I had to think for some time on this one. Finally it occurred to me, that the pieces are some x distance apart on an average.
At any snapshot, the pieces are lying with a Gaussian distribution around x multiples along the belt i.e having sigma at x, 2x, 3x,...nx....
So for the bins to not overlap:
1) their width/span-along-the-belt should be lesser than x
2) And they can be placed at x, 3x/2, 5x/2, 7x/2 (i.e. prime multiples of x/2)
Wow! Learnt something useful today. Thank you. :)
Edit: I realize after posting that, my solution won't work! If somebody can explain how the prime thing works will be great. I can imagine, though, that the bin placements should be such that, at any given time the piece is only in front of a single bin. Meaning, no pair of bins should have a distance of x-multiple. I can guess, perhaps heuristics which work well, can be devised. But it will be great to know the mathematical solution for this.
At any snapshot, the pieces are lying with a Gaussian distribution around x multiples along the belt i.e having sigma at x, 2x, 3x,...nx....
So for the bins to not overlap:
1) their width/span-along-the-belt should be lesser than x
2) And they can be placed at x, 3x/2, 5x/2, 7x/2 (i.e. prime multiples of x/2)
Wow! Learnt something useful today. Thank you. :)
Edit: I realize after posting that, my solution won't work! If somebody can explain how the prime thing works will be great. I can imagine, though, that the bin placements should be such that, at any given time the piece is only in front of a single bin. Meaning, no pair of bins should have a distance of x-multiple. I can guess, perhaps heuristics which work well, can be devised. But it will be great to know the mathematical solution for this.