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{{Infobox Algorithm
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The reason being that APRA has the responsibility of administering: registration of life insurance companies and authorized non-operating holding companies, life insurance company statutory funds, financial management in life companies, judicial management, winding up, among other issues. If you meet with an unfortunate death, then your family will not have the burden of the mortgage debt. Eventually, the melanocytes will grow abnormally, thereby resulting in cancer. <br><br>Because the hundreds of years get passed, the insurance coverage sector has included various kinds of insurance coverage and characteristics. However, it appears that they may be on the rise again. Donald's website is: Life Insurance Hub Also see: Life Insurance Answers. For more information about term life insurance policy, just visit this site. For example we know that it is primarily used to cover financial responsibilities. Yet, we derive greater pleasure when our clients leave our offices, satisfied. 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Later on, to satisfy market demand, cash value policies such as whole and universal life insurance policies were conceived. Term life insurance is in effect for a specific term, like 20 years. If you test positive when you apply for life insurance, you must disclose your HIV positive status to the [http://Photo.net/gallery/tag-search/search?query_string=life+insurance life insurance] company unless they will decline you. Take time to check our page if you want to know more about insurance. This affects the usage of the product as well as the limitations on the collection of the benefit. Special Risk Managers seeks to help people suffering from serious medical conditions find insurance cover.  <br><br>After Reading About This Diet, Snake Oil is Actually Starting to Sound Really Good. Long term life insurance really blurs the line between whole life and term life insurance, with policies often borrowing from both structures to offer the customer even more flexibility. The main advantage of term life insurance over permanent life insurance policy is cost. People continue to make fundamental mistakes when researching on-line for finding the best insurance. Term insurance protects potential loss due to death of the insured. Take into account a situation where you are about to book a flight. For example, a younger, married person with children may opt to purchase a term life insurance to help cover the mortgage or replace lost income if they die during the coverage period.
|name=Median of Medians
|class=[[Selection algorithm]]
|image=
|data=[[Array data structure|Array]]
|best-time= <math>O(n)</math>
|time=<math>O(n)</math>
|space=<math>O(1)</math> auxiliary
|optimal=Yes
}}
 
In [[computer science]], the '''median of medians''' algorithm is a [[selection algorithm]] based on the [[quickselect]] algorithm, and is optimal, having worst-case linear time complexity for selecting the ''k''th largest element. The algorithm consists of an algorithm to find an approximate median in linear time – this is the key step – which is then used as a pivot in quickselect. In other words, it uses an (asymptotically) optimal approximate median-selection algorithm to build an (asymptotically) optimal general selection algorithm.
 
The approximate median-selection algorithm can also be used as a pivot strategy in [[quicksort]], yielding an optimal algorithm, with worst-case complexity O(''n''&nbsp;log&nbsp;''n''). Although this approach optimizes quite well, it is typically outperformed in practice by instead choosing random pivots, which has average linear time for selection and average linearithmic time for sorting, and avoids the overhead of computing the pivot. Median of medians is used in the hybrid [[introselect]] algorithm as a fallback, to ensure worst-case linear performance: introselect starts with quickselect, to obtain good average performance, and then falls back to median of medians if progress is too slow.
 
The algorithm was published in {{harvtxt|Blum|Floyd|Pratt|Rivest|Tarjan|1973}}, and thus is sometimes called '''BFPRT''' after the last names of the authors. In the original paper the algorithm was referred to as '''PICK''', referring to quickselect as "FIND".
 
==Outline==
Quickselect is linear-time on average, but it can require quadratic time with poor pivot choices. This is because quickselect is a [[decrease and conquer]] algorithm, with each step taking O(''n'') time in the size of the remaining search set. If the search set decreases exponentially quickly in size (by a fixed proportion), this yields a [[geometric series]] times the O(''n'') factor of a single step, and thus linear overall time. However, if the search set decreases slowly in size, such as linearly (by a fixed number of elements, in the worst case only reducing by one element each time), then a linear sum of linear steps yields quadratic overall time (formally, [[triangular number]]s grow quadratically). For example, the worst case occurs when pivoting on the smallest element at each step, such as applying quickselect for the maximum element to already sorted data and taking the first element as pivot each time.
 
If one instead consistently chooses "good" pivots, this is avoided and one always gets linear performance even in the worst case. A "good" pivot is one for which we can establish that a constant proportion of elements fall both below and above it, as then the search set decreases at least by a constant proportion at each step, hence exponentially quickly, and the overall time remains linear. The median is a good pivot – the best for sorting, and the best overall choice for selection – decreasing the search set by half at each step. Thus if one can compute the median in linear time, this only adds linear time to each step, and thus the overall complexity of the algorithm remains linear.
 
The median-of-medians algorithm does not actually compute the exact median, but computes an approximate median, namely a point that is guaranteed to be between the 30th and 70th [[percentile]]s (in the middle 4 [[decile]]s). Thus the search set decreases by a fixed proportion at each step, namely at least 30% (so at most 70% left). Lastly, the overhead of computing the pivot consists of recursing in a set of size 20% the size of the original search set, plus a linear factor, so at linear cost at each step, the problem is reduced to 90% (20% and 70%) the original size, which is a fixed proportion smaller, and thus by induction the overall complexity is linear in size.
 
==Algorithm==
 
The ''Select'' algorithm divides the list into groups of five elements. (Left over elements are ignored for now.) Then, for each group of five, the median is calculated (an operation that can potentially be made very fast if the five values can be loaded into [[Processor register|registers]] and compared). (If sorting in-place, then these medians are moved into one contiguous block in the list.) ''Select'' is then called recursively on this sublist of ''n''/5 elements to find their true median. Finally, the "median of medians" is chosen to be the pivot.
 
  ''// returns the index of the median of medians.''
  ''// requires a variant of select, "selectIdx"''
  ''// which returns the index of the selected item rather than the value''
  '''function''' medianOfMedians(list, left, right)
      numMedians = ceil((right - left) / 5)
      '''for''' i '''from''' 0 '''to''' numMedians
          ''// get the median of the five-element subgroup''
          subLeft  := left + i*5
          subRight  := subLeft + 4
          if (subRight > right) subRight  := right
          ''// alternatively, use a faster method that works on lists of size 5''
          medianIdx  := selectIdx(list, subLeft, subRight, (subRight - subLeft) / 2)
          ''// move the median to a contiguous block at the beginning of the list''
          swap list[left+i] and list[medianIdx]
      ''// select the median from the contiguous block''
      '''return''' selectIdx(list, left, left + numMedians - 1, numMedians / 2)
 
== Properties of pivot ==
The chosen pivot is both less than and greater than half of the elements in the list of medians, which is around ''n''/10 elements (½×''n''/5) for each half. Each of these elements is a median of 5, making it less than 2 other elements and greater than 2 other elements outside the block. Hence, the pivot is less than 3(''n''/10) elements outside the block, and greater than another 3(''n''/10) elements inside the block. Thus the chosen median splits the elements somewhere between 30%/70% and 70%/30%, which assures worst-case linear behavior of the algorithm. To visualize:
 
{|class="wikitable" border=1
|+ One iteration on a randomized set of 100 elements from 0 to 99
!
| bgcolor=gray|12||||bgcolor=gray|15||||bgcolor=gray|11||||bgcolor=gray|2||||bgcolor=gray|9||||bgcolor=gray|5||||bgcolor=gray|0||||bgcolor=gray|7||||bgcolor=gray|3||||bgcolor=gray|21||||bgcolor=gray|44||||bgcolor=gray|40||||bgcolor=gray|1||||bgcolor=gray|18||||bgcolor=gray|20||||bgcolor=gray|32||||bgcolor=gray|19||||bgcolor=gray|35||||bgcolor=gray|37||||bgcolor=gray|39
|-
!
| bgcolor=gray|13||||bgcolor=gray|16||||bgcolor=gray|14||||bgcolor=gray|8||||bgcolor=gray|10||||bgcolor=gray|26||||bgcolor=gray|6||||bgcolor=gray|33||||bgcolor=gray|4||||bgcolor=gray|27||||bgcolor=white|49||||bgcolor=gray|46||||bgcolor=white|52||||bgcolor=gray|25||||bgcolor=white|51||||bgcolor=gray|34||||bgcolor=gray|43||||bgcolor=white|56||||bgcolor=white|72||||bgcolor=white|79
|-
! Medians
| bgcolor=gray|17||||bgcolor=gray|23||||bgcolor=gray|24||||bgcolor=gray|28||||bgcolor=gray|29||||bgcolor=gray|30||||bgcolor=gray|31||||bgcolor=gray|36||||bgcolor=gray|42||||bgcolor=red|47||||bgcolor=white|50||||bgcolor=white|55||||bgcolor=white|58||||bgcolor=white|60||||bgcolor=white|63||||bgcolor=white|65||||bgcolor=white|66||||bgcolor=white|67||||bgcolor=white|81||||bgcolor=white|83
|-
!
| bgcolor=gray|22||||bgcolor=gray|45||||bgcolor=gray|38||||bgcolor=white|53||||bgcolor=white|61||||bgcolor=gray|41||||bgcolor=white|62||||bgcolor=white|82||||bgcolor=white|54||||bgcolor=white|48||||bgcolor=white|59||||bgcolor=white|57||||bgcolor=white|71||||bgcolor=white|78||||bgcolor=white|64||||bgcolor=white|80||||bgcolor=white|70||||bgcolor=white|76||||bgcolor=white|85||||bgcolor=white|87
|-
!
| bgcolor=white|96||||bgcolor=white|95||||bgcolor=white|94||||bgcolor=white|86||||bgcolor=white|89||||bgcolor=white|69||||bgcolor=white|68||||bgcolor=white|97||||bgcolor=white|73||||bgcolor=white|92||||bgcolor=white|74||||bgcolor=white|88||||bgcolor=white|99||||bgcolor=white|84||||bgcolor=white|75||||bgcolor=white|90||||bgcolor=white|77||||bgcolor=white|93||||bgcolor=white|98||||bgcolor=white|91
|-
|}
 
(red = "(one of the two possible) median of medians", gray = "number < red", white = "number > red")
 
5-tuples are shown here sorted by median, for clarity. Sorting the tuples is not necessary because we only need the median for use as pivot element.
 
Note that all elements above/left of the red (30% of the 100 elements) are less, and all elements below/right of the red (another 30% of the 100 elements) are greater.
 
== Proof of O(''n'') running time ==
 
The median-calculating recursive call does not exceed worst-case linear behavior because the list of medians is 20% of the size of the list, while the other recursive call recurses on at most 70% of the list, making the running time
:<math>T(n) \leq T(n \cdot 2/10) + T(n \cdot 7/10) + c \cdot n.</math>
 
The O(''n'') term ''c n'' is for the partitioning work (we visited each element a constant number of times, in order to form them into n/5 groups and take each median in O(1) time).
 
From this, using induction one can easily show that
:<math>T(n) \leq 10 \cdot c \cdot n \in O(n).</math>
 
== Analysis ==
The key step is reducing the problem to selecting in two lists whose total length is shorter than the original list, plus a linear factor for the reduction step. This allows a simple induction to show that the overall running time is linear.
 
The specific choice of groups of five elements is explained as follows. Firstly, computing median of an odd list is faster and simpler; while one could use an even list, this requires taking the average of the two middle elements, which is slower than simply selecting the single exact middle element. Secondly, five is the smallest odd number such that median of medians works. With groups of only three elements, the resulting list of medians to search in is length ''n''/3 (33 1/3%), and reduces the list to recurse into to length 2''n''/3 (66 2/3%), since it is greater than 1/2 × 2/3 = 1/3 of the elements and less than 1/2 × 2/3 = 1/3 of the elements. Thus this still leaves ''n'' elements to search in, not reducing the problem sufficiently. The individual lists are shorter, however, and one can bound the resulting complexity by the [[Akra–Bazzi method]], but it does not prove linearity.
 
Conversely, one may instead group by ''g'' = seven, nine, or more elements, and this does work. This reduces the size of the list of medians to ''n''/''g,'' and the size of the list to recurse into asymptotes at 3''n''/4 (75%), as the quadrants in the above table approximate 25%, as the size of the overlapping lines decreases proportionally. This reduces the scaling factor from 10 asymptotically to 4, but accordingly raises the ''c'' term for the partitioning work. Finding the median of a larger group takes longer, but is a constant factor (depending only on ''g''), and thus does not change the overall performance as ''n'' grows.
 
If one instead groups the other way, say dividing the ''n'' element list into 5 lists, computing the median of each, and then computing the median of these – i.e., grouping by a constant fraction, not a constant number – one does not as clearly reduce the problem, since it requires computing 5 medians, each in a list of ''n''/5 elements, and then recursing on a list of length at most 7''n''/10. As with grouping by 3, the individual lists are shorter, but the overall length is no shorter – in fact longer – and thus one can only prove superlinear bounds. Grouping into a square of <math>\sqrt{n}</math> lists of length <math>\sqrt{n}</math> is similarly complicated.
 
== References ==
{{reflist}}
{{refbegin}}
* {{wikicite|ref={{harvid|Blum|Floyd|Pratt|Rivest|Tarjan|1973}}|reference={{cite doi|10.1016/S0022-0000(73)80033-9}}}}
{{refend}}
 
== External links ==
* "[http://www.ics.uci.edu/~eppstein/161/960130.html Lecture notes for January 30, 1996: Deterministic selection]", ''ICS 161: Design and Analysis of Algorithms,'' David Eppstein
 
[[Category:Selection algorithms]]

Revision as of 15:00, 25 February 2014

Another reason, you may to do no exam life insurance, even if you have weeks to get your policy, is your unknown health status. At least 1 term paper is required per class; and sometimes, the deadlines for these papers coincide with each another. But life insurance has come a long way since the early days and these days there you can cover yourself with cheap term life insurance. Although membership of a professional body will be encouraged, firms will retain responsibility for the standard of advice given by the advisers working within the firm. Term is regarded as being the temporary insurance which may last from a decade's to 30 years. Section 125 deductions are exempt from income tax and not deemed as income for tax computation and FICA (social security and Medicare) purposes. Insurance companies may use both to determine whether to insure someone and the price to charge.

Use a term life insurance calculator to accurately estimate the amount of coverage you will need to adequately protect your beneficiaries and rest easy secure in the knowledge that you will have a financially secure future. At the same time, however, the policy holder is also making an investment for his or her future. If you took out a term life policy when you were making $30,000 a year, you should have purchased a death benefit of at least $300,000 to adequately protect your loved ones. An applicant simply has to log on to the websites of the many life insurance companies and fill in the relevant details. As a form of permanent life insurance, the policy remains in effect for the life of the policy if payments are made as scheduled. Once you provide this information the websites will be able to give you a comprehensive term life insurance quote from different companies. In simple words if we say, life insurance plays a dual role in your life, saving for life.

Without LTCI you also cannot force a nursing home to take you in and reiterate that apart from your functional limitations, your hypertension has gotten worse and your doctor's recommendation is that you stay in a nursing home. He specializes in the different cheap life insurance and getting cheap life insurance rates. So consider very strongly sticking with simple term insurance. It is important to note that rates do slowly rise as you age. If you loved this post and you would certainly like to receive even more information regarding termlifepolicy kindly browse through our own website. The reason being that APRA has the responsibility of administering: registration of life insurance companies and authorized non-operating holding companies, life insurance company statutory funds, financial management in life companies, judicial management, winding up, among other issues. If you meet with an unfortunate death, then your family will not have the burden of the mortgage debt. Eventually, the melanocytes will grow abnormally, thereby resulting in cancer.

Because the hundreds of years get passed, the insurance coverage sector has included various kinds of insurance coverage and characteristics. However, it appears that they may be on the rise again. Donald's website is: Life Insurance Hub Also see: Life Insurance Answers. For more information about term life insurance policy, just visit this site. For example we know that it is primarily used to cover financial responsibilities. Yet, we derive greater pleasure when our clients leave our offices, satisfied. The largest potential challenge with all of these policies is to ensure that the cash value of the investment component is generating a rate of return as good as other potential investments for the same cost, which is not always the case.

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If you will not need to make a cash withdrawal from your annuity, you can purchase an immediate annuity which skips the accumulation phase altogether. Later on, to satisfy market demand, cash value policies such as whole and universal life insurance policies were conceived. Term life insurance is in effect for a specific term, like 20 years. If you test positive when you apply for life insurance, you must disclose your HIV positive status to the life insurance company unless they will decline you. Take time to check our page if you want to know more about insurance. This affects the usage of the product as well as the limitations on the collection of the benefit. Special Risk Managers seeks to help people suffering from serious medical conditions find insurance cover.

After Reading About This Diet, Snake Oil is Actually Starting to Sound Really Good. Long term life insurance really blurs the line between whole life and term life insurance, with policies often borrowing from both structures to offer the customer even more flexibility. The main advantage of term life insurance over permanent life insurance policy is cost. People continue to make fundamental mistakes when researching on-line for finding the best insurance. Term insurance protects potential loss due to death of the insured. Take into account a situation where you are about to book a flight. For example, a younger, married person with children may opt to purchase a term life insurance to help cover the mortgage or replace lost income if they die during the coverage period.

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