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CMB2:

Homework 7

29 March 2019. Deadline: Wednesday, 10 April, 11:00.

Please download the file homework7.R and write your results there. Send the your answers to my mailbox.

1. Exploring vectors

You will program your own version of some standard functions using only for(), if() and indices. All the following functions receive a vector.

Please write your version of the following functions:

  1. vector_min(x), equivalent to min(x). Returns the smallest element in x.

  2. vector_max(x), equivalent to max(x). Returns the largest element in x.

  3. vector_which_min(x), equivalent to which_min(x). Returns the index of the smallest element in x.

  4. vector_which_max(x), equivalent to which_max(x). Returns the index of the largest element in x.

You can test your function with the following code.

The two results must be the same. Obviously, you have to replace min and vector_min with the corresponding functions.

2. Merging vectors

Please write a function called vector_merge(x, y) that receives two sorted vectors x and y and returns a new vector with the elements of x and y together sorted. The output vector has size length(x)+length(y).

You must assume that each of the input vectors is already sorted.

For that you have to use three indices: i, j, and k; to point into x, y and the output vector ans. On each step you have to compare x[i] and y[j]. If x[i] < y[j] then ans[k] <- x[i], otherwise ans[k] <- y[j].

When either of the input vectors is finished, the remaining of the other input vector must be copied to the output vector.

You have to increment i or j, and k carefully. To test your function, you can use this code:

 [1] "c" "f" "g" "i" "k" "l" "q" "t" "u" "v" "w" "x" "z"
 [1] "a" "b" "d" "e" "h" "j" "m" "n" "o" "p" "r" "s" "y"
 [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j" "k" "l" "m" "n" "o" "p"
[17] "q" "r" "s" "t" "u" "v" "w" "x" "y" "z"

The output must be a sorted alphabet.

Sorting

Please write a function called vector_mergesort(x) that takes a single vector x and returns a new vector with the same elements of x but sorted from the smallest to the largest.

To do so you have to use a recursive strategy as follows:

How can you test this function?

Remember: The more exercises you do, the more chances you have to pass the course.

Deadline: Wednesday, 10 April, 11:00.