Programming Assignment 4 average length of polymer

Please complete all parts and share your all code in C++.

Polymers such as proteins consist of long chains of atoms or molecules. While there are some restrictions on how they can form and what shape they have, to a large extent they can be modeled by a random walk.

We'll consider a simplified example in which you can assume that

1) that each "step" has the same length of 1 unit,

2) while each link must be connected to the previous link, it may be connected at any angle, i.e., the probability of any angle is the same (there is a uniform distribution on the angles).

3) to simplify the problem, do this in 2 dimensions, not 3.

By running many simulations, estimate the average length from one end of the polymer to the other if the polymer consists of 4000 links.

4) the monomer can overlap and cross. (If we dont make this simplifying assumption, then the problem becomes significantly more difficult.)

Hint: as we discussed in class, you would find out the true nature of a coin by flipping it many times. You want to find true nature of these polymers, in specific, the average end-to-end length, by creating many of them.