I am trying to find the best way to solve the following problem. By best way I mean less complex.
As an input a list of tuples (start,length) such:
[(0,5),(0,1),(1,9),(5,5),(5,7),(10,1)]
Each element represets a sequence by its start and length, for example (5,7) is equivalent to the sequence (5,6,7,8,9,10,11) - a list of 7 elements starting with 5. One can assume that the tuples are sorted by the start element.
The output should return a non-overlapping combination of tuples that represent the longest continuos sequences(s). This means that, a solution is a subset of ranges with no overlaps and no gaps and is the longest possible - there could be more than one though.
For example for the given input the solution is:
[(0,5),(5,7)] equivalent to (0,1,2,3,4,5,6,7,8,9,10,11)
is it backtracking the best approach to solve this problem ?
I'm interested in any different approaches that people could suggest.
Also if anyone knows a formal reference of this problem or another one that is similar I'd like to get references.
BTW - this is not homework.
Edit
Just to avoid some mistakes this is another example of expected behaviour
for an input like [(0,1),(1,7),(3,20),(8,5)] the right answer is [(3,20)] equivalent to (3,4,5,..,22) with length 20. Some of the answers received would give [(0,1),(1,7),(8,5)] equivalent to (0,1,2,...,11,12) as right answer. But this last answer is not correct because is shorter than [(3,20)].
