$3.$ Dynamic Programming: $(5$ points$)$ Describe the principle underlying the algorithm design strategy based on Dynamic Programming using the example of computing C$($N$)$ in the Figure below. Give an algorithm$/$code for computing C$($N$)$ in O$($N$).$ Compare this computational complexity with the simple recursion$-$based approach. See Fig. $10\mathrm{.}44$ and $10\mathrm{.}45$ in M$.$ A$.$ Weiss$$s text book.