|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{Infobox Algorithm
| | Yet in the late 1800's lots of people, particularly women, would ingest tapeworm cysts (baby tapeworms) to help shed those unwanted pre-tapeworm pounds. Like any life insurance policy, it has its benefits and its disadvantages. However, receiving cheap term life insurance quotes will not translate into cheap rates if you are not careful about filling up the quote form. Your life insurance car loan calculator can assist you see how a lot you're worthy of (in insurance coverage), and exactly how much you'll want to spend to have this insurance coverage; along with - Several. In case you loved this information along with you wish to acquire more information concerning [http://www.termlifepolicy.com/insurance-agents/texas/euless.html what is the definition of term life insurance] generously visit the web page. Make sure the policy will remain in force until at least age 65, or is renewable until at least age 65 without regard to the condition of your health. You have hundreds of insurance companies that you can choose from. They forget to look at the company's reputation and standing in the industry. <br><br>Term life insurance can be quite affordable, especially if you are young and healthy. Death is a pretty delicate topic and lots of people prevent talking about this due to exactly how painful it can be for them. You may have heard that term life [http://wordpress.org/search/insurance insurance] is generally a better value than whole life. This means that you would be able to pick a term life insurance policy that offers overall security for your dependents and family;. It's about large group of people that all share risk together. Term life insurance online is an easy, inexpensive way to insure yourself for your family"s sake. So when the policy owner dies, his or her beneficiaries receive the death benefit plus the cash value. <br> <br> Additionally, this act has the role of protecting interests of persons who are involved in providing life insurance business. Bipolar Disorder I is more serious than Bipolar Disorder II. It costs more than term but if you keep it for 20 or 30 years or longer you will likely get back whatever you have paid into it if you choose to surrender it for it's cash value. I'm an advocate of "many buckets" with a whole life policy being one of them. Some of these occupations include commercial fishing, logging, helicopter or airplane piloting, and roofing. For most families, this means getting term life insurance coverage until all of the children are living on their own. Even so, it will be most ideal for all those who get paid a dwelling for his or her family members. <br> <br> You should be very diplomatic while assigning anything. The rate class is fed into a mathematical formula, and what comes out the other end is the price that the insurer offers you. The majority of couples choose combined term life insurance because it is less expensive than purchasing two person term life insurance policies. Specifically, as the term of the policy goes on, the monthly premium will rise. They haven't considered other options for paying for long term care. These policies accumulate a cash value over their lifetime. With the passing of time, as your age moves forward, you need to pay a considerably big amount for the policy premium. <br> <br> In case of life insurance the ultimate beneficiaries are the near and dear ones of the policy holder. We specialise in life insurance and will search the market and help you find the right cover at the best price available. Death is not something most young people want to consider, but life insurance is really not about death. While the majority of people use these policies to save for retirement, it is possible to withdraw funds from the annuity at any point in time. In a new marriage, two lives are merging and many assets are being combined. The above reasons will definitely delay the payment of a claim while they decide to pay or not the claim. how much coverage you need and how much you can afford for premiums each month. <br> <br> For further details please visit the provided links. Some banks, franchisors, and even business partners won't require a life insurance policy so it's best to find out first before you enter into any financial agreements for the business. It will not only cover future funeral, medical and burial expenses but it can also be used as an income replacement for the surviving children and spouses. Banks may also require life insurance coverage before they give you a loan. Some companies take approximately 3 days to issue your policy and there are companies that qualify you instantly and you can actually print your no exam term life insurance policy right then and there. , term life policies range from 5 to 40 years based on how old you are when you buy your policy. Dennis Jarvis is a licensed insurance agent concentrating on getting the best term life insurance quote. <br> <br> When creating a life insurance policy, never name your minor children as the beneficiary. Your life insurance plan should be just like you: unique. So why do you need to consider taking out a life insurance policy and what should you be looking for from your policy. Mostly this benefit is applicable for Regular polices and not for Single policies. It is important to note that the purchase of term insurance from the better life insurance companies allows you the opportunity to convert to permanent life insurance at a later date. The particular coverage case confirms to cover any established sum or perhaps quality with typical time periods or perhaps inside large total sum inturn. If the insurance coverage holder dies through the time period, demise advantages straight go to the beneficiary. |
| |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'' log ''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]]
| |
Yet in the late 1800's lots of people, particularly women, would ingest tapeworm cysts (baby tapeworms) to help shed those unwanted pre-tapeworm pounds. Like any life insurance policy, it has its benefits and its disadvantages. However, receiving cheap term life insurance quotes will not translate into cheap rates if you are not careful about filling up the quote form. Your life insurance car loan calculator can assist you see how a lot you're worthy of (in insurance coverage), and exactly how much you'll want to spend to have this insurance coverage; along with - Several. In case you loved this information along with you wish to acquire more information concerning what is the definition of term life insurance generously visit the web page. Make sure the policy will remain in force until at least age 65, or is renewable until at least age 65 without regard to the condition of your health. You have hundreds of insurance companies that you can choose from. They forget to look at the company's reputation and standing in the industry.
Term life insurance can be quite affordable, especially if you are young and healthy. Death is a pretty delicate topic and lots of people prevent talking about this due to exactly how painful it can be for them. You may have heard that term life insurance is generally a better value than whole life. This means that you would be able to pick a term life insurance policy that offers overall security for your dependents and family;. It's about large group of people that all share risk together. Term life insurance online is an easy, inexpensive way to insure yourself for your family"s sake. So when the policy owner dies, his or her beneficiaries receive the death benefit plus the cash value.
Additionally, this act has the role of protecting interests of persons who are involved in providing life insurance business. Bipolar Disorder I is more serious than Bipolar Disorder II. It costs more than term but if you keep it for 20 or 30 years or longer you will likely get back whatever you have paid into it if you choose to surrender it for it's cash value. I'm an advocate of "many buckets" with a whole life policy being one of them. Some of these occupations include commercial fishing, logging, helicopter or airplane piloting, and roofing. For most families, this means getting term life insurance coverage until all of the children are living on their own. Even so, it will be most ideal for all those who get paid a dwelling for his or her family members.
You should be very diplomatic while assigning anything. The rate class is fed into a mathematical formula, and what comes out the other end is the price that the insurer offers you. The majority of couples choose combined term life insurance because it is less expensive than purchasing two person term life insurance policies. Specifically, as the term of the policy goes on, the monthly premium will rise. They haven't considered other options for paying for long term care. These policies accumulate a cash value over their lifetime. With the passing of time, as your age moves forward, you need to pay a considerably big amount for the policy premium.
In case of life insurance the ultimate beneficiaries are the near and dear ones of the policy holder. We specialise in life insurance and will search the market and help you find the right cover at the best price available. Death is not something most young people want to consider, but life insurance is really not about death. While the majority of people use these policies to save for retirement, it is possible to withdraw funds from the annuity at any point in time. In a new marriage, two lives are merging and many assets are being combined. The above reasons will definitely delay the payment of a claim while they decide to pay or not the claim. how much coverage you need and how much you can afford for premiums each month.
For further details please visit the provided links. Some banks, franchisors, and even business partners won't require a life insurance policy so it's best to find out first before you enter into any financial agreements for the business. It will not only cover future funeral, medical and burial expenses but it can also be used as an income replacement for the surviving children and spouses. Banks may also require life insurance coverage before they give you a loan. Some companies take approximately 3 days to issue your policy and there are companies that qualify you instantly and you can actually print your no exam term life insurance policy right then and there. , term life policies range from 5 to 40 years based on how old you are when you buy your policy. Dennis Jarvis is a licensed insurance agent concentrating on getting the best term life insurance quote.
When creating a life insurance policy, never name your minor children as the beneficiary. Your life insurance plan should be just like you: unique. So why do you need to consider taking out a life insurance policy and what should you be looking for from your policy. Mostly this benefit is applicable for Regular polices and not for Single policies. It is important to note that the purchase of term insurance from the better life insurance companies allows you the opportunity to convert to permanent life insurance at a later date. The particular coverage case confirms to cover any established sum or perhaps quality with typical time periods or perhaps inside large total sum inturn. If the insurance coverage holder dies through the time period, demise advantages straight go to the beneficiary.