Experiments

Overview¶

In this part of the assignment, you will run some code that uses the data structures you implemented in the previous part, and then analyze the resulting behavior. This will generally involve the following steps:

1. Read through the experiment runtime methods and make a prediction about their resulting behavior.
2. Run the experiment code and save an image of the resulting plot. (A window displaying the plot should open automatically as the experiment runs.)
3. Answer the discussion questions for each specific experiment in order to explain how or why the experiment produced those results.

The hypothesis/predict-based-on-the-code portions of your write-up will be graded based on completion, so just write down your honest thoughts before running the experiment. Please submit all plots generated along with your answers. The post-experiment analysis portions will be graded based on the clarity of your explanations and whether they match up with your plot.

Your completed write-up must be in PDF format. If you have a partner, you will work on this write-up and submit together.

Experiments and Discussion Prompts¶

For each of the experiments, make a prediction according to the bolded prompt in your write-up before running the experiment or opening its discussion prompts below.
Then, run the experiment, expand the discussion prompts, and answer the questions inside.
Also include the PNGs of the plots inside your write-up PDF.

Include 1–2 sentences of justification for your predictions, and try to keep answers to discussion questions to a maximum of 2–3 sentences.

Experiment 1: ArrayMap Remove Order¶

This experiment plots the runtime of removing all entries from your array map, but with two different orderings. Read through the code for each runtime method. Then, predict the order of growth (constant, logarithmic, linear, $\bm{n\log(n)}$, quadratic, exponential) of each experiment method’s runtime as its size increases.

Experiment 2: Chaining with Different hashCodes vs. AVL trees¶

This experiment explores how different hash code functions affect the runtime of a ChainedHashMap and compares that to the runtime of an AVLTreeMap.

First, we’ll look at the methods involving the ChainedHashMap: runtime1, runtime2, and runtime3. Each runtime method uses a different class as keys for a ChainedHashMap. Each of the different FakeString objects represents a string (by storing an array of chars) but each class has a different implementation of the hashCode method.

Keep in mind that hashCode functions are used to determine where keys belong in a hash table. Without good hashCode functions, the keys in our hash table will frequently collide, which will negatively affect the runtime of our hash table.

Read over the implementations of hashCode in FakeString1, FakeString2, and FakeString3, and expand the box below to show some plots to help illustrate the output distributions of these hash functions.

Predict which runtime method will be asympotically fastest and which runtime method will be asympotically slowest.

Experiment 3: Load Factor Thresholds for Resizing¶

This experiment tests the runtime for ChainedHashMap‘s put method across different values of the load factor threshold for resizing.

First, answer the following prompts:

1. Briefly describe the difference between runtime1 and runtime2.
2. Predict which of the two methods’ runtimes will have a higher order of growth. If they have the same order of growth, also predict which will run asymptotically slower.

Submission¶

When you submit, mark which pages correspond to the questions we ask. After submitting, the partner who uploaded the PDF must add the other partner as a group member on Gradescope. Do not have each member submit individually. The process for adding group members is the same as for the programming portion; if you need a reminder, here’s the video demonstrating the process.

We may deduct points if you do not correctly submit as a group or do not properly assign your pages/problems.