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This problem can be solved purely mathematically, without any iteration.
Assume that there exists some k number of jumps, at which they will meet: x1 + k(v1) = x2 + k(v2)
Solving for k: k = (x2 - x1) / (v1 - v2)
If k would be a positive integer, they will land at the same location in k jumps.
(Note: If k is negative, they would have to hop backwards. If k is not an integer, they will pass eachother while in the air.)
So you just need to evaluate if that function would result in a positive integer. You don't even need to actually determine a value for k. And no iteration is required.
The code for this is left as an exercise for the reader.
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Number Line Jumps
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This problem can be solved purely mathematically, without any iteration.
Assume that there exists some k number of jumps, at which they will meet:
x1 + k(v1) = x2 + k(v2)Solving for k:
k = (x2 - x1) / (v1 - v2)If k would be a positive integer, they will land at the same location in k jumps.
(Note: If k is negative, they would have to hop backwards. If k is not an integer, they will pass eachother while in the air.)
So you just need to evaluate if that function would result in a positive integer. You don't even need to actually determine a value for k. And no iteration is required.
The code for this is left as an exercise for the reader.