### General instructions

For every one of the questions, we are asking that you write a function that returns some value. This means that the function must return, rather than print that value. For example, the following function returns the square of its argument:

f <- function(x){
x**2
}

On the other hand, the following function only prints the value, and would not earn any credit for this assignment:

f <- function(x){
cat(x**2)
}

Do not use cat or print inside functions.

You must test your functions thoroughly. This means you must try calling the functions (i.e., using them) with different inputs, and make sure that they return the right thing. You must also make sure that your submission passes all of the tests on Gradescope. However, passing all the visible tests on Gradescope does not guarantee that you will earn a perfect score: we may also have hidden tests on Gradescope. You should submit one file containing all the functions. The name of the file must be ps1.R.

### Problem 1: Range

The range of a set numbers can mean the the interval between the smallest and the largest number of the set, or it can mean the length of that interval. For example, we might say that the range of c(-2, 10, -10, 50) is the interval $$[-10, 50]$$, or we might say that the range is $$60$$. R’s built-in range function computes the interval. Write a function named range.len which takes in a vector of numerics vec and returns the length of the range interval of the vector. For example, range.len(c(-2, 1, 5)) should be 7. You may assume the vector has at least one element.

### gapminder problems

In the following problems, you will be working with data frames that have the same columns as gapminder:

library(gapminder)
colnames(gapminder)
##  "country"   "continent" "year"      "lifeExp"   "pop"       "gdpPercap"

However, you must not rely on the actual data being the same as what is in gapminder. The actual data will be given to the function.

Write a function named compute.gdp.col which takes in a gapminder-like dataframe, and returns a version of this dataframe which also has a gdp column, containing the GDP of each country in each given year. (The order of the rows should be the same as in the original data frame.)
Write a function named cont.gdp that takes in a gapminder-like data frame, and returns a data frame which contains the GDP of each continent for each year. The GDP of a continent is the sum of the all the countries on that continent. The rows in the data frame you return must be in alphabetical order of continents; for each continent, rows corresponding to earlier years should be above rows corresponding to later years.
For each country in gapminder, we can compute the range of the gdpPercap measurements over the years. Write a function named median.gdppc.range that takes in a gapminder-like data frame, and returns the name of the country whose range of gdpPercap measurements is closest to the median of the ranges in the dataset. If there are two such countries, you can return the name of either one of them. (This means you don’t need to worry what to do if you have an even number of countries – just pick one of the two that are closest to the median).