The farthest reach

If from each box you can jump forward at most values[i], can you get to the end? You do not have to decide which box to jump to. Carry one number: the farthest box I can reach so far. If you can reach a box, you can reach every box before it too.

1reach = 0
2for i, jump in enumerate(values):
3    if i > reach:
4        return False
5    reach = max(reach, i + jump)
6return True

At every box you ask first "could I get here?"; if not, everything after it is closed too. If you could, you update the farthest with the reach this box offers (i + jump).

The same idea meets you on a grid as the rule "go to the nearest target": collecting the nearest each time is usually a good plan and easy to work out. Mind the word "usually": nearest does not guarantee the shortest total way; with limited energy you have to measure it.

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