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Choose a problem that lends to an implementation that uses dynamic programming. Clearly state the problem and then provide high-level pseudocode for the algorithm. Explain why this algorithm can benefit from dynamic programming.

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The selected problem for this analysis is computing the nth Fibonacci number. As we recall, this is a sequence defined recursively as F(n)=F(n-1) + F(n-2) with initial conditions F0=0 and F1=1.
The problem can be solved by simple recursion, but in this case the running time becomes exponential as shown by the below diagram of recursive calls (practically, the same sub-problems are computed repeatedly and the efficiency of this approach is low)....

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