Activity Selection Problem with allowing shifting starting time

Hi

As you would know, activity selection is well known problem and has a nice solution with dynamic programming and also greedy approach.

I encountered a modified version of the problem where, each activity can be shifted to earlier or later in time by maximum t seconds which is given. Duration remains same after shifting. By this flexibility, we would have more selected activity than the original problem.

However, I could not figure out how to design the algoritm. Can anyone help me?

Thanks

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