# Algorithms for Data Science using dynamic programming

Algorithms for Data Science
Assignment 3
Portfolio Optimization
In this assignment, you will be using dynamic programming to select a set of investment options
that maximize your return on investment. You will be given a file of investment options along
with the estimated return on investment for each one. You also have a given amount of money
to invest.

The specific file of investment options you will be given will vary, but you will always
have the following three pieces of information you can obtain from the file:
Investment Name, Investment Cost, Estimated Return On Investment
For example:
A,10,60
B,20,100
C,30,120
Start by putting all your code in a file called portfolio.py. Create a function called
load Investments that takes in the investment Filename and returns a list of possible investment
options: name, cost, and estimated return. You will be given a file of actual investment options
along with specific directions for that file on how to obtain the three pieces of information
necessary for this assignment.

Then make a function called optimize Investments that takes the list of possible investments
along with the amount of money available to spend. This function should return both the
optimal return on investment amount as well as the actual investments selected to achieve this
optimal return. Implement this function using dynamic programming.

For dynamic programming, one needs a recursive breakdown of the problem. We have a
number of possible investments and an amount we are able to spend. At each step, we can
decide to either include investment x or exclude it.

If we include it, then we are left with a smaller problem of finding the optimal return with all the possible investments without investment x with a smaller amount we are able to spend (because we purchased investment x). If we exclude it, then we are left with a smaller problem of finding the optimal return with all the possible investments without investment x but with the same amount of money to spend as we had before. A DAC solution could be attempted, but it ends up having too much-repeated work. Therefore, we will implement our solution with dynamic programming. Note that this is a 2-D problem (number of investments and amount of money to spend). Thus, we will need a 2-D table.

The second step is filling in the base cases. Note that when we don’t select any investments, no
matter how much money we have to spend (top row), then we get no return on investment.
This is a natural base case. The third step is to identify the goal location in the table. This will be
the position where we are allowed to include all investments with our full allocation of funds to
spend. This will be the lower-right corner.

The last step in computing any optimal table is to determine the order in which to fill in the table, keeping in mind that one always needs all the results for the recursive subproblems available to fill in the next location.

After the optimal table is computed, a traceback table needs to be added to the
implementation so we can find the actual investments that produce the optimal. Recall that
traceback tables store the “winning” options at each step and are then used at the end to trace
back through these winning options.

Your code should return the optimal return on investment number as well as a list of the investment names used to obtain this optimal number. Note that this is a similar problem to the 0/1 Knapsack problem, and you should use that idea to help guide you through your implementation