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The “bubble sort” algorithm is a procedure for sorting. If the input is a
collection of random letters, the following “pseudo-code” provides a set of
instructions that will lead to sorting the collection alphabetically. To test
that the steps will succede, pretend to “compute” the procedure for the array of
letters ['q', 'e', 'd']
.
A
refer to some collection of lettersn
refer to the number of letters in A
i
referring to any positive integer, let A[i]
refer to the i
^{th} letter in A
swapped
refer to ‘No’i
refer to 0i
refer to the value of i + 1
A[i + 1]
comes before A[i]
in the alphabet, then swap them in the collection A
and let swapped
refer to ‘Yes’i
is less than n
go back to step 6, but otherwise continue to step 9.swapped
refers to ‘Yes’, go back to 4, otherwise A
is in alphabetical orderThe following is a script in the R programming language
that implements bubble sort, beginning from the assumption that A
already
refers to an array of letters.
n <- length(A)
swapped <- TRUE
while (swapped) {
swapped <- FALSE
for (i in seq(1, n - 1)) {
if (A[i+1] < A[i]) {
a <- A[i+1]
A[i+1] <- A[i]
A[i] <- a
swapped <- TRUE
}
}
}
If you understand the pseudo-code, then you know what the R code is accomplishing even though you can’t read the R language. However, you can probably deduce what a lot of it is doing!
What do you think the combination of characters <-
means? What about the pattern {...}
?
Which pseudo-code step is implemented by the if (...) {...}
block?
What is the role of a
?
What word in the code tells the interpreter to repeat a set of unstructions an unspecified number of times? What word causes a set of instructions to repeat a fixed number of times?
Complete the following pseudo-code to sum a given array of integers:
A
refer to the array of integers.n
refer to the length of A
sum
refer to 0Complete the following pseudo-code with instructions to test whether a given
integer is even or odd. Assume you can use a pre-existing capability to round
any number to its nearest integer, as well as the arithmatic operators *
and
/
.
i
refer to a given integeri
is less than zero, let i
refer to -1 * i
Refer back to the bubble-sort algorithm. Step 7 says to “swap” elements of an
array, but in the implementation that takes 3 lines of code including creation
of a dummy variable. The implementation would be easier to read (since we, the
reader, already understand what “swap” means) and “modular” if we replaced those
lines with a swap
function defined outside the loops.
Just using what you can infer from the pseudo-code and R code above, what would
you replace each ...
with below to improve our bubble-sort implementation.
swap <- function(j, x) {
...
return(x)
}
n <- length(A)
swapped <- TRUE
while (swapped) {
swapped <- FALSE
for (i in seq(1, n - 1)) {
if (A[i+1] < A[i]) {
...
swapped <- TRUE
}
}
}