The core of the solution is a dynamic programming algorithm. To start with, sort the points in ascending order of x-coordinates, breaking ties in ascending order of y-coordinates.

Let ~dp(L)~ be the largest amount of energy Barica can have after getting from plant ~1~ to plant ~L~.

Barica can reach plant ~L~ jumping to the right or upwards. As the length of the jump is insignificant, of all plants ~P~ with the same x-coordinate (and smaller y-coordinate) as plant ~L~, we want the one we can reach with the largest amount of energy, that is for which ~dp(P)~ is largest. We apply the same reasoning to plants with the same y-coordinate.

Finally, ~dp(L)~ is calculated as the better of two cases (jumping upwards from the best plant with the same x-coordinate, or jumping to the right from the best plant with the same y-coordinate).

To reconstruct the frog's route, remember for each plant the best plant to have come from.