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The problem I am trying to solve has a list of intervals on the number line, each with a pre-defined score. I need to return the maximum possible total score. The catch is that the intervals overlap, and of the overlapping intervals I can use only one. Here is an example. Intervals - Score 0- 5 - 15 4- 9 - 18 10-15 - 12 8-21 - 19 25-30 - 25 Here, the intervals 0-5, 4-9 and 8-21 overlap. The intervals 10-15 and 8-21 also overlap. The maximum sum would be 55 (18+12+25). It is important to note here that we select the interval 4-9 of the first batch of overlapping intervals even though it does not have the highest score of the three. This is because selecting the interval 8-21 would prevent us from using the interval 10-15 later on, thereby reducing the overall sum (In that case, the overall sum would be 19+25=44). I am looking for an O(nlogn) or O(n) solution to this problem. I think dynamic programming can be used, but I may be wrong. Could someone suggest a solution/algorithm(s) that could do the trick here? Edit: The intervals are in no particular order.

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