• The General Situation:
  • We commonly want to determine the interval that contains a particular value
• The Specific Situation:
  • The intervals are defined by the values in a single array
  • The intervals are disjoint
  • The union of the intervals is the set of real numbers
• Other Related Situations:
  • Conformal arrays (e.g., named left and right) that contain the left and right boundaries
  • Intervals that don't cover the reals (and, hence, the value might not be in any interval)
  • Discrete sets (e.g., of int values, of String values)

• The Boundaries:
  • \(b_0, b_1, \ldots, b_{n-1}\)
• The Intervals:
  • Interval \(0\): \([-\infty, b_0)\)
  • Interval \(1\): \([b_0, b_1)\)
  • Interval \(2\): \([b_1, b_2)\)
  • \(\vdots\)
  • Interval \(n-1\): \([b_{n-2}, b_{n-1})\)
  • Interval \(n\): \([b_{n-1}, \infty]\)

javaexamples/programmingpatterns/intervalmembership/IntervalMembership.java (Fragment: indexOf)

The following fragment uses interval membership to determine the tax bracket for a single individual in 2017.

javaexamples/programmingpatterns/intervalmembership/IntervalMembership.java (Fragment: taxBracket)

This can be combined with a look-up array to get the marginal tax rate.

javaexamples/programmingpatterns/intervalmembership/IntervalMembership.java (Fragment: taxRate)

• A Temptation:
  • Combine the interval membership functionality and look-up array functionality in a single method
• The Tax Example Revisited:
  • javaexamples/programmingpatterns/intervalmembership/IntervalMembership.java (Fragment: taxes)
     
• The Downside:
  • One often wants to perform more than one look-up using the same index

javaexamples/programmingpatterns/intervalmembership/IntervalMembership.java (Fragment: grades)