Databases
StackOverflow2013
Postsdbo
POExpected running time in randomized algorithm
 

Note that there are some explanatory texts on larger screens.

plurals
  1. POExpected running time in randomized algorithm
    primarykey
    data
    text
    <blockquote> <p>In most of the calculation analysis of running times, we have assumed that all inputs are equally likely. This is not true, because nearly sorted input, for instance, occurs much more often than is statistically expected, and this causes problems, particularly for quicksort and binary search trees.</p> <p>By using a randomized algorithm, the particular input is no longer important. The random numbers are important, and we can get an expected running time, where we now average over all possible random numbers instead of over all possible inputs. Using quicksort with a random pivot gives an O(n log n)-expected-time algorithm. This means that for any input, including already-sorted input, the running time is expected to be O(n log n), based on the statistics of random numbers. An expected running time bound is somewhat stronger than an average-case bound but, of course, is weaker than the corresponding worst-case bound. </p> <p>First, we will see a novel scheme for supporting the binary search tree operations in O(log n) expected time. Once again, this means that there are no bad inputs, just bad random numbers. From a theoretical point of view, this is not terribly exciting, since balanced search trees achieve this bound in the worst case. Nevertheless, the use of randomization leads to relatively simple algorithms for searching, inserting, and especially deleting.</p> </blockquote> <p>My question on above text is</p> <ol> <li><p>What does author mean by "An expected running time bound is somewhat stronger than an average-case bound but, of course, is weaker than the corresponding worst-case bound" ? in above text.</p></li> <li><p>Regrading binary search trees what does author meant by "since balanced search trees achieve this bound in the worst case"? my understanding for binary search trees worst case is O(d), where d is depth of the node this can be "N" i.e., O(N). what does author mean by this is same as worst case above?</p></li> </ol> <p>Thanks!</p>
    singulars
    1. PO
      singulars
      1. PTAnswer
    1. This table or related slice is empty.
    1. PTQuestion
    1. This table or related slice is empty.
    1. USvenkysmarty
    plurals
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. PO
      singulars
      1. PTAnswer
    2. PO
      singulars
      1. PTAnswer
    3. PO
      singulars
      1. PTAnswer
    1. VO
      singulars
      1. POExpected running time in randomized algorithm
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
      singulars
      1. POExpected running time in randomized algorithm
      1. USvenkysmarty
      1. VTFavorite
    1. COWhat's your reference?
      singulars
      1. POExpected running time in randomized algorithm
      1. USSaeed Amiri
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload