## List Intersection And Union

### November 16, 2012

You are given two linked lists of integers with no duplicates. The intersection of the two lists is a list of integers that are in both lists, and the union of the two lists is a list of integers that are in either list. For instance, if list A contains the integers 4, 7, 12, 6, 17, 5 and 13 and list B contains the integers 7, 19, 4, 11, 13, 2, and 15 their intersection is the list 4, 7, and 13 and their union is the list 4, 7, 12, 6, 17, 5, 13, 19, 11, 2 and 15.

Your task is to write as many different versions of the functions that perform intersection and union as you can think of; you should have versions with time complexities of *O*(*n*^{2}), *O*(*n* log *n*) and *O*(*n*), and you should perform timing tests to show that the various time complexities are achieved. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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[...] today’s Programming Praxis exercise, our goal is to write union and intersection functions for lists in [...]

My Haskell version (see http://bonsaicode.wordpress.com/2012/11/16/programming-praxis-list-intersection-and-union/ for a version with comments):

A Python version. With the results below. The full code is here.

Coeff: e.g. for inter1 timings are 8.78e-5*n^2

Ratio: How much worse fits alternative model (indicated by alt)

inter1 O(n2) coeff: 8.78e-05 ratio: 704 alt: O(nlogn) Loop over a and b and check if there are doubles

inter2 O(n2) coeff: 3.12e-05 ratio: 1958 alt: O(nlogn) Loop over a and check if present in b

inter3 O(n2) coeff: 3.47e-05 ratio: 510 alt: O(nlogn) Output a after removing all elements in b

inter4 O(nlogn) coeff: 1.03e-05 ratio: 34 alt: O(n) Make heaps of a and b. Copy to output elements that are in a and b

inter99 O(n) coeff: 2.71e-07 ratio: 5 alt: O(nlogn) Make set of a and b. Output list of intersection.

union1 O(n2) coeff: 5.83e-05 ratio: 7656 alt: O(nlogn) Loop over the elements of a+b

union2 O(n2) coeff: 3.06e-05 ratio: 1225 alt: O(nlogn) Output a + Loop over b and check if present in a

union4 O(nlogn) coeff: 1.09e-05 ratio: 3 alt: O(n) Make heaps of a and b. Copy to output elements that are in a or b

union99 O(n) coeff: 2.94e-07 ratio: 4 alt: O(nlogn) Make set of a and b. Output list of union.

union99a O(nlogn) coeff: 2.30e-07 ratio: 1 alt: O(n) Output list of set of a + b.

[...] Pages: 1 2 [...]

[...] three different list algorithms three times, each with a different runtime complexity. From their first post last week we have list intersection and union and from a newer post yesterday we have the [...]

Here’s my try in Racket and Python (including the list difference from the next post): List algorithms and efficiency

And just the source code: python, racket

I went ahead and graphed the timings as well, to show that they were actually O(n2), O(n log n), and O(n). I was actually a little surprised at how well that turned out.

Here are my tries in Scheme. I have not run time tests but simply reasoned about the performance.

[…] to show that the various time complexities are achieved. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments […]