccessible cells to negative infinity or any other suitable value that indicates they are not reachable.

Update the transition rules: When calculating the maximum number of coins collected at each cell, consider only the cells that are accessible. Exclude the inaccessible cells from the calculations. This ensures that the robot does not consider inaccessible cells as valid options for movement.

Handle boundary cases: If the starting cell or the destination cell is inaccessible, adjust the initialization and termination conditions accordingly. For example, if the starting cell is inaccessible, set the value of the starting cell in the dynamic programming table to 0 or any other suitable value.

By incorporating these modifications, the dynamic programming algorithm will properly handle the presence of inaccessible cells on the board and compute the maximum number of coins the robot can collect while avoiding those inaccessible cells.