cs2223 Class 18

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cs2223, D97/98 Class 18

Dynamic Programming

Dynamic programming is a way of optimizing some value or "cost". A key element is the use of recursion to reduce the calculation time required to perform the optimization. Several steps are involved in using dynamic programming algorithms to solve problems.

Select a numerical cost function which is to be optimized. It is important to use a function which can be defined recursively.
Write a recursive program which calculates and stores intermediate optimal cost values. This function can calculate an exhaustive table of values, as in the change algorithm shown in Section 8.2 of the text, or it can calculate the values only as needed, as shown in the fibonacci sequence algorithm in Class 17.
Devise and implement an algorithm for selecting the optimal cost.
Devise and implement a method for determing the path by which the optimal cost was obtained. This can be done by finding an algorithm for regenerating the path from the cost or by creating an additional array with information about how each value in the cost table was derived.

We demonstrated this process with the example of the change algorithm shown in Section 8.2 of the text. Note that some modifications of this algorithm may be required if there is no unit coin in the coinage system.