7
$\begingroup$

How to find the intersection between a set of two ranges of number.

let me explain the question with an example,

{2,3} {3,8} would result to 0
{2,5} {3,8} would result to 2
{3,6} {3,8} would result to 3
{4,5} {3,8} would result to 1
{4,5} {3,8} would result to 1
{8,9} {3,8} would result to 0

Note:This could be easily done with series of if in a computer application, I am hungry for a mathematical solution!

  • 0
    By "intersection", you mean the number of "units" of overlap between the two given intervals?2010-12-29
  • 1
    What are "tow ranges"?2010-12-29
  • 0
    @ J.M yes , and @ Pete L.Clark I mean set of two numbers2010-12-29
  • 1
    There is a great grief about this notation of yours, $(3,8)$ usually indicates all the real numbers which are strictly greater than $3$ and strictly smaller than $8$. Not just the integers, which is what seems to be your meaning.2010-12-29
  • 0
    @Asaf Karagila I have changed to {,} I am new so not sure this is correct ,thanks2010-12-29
  • 0
    @Thunder: This is still not correct. But nevermind, I hope that whoever reads the question will look at my answer and figure out the correct meaning anyway.2010-12-29

1 Answers 1

11

If I understood you correctly, you have $\{x,x+1,\ldots,x+n\}$ and $\{y,y+1,\ldots,y+k\}$ and granted $x,y$ are integers you want to find out the number of elements in the intersections (i.e. how many numbers appear in both sets).

Well, take: $$\max\{0,\min\{y+k,x+n\}-\max\{x,y\}\}$$ and that should be it.

  • 0
    well the result is not a set but a number , that represents the value in the intersection set.2010-12-29
  • 1
    @Thunder: Yes, and Asaf's construction does return the number you (seem to) want.2010-12-29
  • 0
    yes this the correct answer ... thanks2010-12-29