ex1)

The optimal route for Farmer John is as follows:

At time 1, move to node 3, which now has 1⋅2=2 grass and so needs 2 fertilizer.

At time 2, move to node 5, which now has 2⋅4=8 grass and so needs 8 fertilizer.

At time 3, move back to node 3, which we already fertilized and so don't need to fertilize again.

At time 4, move to node 4, which now has 4⋅1=4 grass and so needs 4 fertilizer.

At time 5, move back to node 3, which we already fertilized.At time 6, move back to node 1.

At time 7, move to node 2, which now has 7⋅1=7 grass and so needs 7 fertilizer.

At time 8, return to node 1.

This route takes 8 time and uses 2+8+4+7=21 fertilizer. It can be shown that 8 is the least possible amount of time for any route that returns to node 1 at the end and 21 is the least possible fertilizer used for any route that returns to node 1 and takes 8 time.

ex2)

The optimal route for Farmer John is as follows:

At time 1, move to node 2, which now has 1⋅1=1 grass and so needs 1 fertilizer.

At time 2, move back to node 1.

At time 3, move to node 3, which now has 3⋅2=6 grass and so needs 6 fertilizer.

At time 4, move to node 5, which now has 4⋅4=16 grass and so needs 16 fertilizer.

At time 5, move back to node 3, which we already fertilized and so don't need to fertilize again.

At time 6, move to node 4, which now has 6⋅1=6 grass and so needs 6 fertilizer.

This route takes 6 time and uses 1+6+16+6=29 fertilizer. It can be shown that 6 is the least possible amount of time for any route and 29 is the least possible fertilizer used for any route that takes 6 time.

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Fertilizing Pastures timer 1s memory 32MB

#5507

Fertilizing Pastures 1s 32MB