Context and Problem Statement: A web search engine returns you a list of web-links that match the set of words in your query. Each web-link is assigned an integer for identification purposes(page-ID) This is done by maintaining an ”inverted index”. An inverted index, at a very elementary level, is a mapping that takes a word and returns to you a list of web-links which contains the word.That list would be a sorted(ranked) array of page-IDs where the web-link with the highest rank for the query is displayed on top. When your query to the web search engine contains multiple words, the search engine needs to find the sorted array for each word and then computes the intersection of these arrays. Given the number of web-pages existing in the world-wide-web, this work is very computationally challenging ! In this assignment you are required to write programs which takes as input two sorted arrays and retur
Context and Problem Statement: A web search engine returns you a list of
web-links that match the set of words in your query. Each web-link is assigned
an integer for identification purposes(page-ID) This is done by maintaining an
”inverted index”.
An inverted index, at a very elementary level, is a mapping that takes a word
and returns to you a list of web-links which contains the word.That list would
be a sorted(ranked) array of page-IDs where the web-link with the highest rank
for the query is displayed on top. When your query to the web search engine
contains multiple words, the search engine needs to find the sorted array for each
word and then computes the intersection of these arrays. Given the number of
web-pages existing in the world-wide-web, this work is very computationally
challenging !
In this assignment you are required to write
two sorted arrays and returns a new array containing the elements found in
both the sorted arrays. It is alright if the input arrays have duplicates but the
returned array should be duplicate free !
Below is how the arrays are represented
ARRAY1[] = [1, 5, 6, 6, 9, 9, 9, 11, 11, 21]
Here length of ARRAY1 is m.
ARRAY2[] = [6, 6, 9, 11, 21, 21, 21]
Here length of ARRAY2 is n.
Array to be returned would be:
ARRAY[] = [6, 9, 11, 21]
ATTN : Please be reminded that you cannot use library functions to do any of
the tasks required above. Doing so would straight up result in a score of Zero !
You will solve the problem in three ways:-
(1) [40 points] Implement the function in such a way that your solution solves
the problem with O(mn) time complexity. O(mn) is same as O(m ∗ n).
This brute-force method suggested has a name called ”loop-join” where
you basically just traverse through the elements of one array comparing
it to the elements of the other array.
(2) [40 points] In a separate implementation, code up a solution in such a way
that your solution solves the problem with O(nlog(m)) time complexity
2
or O(mlog(n)) time complexity. Here log means to the base of 2. I’m sure
you already know that the hint is to use Binary Search.
(3) [20 points] In the form of sentences, as a comment in your code (at the
bottom of your Solution2), you are required to suggest how can Solution2
be improved by leveraging the fact that both the arrays are already sorted.
Suggest a solution so that your suggested solution can run linearly with
O(m + n) time complexity. Your suggestion should be no more than 5
sentences :)
Very Very Important :
(1) Your code should be well commented which explains all the steps you are
performing to solve the problem. A submission without code comments
will immediately be deducted 15 points !
(2) As a comment in your code, please write your test-cases on how you would
test your solution assumptions and hence your code.
A submission without test cases will immediately be deducted 15 points !
Example of cases to be tested for are like : What if the array input which
is expected does not exist - that is , input is a null. How should your code
handle such a situation ? Maybe output some message like ”Null input
case, so no output”? What if the length of the array is one ?....so on and
so forth.
Please Remember : Although, written as comments - You will address
your test cases in the form of code and not prose :)
*****MUST NOT USE LIBRARY FUNCTIONS AND MUST BE IN JAVA*****
EXACT OUTPUT TO PRINT:
ARRAY[] = [6, 9, 11, 21]
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