lecture15 - COMP 250 Winter 2010 15 recurrences 2 Notation...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
COMP 250 Winter 2010 15 - recurrences 2 Feb 10, 2010 Notation: floor and ceiling (rounding) The recurrence equations we will work with have arguments that are positive integers. If we have a fractional number and we wish to round it down (floor) or up (ceiling) to the nearest integer, then we sometimes use the following notation: x is the largest integer that is less than or equal to x . ⌊⌋ is called the floor operator. x is the smallest integer that is greater than or equal to x . ⌈⌉ is called the ceiling operator. Example 4: converting decimal to binary Recall the recursive version of the algorithm for converting a decimal number n to binary (see lecture 11). What is the asymptotic running time of this algorithm? We can write a recurrence relation as follows: t ( n ) = 1 + t ( n/ 2 ) where the floor operator is there to remind ourselves that we are ignoring the fractional part if n is odd. The “floor” operator is a bit annoying, so we bound the recurrence as follows. Let k = log n , where log n log 2 n (i.e 2 is the default base of log in this course). That is, k
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern