I'm trying to solve a problem, so I'm not looking for code, but for similar algorithms so I can solve it myself.

I am given n bookcases each with a size amount of books inside. I am to move some of these bookcases to a new room as follows:

• The first bookcase will always be moved;
• I will keep the order of the bookcases in the new room (I can't change positions in the new room);
• Bookcase i cannot be placed next to either of the bookcases i-1 or i+1 (ex: I can't place ?-4-5-?/?-5-6-?/?-4-5-6-?);

So bookcase 1 is always in the new room. Furthermore, if bookcase i is in the room, then neither i-1, nor i+1 will be in the room.

Which configuration of bookcases will offer me the largest amount of books?

I understand that this is solved using a dynamic programming algorithm, but I am not sure which one. I initially thought it would be similar to the knapsack problem, but I don't have a limit of books so it's clearly different (at least I think it is). The target complexity is O(n), but any idea that will help me will do.

Any suggestions are greatly appreciated!

small edit: This was originally posted on SO, but I was told that this would be a better place for this question.

I'm trying to solve a problem, so I'm not looking for code, but for similar algorithms so I can solve it myself.

I am given n bookcases each with a size amount of books inside. I am to move some of these bookcases to a new room as follows:

• The first bookcase will always be moved;
• I will keep the order of the bookcases in the new room (I can't change positions in the new room);
• Bookcase i cannot be placed next to either of the bookcases i-1 or i+1 (ex: I can't place ?-4-5-?/?-5-6-?/?-4-5-6-?);

So bookcase 1 is always in the new room. Furthermore, if bookcase i is in the room, then neither i-1, nor i+1 will be in the room.

Which configuration of bookcases will offer me the largest amount of books?

I understand that this is solved using a dynamic programming algorithm, but I am not sure which one. I initially thought it would be similar to the knapsack problem, but I don't have a limit of books so it's clearly different (at least I think it is). The target complexity is O(n), but any idea that will help me will do.

I'm trying to solve a problem, so I'm not looking for code, but for similar algorithms so I can solve it myself.

I am given n bookcases each with a size amount of books inside. I am to move some of these bookcases to a new room as follows:

• The first bookcase will always be moved;
• I will keep the order of the bookcases in the new room (I can't change positions in the new room);
• Bookcase i cannot be placed next to either of the bookcases i-1 or i+1 (ex: I can't place ?-4-5-?/?-5-6-?/?-4-5-6-?);

Which configuration of bookcases will offer me the largest amount of books?

I understand that this is solved using a dynamic programming algorithm, but I am not sure which one. I initially thought it would be similar to the knapsack problem, but I don't have a limit of books so it's clearly different (at least I think it is). The target complexity is O(n), but any idea that will help me will do.

Any suggestions are greatly appreciated!

small edit: This was originally posted on SO, but I was told that this would be a better place for this question.

I'm trying to solve a problem, so I'm not looking for code, but for similar algorithms so I can solve it myself.

I am given n bookcases each with a size amount of books inside. I am to move some of these bookcases to a new room as follows:

• The first bookcase will always be moved;
• I will keep the order of the bookcases in the new room (I can't change positions in the new room);
• Bookcase i cannot be placed next to either of the bookcases i-1 or i+1 (ex: I can't place ?-4-5-?/?-5-6-?/?-4-5-6-?);

So bookcase 1 is always in the new room. Furthermore, if bookcase i is in the room, then neither i-1, nor i+1 will be in the room.

Which configuration of bookcases will offer me the largest amount of books?

I understand that this is solved using a dynamic programming algorithm, but I am not sure which one. I initially thought it would be similar to the knapsack problem, but I don't have a limit of books so it's clearly different (at least I think it is). The target complexity is O(n), but any idea that will help me will do.

Any suggestions are greatly appreciated!

small edit: This was originally posted on SO, but I was told that this would be a better place for this question.