The objective is to consecutively calculate the n-th fibonacci where each n is taken from a sequence. Solution 1 is a recursive algorithm. This divides the problem into sub-problems and builds the final solution by combining solutions to individual sub-problems. This solution does not make any other attempts at gaining faster speeds. Solution 2 is also recursive but, uses a map to hold the results of sub-problems encountered during the calculation. That way for each subsequent n in the sequence, the results of sub-problems from the previous run are re-used. The same can be achieved with memoization.

As seen in the profiling results Solution 2 not only saves execution cycles but also saves itself from the overhead of context switching into the sub-problems.

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**Solution 1** without state

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**Solution 2** (with state in a class)

Now we profile the two solutions by calculating over a list of 10 numbers and the results are shown below.

**Results**