N-acetylphosphatidylethanolamine-hydrolysing phospholipase D

From formulasearchengine
Jump to navigation Jump to search

Template:More footnotes

File:Image of an anatree1.png
Anatree
File:Image of a mixed anatree.png
Mixed Anatree

An Anatree [1] is a data structure designed to solve anagrams. Solving an anagram is the problem of finding a word from a given list of letters. These problems are commonly encountered in word games like wordwheel, scrabble or crossword puzzles that we find in newspapers. The problem for the wordwheel also has the condition that the central letter appear in all the words framed with the given set. Some other conditions may be introduced regarding the frequency (number of appearances) of each of the letters in the given input string. These problems are classified as Constraint satisfaction problem in computer science literature.

An anatree is represented as a directed tree which contains a set of words (W) encoded as strings in some alphabet. The internal vertices are labelled with some letter in the alphabet and the leaves contain words. The edges are labelled with non-negative integers. An anatree has the property that the sum of the edge labels from the root to the leaf is the length of the word stored at the leaf. If the internal vertices are labelled as α1, α2 ... αl, and the edge labels are n1, n2 ... nl, then the path from the root to the leaf along these vertices and edges are a list of words that contain n1 α1 s, n2 α2 s and so on. Anatrees are intended to be read only data structures with all the words available at construction time.

A Mixed Anatree is an anatree where the internal vertices also store words. A mixed anatree can have words of varying lengths, where as in a regular anatree, all words are of the same length.

Data Structures for solving Anagrams

A number of data structures have been proposed to solve anagrams in constant time. Two of the most commonly used data structures are the Alphabetic map and the Frequency map. The Alphabetic map maintains a hash table of all the possible words that can be in the language (this is referred to as the lexicon). For a given input sting, sort the letters in alphabetic order. This sorted string maps onto a word in the hash table. Hence finding the anagram requires sorting the letters and a looking up the word in the hash table. The sorting can be done in linear time by the counting sort and hash table look up can be done in constant time.

For example for the word ANATREE, the alphabetic map would produce a mapping of {AAEENRT>{anatree}}.

A Frequency map also stores the list of all possible words in the lexicon in a hash table. For a given input string, the frequency map maintains the frequencies (number of appearances) of all the letters and uses this count to perform a look up in the hash table. The worst case execution time is found to be linear in size of the lexicon.

For example for the word ANATREE, the alphabetic map would produce a mapping of f(A)>2,f(E)>2,f(N)>1,f(R)>1,f(T)>2. The words that do not appear in the string are not written in the map.

Construction of an Anatree

The construction of an Anatree begins by selecting a label for the root and partitioning words based on the label chosen for the root. This process is repeated recursively for all the labels of the tree. Anatree construction is non-canonical for a given set of words, depending on the label chosen for the root, the anatree will differ accordingly. The performance of the anatree is greatly impacted by the choice of labels.

The following are some heuristics for choosing labels:

  • Start labeling vertices in alphabetical order from the root. This approach reduces construction overhead
  • Start labeling vertices based on the relative frequency. A probabilistic approach is used to assign labels to vertices. If Wnα is the set of words that contain nαs, then we label the vertex with α if it maximizes the expected distance to the leaf. This approach has the most frequently appearing characters (like E) labeled at the root and the least frequently appearing characters labeled at the leaves. The following equation is maximized Dα=nn|Wnα||W|. This approach prevents long sequences of zero labeled edges since they do not contribute letters to the words generated by the anatree.

Finding Anagrams in an Anatree

To find a word in an anatree, start at the root, depending on the frequency of the label in the given input string, follow the edge that has that frequency till the leaf. The leaf contains the required word. For example, consider the anatree in the figure, to find the word dog, the given string may be ogd. Start at the root and follow the edge that has 1 as the label. We follow this label since the given input string has 1 d. Traverse this edge until the leaf is encountered. That gives the required word.

Space and Time Requirements

A lexicon that stores w words (each word can be l characters long) in an alphabet A has the following space requirements.

Data Structure Space Requirements
Alphabetic Map O(wl(log|A|)
Frequency Map O(w(|A|logl+llog|A|))
Anatree O(w|A|(log|A|+l))

The worst case execution time of an anatree is O(|w|(l+w|A|2))

See also

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

  1. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  2. Template:Cite web
  3. Template:Cite web