Pre-probelm lesson:

IO

First, import the following really important libraries:

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

If you get import errors when you try importing them, install pip: (https://pythonprogramming.net/using-pip-install-for-python-modules/) and type pip install matplotlib and pip install numpy into your terminal

Today we are going to be learning how to do input/output with data, and how to visualize data.

For basic input/output (IO) you can use the with function in python:

with open("data.txt", "r") as f:
  for line in f:
    print(line)

The r parameter in the open function is VERY important. It can have a couple different values

• r: read mode
• w: write mode
• wa: append write mode
• r+: read and write mode

One really important thing to know is that opening a file with w will overwrite its contents. You won’t be able to get them back! So don’t do that. w mode is for creating new files with a program.

For reading in special file types like csvs, xmls, jsons, xlsxs, which have computer readable data, you will want to use a different function to read the file. pandas is great for IO with tables. For example,

import pandas as pd
pd.read_csv("data.csv")

df = pd.DataFrame({"alek tennis score": [1,2,3,4], "max tennis score":[5,56,7,7]})
df.to_csv("tennis.csv")

json is great for json files:

import json

with open("data.json", "r") as f:
  json.load(f)


with open("data.json", "w") as f:
  json.dump(data, f)

BeautifulSoup is super helpful for parsing html and xml.

plotting data

Plotting data is a really good thing to be able to do too. matplotlib is the basic plotting library, seaborn is a nice wrapper around matplotlib.

Here are some examples of plots:

import numpy as np
import matplotlib.pyplot as plt
plt.plot(np.sin(np.linspace(0,10,1000)))
plt.show()

# flip some coins, wow binomial distribution!
coins = [sum([np.random.randint(2) for j in range(100)]) for i in range(1000)]
plt.hist(coins)
plt.show()

Problem 1

Plot a sine wave. Plot another sine wave. Add them together!

Problem 1.75

Write some text to a file called data.txt. Specifically write out this text:

data = "The cup game is a classic problem in computer science that models work scheduling. In the cup game on n cups, a filler and an emptier take turns adding and removing water from cups (i.e. new tasks come in and the scheduler must allocate processors to handle the incoming work). On each round the filler will distribute some new amount of water among the cups, and the emptier will remove some amount of water from some of the cups. The filler can distribute the water however it wants (as long as it places at most 1 water in each cup), but the emptier has an added discretization constraint: it can only remove water from some fixed number of cups. The problem is to analyze how well each player can do, that is, how much water can the filler force to be in the fullest cup, and what is the upper bound on this fill that an appropriate emptying strategy can guarantee? We study several variants of the problem and answer some open questions."

Problem 1.5

Read in that file called data.txt and print it out

Problem 2

Make a histogram of how many times each character occurs in that file

Problem 3

Generate some data of “happiness versus sleep”. It should be slightly random noise added to some distribution (e.g. happiness = 1000-(sleep-7)**2 + np.random.random()).

Problem 4

Write that data out to a csv happydata.csv Hint: use import pandas, or import json

Problem 5

Read the data in from happydata.csv, and make a parabola of best fit (or whatever is appropriate based on your model). Hint: use numpy

Problem 6

Make a heat map of gcd(i,j) \[i,j\in\{1,2,\ldots, n\}\]

Problem 7

Make a graph of the primes.