I encountered a problem called Frog Jump:
A frog is crossing a river. The river is divided into x units and at each unit there may or may not exist a stone. The frog can jump on a stone, but it must not jump into the water.
Given a list of stones' positions (in units) in sorted ascending order, determine if the frog is able to cross the river by landing on the last stone. Initially, the frog is on the first stone and assume the first jump must be 1 unit.
If the frog's last jump was k units, then its next jump must be either k - 1, k, or k + 1 units. Note that the frog can only jump in the forward direction.
The number of stones is ≥ 2 and is < 1,100.
Each stone's position will be a non-negative integer < 231.
The first stone's position is always 0.
There are a total of 8 stones.
The first stone at the 0th unit, second stone at the 1st unit,
third stone at the 3rd unit, and so on...
The last stone at the 17th unit.
Return true. The frog can jump to the last stone by jumping
1 unit to the 2nd stone, then 2 units to the 3rd stone, then
2 units to the 4th stone, then 3 units to the 6th stone,
4 units to the 7th stone, and 5 units to the 8th stone.
Return false. There is no way to jump to the last stone as
the gap between the 5th and 6th stone is too large.
next jump must be either k - 1, k, or k + 1 units
there is no way to jump to the last stone as the gap between the 5th and 6th stone is too large
In the first example, he decides to skip the fifth stone as because his next jump (of length
2) would not enable him to get to the subsequent stone (which is
4 beyond that). On the other hand, if he goes directly to the sixth stone (a jump of
3), the subsequent jump of
4 is permissible.
In the second example, you need to be able to jump at least
4 from the fifth stone, however you cannot land on it with a jump of more than
2. Thus it's impossible.
Think of this in the same way as momentum in physics and it may make a bit more sense.