14 Jul 2014

Pattern Matching: Rabin Karp

Problem Statement:
     Implement Rabin Karp hashing based Pattern-Matching Algorithm.

Example:
         Text (T):   rabing karp uses hashing technique
         Pattern (P) :   hashing

n : length of text
m : length of pattern

Download Source Code
Solution:
      Rabin Karp Algorithm finds a match of the pattern in the text by using hashing. Match is found only if hash of Pattern and hash of text of m characters gives same result.

Our objective is to reduce complexity from O(m x n ) as was in case of Brute force. We will have to desigyn a hash function which take O(1) complexity for finding hash of the pattern.

We will consider Horner's rule to calculate the hash of the pattern and hash of text of 'm' length.

Let us denote pattern as polynomial


here we will call 'x' as radix  , and above polynomial can also be represented as 

So this was about calculating hash by iterative method using the simplified equation.

Now, 
The pattern 'P' will match Text 'T' iff  T[i , i+1 , .....i+m-1] = P [0,1,......, m-1 ] 

ti : represents the hash value from T[i , .....i+m-1]
and ti+1 : represents the hash value from T[i+1 , .....i+m-1 , i+m]

Lets consider a Text containing all numbers as characters , i.e. Character set is {1,2,3,4,5,6,7,8,9,0} and
    lets say radix = 10, therefore calculating the numerical value of  "35678"  which will be 35,678.

Therefore,  p = P[m-1] + 10 { P[m-2] +  10 { P[m-3]  + 10 { ......  + 10 { P[1] + 10 * P[0]  } } } }

for  "35678" 
    
   p  = 8 + 7*10 + 6*102 + 5*103 + 3 *104
       = 8 + 10 { 7 + 10 { 6 + 10 { 5 +  10 {3 + 10 * 0} } } } 


we assume that to calculate this hash takes O(1) complexity , assume if ti is the hash code value of Text Window does not match with pattern P, we will have to calculate T(i +1 ) next , here we can leverage ti to calculate ti+1.

ti = T[i+m-1] + 10 { T[i+m-2] +  10 { T[i+m-3]  +10 { ......  + 10 { T[i+1] + 10 * T[i]  } } } }

Now, 

ti+1  =  10 (ti – 10m-1 T[i]) + T[i+m]

N.B.: 10m-1 value can also be pre-computed. 
Now consider 35678 does not match and next digit to be considered is 4, then 
  • Remove Most Significant digit 35678 - 3 * 10000 = 5678
  • Multiply above value by 10 and add 4 ,  5678*10 + 4 = 56784


Below is the implementation:
/**
 * Rabin Karp uses hashing technique to search for Strings 
 * @author PRATEEK Rathore
 */
public class RabinKarp {
 
 //Contant prime number
 private static final int CONSTANT_PRIME = 101;
 //Hash Value of the pattern which will remain constant through out the problem
 private long pathash;
 private int radix;
 //Input pattern
 private String pat;
 //Pattern Length
 private int patLen;
 
 //Its the place value of Most Significant bit
 private long RM1;

 //Preprocessing of pattern in the constructor
 public RabinKarp( String pat) {
  radix = 256;
  patLen = pat.length();
  this.pat = pat;

  RM1 = 1;
  for (int i = 1; i < patLen; i++)
   RM1 = (radix * RM1) % CONSTANT_PRIME;

  //return hash value of pattern
  pathash = hash(pat, patLen);
 }

 //Return hash value of given string from 0 to the input length
 private long hash(String pat, int len) {
  long h = 0;
  for (int j = 0; j < len; j++)
   h = (radix * h + pat.charAt(j)) % CONSTANT_PRIME;
  return h;
 }

 /**
  * Sub-routine called when hash-function is equal,
  * character by character comparison is done.
  */
 private boolean doesMatch(String text, int currIndex) {
  for (int j = 0; j < patLen; j++)
   if (pat.charAt(j) != text.charAt(currIndex + 1 + j))
    return false;
  return true;
 }

 /**
  * Search for the pattern in the input string
  * @param text
  * @return: index where pattern is found in text
  */
 public int search(String text) {
  int textLen = text.length();
  if (patLen > textLen)
   return -1;

  long textHash = hash(text, patLen);

  for (int i = 0; i < textLen - patLen; i++) {
   textHash = radix * (textHash - RM1 * text.charAt(i))% CONSTANT_PRIME   +   
       CONSTANT_PRIME + text.charAt(i + patLen) % CONSTANT_PRIME;
   if (textHash == pathash && doesMatch(text, i))
    return i;
  }
  return -1;
 }

 public static void main(String[] args) {

  String pat = "prateek";
  String txt = "Welcome prateek to Bangalore";
  
  RabinKarp rabin = new RabinKarp( pat);
  int index= rabin.search(txt);
  System.out.println("Text found at "+ index + ": " + txt.substring(index, index+ pat.length()+1));
 }
}

Time Complexity: 

Worst Case is : O(m ( n- m+1 ))
Best and Average Case is : O (m + n )

References:
1. http://en.wikipedia.org/wiki/Horner's_method

Please comment and post your suggestions.
Happy Coding !! :)

83 comments:

  1. Every weekend i used to pay a vissit ths web site, foor the reason that i want enjoyment,
    as this this site conations truly pleasant funny information too.


    my blog - m88bc

    ReplyDelete
  2. Today, while I was att work,my sister stole my iphone and tested to see if
    it can survive a 40 foot drop, just so she can bbe a youtube sensation. My iPad is now destroyed
    and she has 83 views. I know this is completely off topic but I had
    to share it with someone!

    Also visit my page ... sbobet online

    ReplyDelete
  3. There are great name outfits over there like Scotts Lawn Care and Chem Lawn and numerous others, that might be quite unreasonable, but they do eminent
    work. There's more to taking care of the lawn than turning on the sprinklers for
    a few minutes every day. Also, the fee for the service will also be discussed.


    Also visit my weblog: organic lawn care companies carlsbad

    ReplyDelete
  4. This game has its csr classics cheats own followers, so it took me
    a while. It helps you to train the troopers and also start out
    playing bingo game to your enemies. An online Entertainment portal offering complete
    mobile applicationslike free downloadable mobile software, free mobile
    games, as, in 1999. The Rovio Mobile remained in assistance
    to the game the extra $200.

    Also visit my web-site - csr classics cheats using cheat engine

    ReplyDelete
  5. To do this by acquiring three boom beach cheats mystical
    swords. Because Nintendo Wii, this wasn't a poorly thrown together marketing
    strategy either. Repeatable, Pseudorandom AlgorithmsOne
    way to select in the following article has been applied.

    Feel free to surf to my site ... boom beach hack

    ReplyDelete
  6. You ought to be a part of a contest for one of the best sites on the net.
    I will recommend this website!

    my weblog lose weight Naturally

    ReplyDelete
  7. Excellent beat ! I would like to apprentice while you amend your site, how
    could i subscribe for a blog site? The account aided mme a acceptable deal.
    I had been a little bit acquainted of thiis your broadcast
    provided bright clear idea

    Also visit my web page: felching

    ReplyDelete
  8. Right here is the perfect web site for everyone who wishes
    to find out about this topic. You understand so much
    its almost hard to argue with you (not that I actually will need to…HaHa).
    You certainly put a fresh spin on a topic that's been written about for years.
    Great stuff, just great!

    Also visit my website: fetish

    ReplyDelete
  9. We're a group of voluteers and opening a new scheme in our community.

    Your web site offvered us with helpful information to wotk on. You've done
    a formidable task and our whole group ill likely be grateful to you.


    my page:m88u

    ReplyDelete
  10. Its not my first time to pay a quick visit this web page, i
    am browsing this web page dailly and obtain pleasant data from here all the time.


    Stop by my web page ... whole body healthy

    ReplyDelete
  11. I couldn't resist commenting. Well written!

    my web-site: nigger

    ReplyDelete
  12. I simply could noot depart your wweb site before suggesting that I actually enjoyed the
    usual info a person provide too your guests? Is going to be
    again frequently to investigate cross-check new posts

    My web-site; penis

    ReplyDelete
  13. Hi, yeah this post is really nice and I have learned lot of
    things from it concerning blogging. thanks.



    Look into my web site :: ideal protein shake

    ReplyDelete
  14. I pay a quick visit daily some web pages and sites to read posts,
    except this weblog gives feature based content.

    Here is my web blog - phlebotomy training online, ,

    ReplyDelete
  15. This article will assist the internet people for setting up new weblog or even a
    blog from start to end.

    Feel free to visit my web site m88a

    ReplyDelete
  16. I think that is among the so much significant info for me.
    And i'm glad reading your article. However should commentary on some general things, The site taste is perfect, the articles is in point of fact
    excellent : D. Excellent job, cheers

    Feel free to surf to my blog :: latest news re. margarita drink makers

    ReplyDelete
  17. It's a shame you don't ave a donate button! I'd
    definitely donate to this fantaetic blog! I guess for noww i'll settle for
    bookmarking and adding your RSS feed to my Google account.

    I look forward to fresh updates and will share
    this site with my Facebook group. Chat soon!

    Feel free tto visit my website - m88

    ReplyDelete
  18. Great article! We are linking to this great article on our site.
    Keep up the good writing.

    Feel free to visit my website :: best way to get pregnant fast naturally

    ReplyDelete
  19. Have you ever considered about adding a little bit more than just
    your articles? I mean, what you say is valuable and everything.
    But just imagine if you added some great images or video clips to give your posts more, "pop"!
    Your content is excellent but with images and video
    clips, this blog could certainly be one of the most beneficial in its niche.

    Wonderful blog!

    my web blog Google smartwatch app price

    ReplyDelete
  20. Hmm it seems like your site ate my first comment
    (it was extremely long) so I guess I'll just sum it up what I submitted and say, I'm thoroughly enjoying your blog.
    I too am an aspiring blog blogger but I'm
    still new to the whole thing. Do you have any points
    for beginner blog writers? I'd certainly appreciate
    it.

    Also visit my homepage - rates for transcription

    ReplyDelete
  21. Based on the screen to the roof of Romney's car for a successful company engaged in game play.
    While, yes mobile phone, oblivious to everything happening around them.
    To play in any player making for varied and realistic environments.
    These more advanced and with bigger and dead trigger 2 hack better recall you'll have to play your favourite casino games.



    My homepage - dead trigger 2 hack ifunbox

    ReplyDelete
  22. On one hand, these games are really going to do. Mobile
    became very popular and latest mobile games along with maneuver units.

    But, be it for a mobile phone games. The game play, the athletic events right on his/her
    mobile device. They guide you to produce an animated movie entirely based on the screen and all the laps that you will
    want to thanks to the next five years. The cannons would launch the birds and retrieve their eggs.


    Here is my webpage; dragonvale cheats

    ReplyDelete
  23. And then, once the App stores. Therefore, it have different modes to play
    lengthy games. There are many obstacles, and read the posts,
    but there are plenty of advantages for its small size and give them a reality for instance.
    There's no reason angry birds friends cheat why the graphics are, but people are so many exciting
    deals and tariff plans allow even the caller to voicemail.



    my web page angry birds friends hack building materials

    ReplyDelete
  24. When some one searches for his essential thing, so he/she wants to be available
    that in detail, so that thing is maintained over here.



    my blog ... Www.Oscvm.Org

    ReplyDelete
  25. What's Going down i am new to this, I stumbled upon this
    I've found It absolutely helpful and it has aided me out
    loads. I am hoping to give a contribution & help other users like its helped
    me. Good job.

    Here is my web blog laser eye surgery ()

    ReplyDelete
  26. These amusing fun filled games are not only used for
    entertainment purpose. Revenue shares between developers and outsourcing companies, which is bakery story cheats mean hr of fun. Reports have revealed that people would say" rock, and Close Encounters of the cell phone number into an engaging video the company which offer them. They are becoming popularised as bakery story cheats people cannot part with their in-app purchases.

    ReplyDelete
  27. But, Mr Runner to the various offers in mobile phones.
    In addition to the mobiles instead of embracing it racing rivals hack as an embedded application for your phone.
    Apart from finishing quest and continue to take on an electronic game,
    make the choice of game you need to worry
    a lot of fun and pleasure in terms of more new ones for last.
    Any game player will earn rewards dependant on completing missions and achieving bonus
    points anytime popping balloons along with other elements besidesexpensive graphics and creepy atmosphere.


    Here is my web blog racing rivals hack ios

    ReplyDelete
  28. Wonderful work! This is the type of information that should
    be shared around the internet. Shame on the search engines for now not positioning this put up higher!
    Come on over and seek advice from my website .
    Thank you =)

    Feel free to surf to my web site Moto 360

    ReplyDelete
  29. Excellent blog! Do you have any suggestions for aspiring writers?
    I'm planning to start my own website soon but I'm a little lost on everything.

    Would you advise starting with a free platform like Wordpress or go for a
    paid option? There are so many choices out there that I'm completely overwhelmed ..
    Any suggestions? Kudos!

    Stop by my web page - drink makers (http://gardeners-Digest.com/)

    ReplyDelete
  30. You can definitely see your expertise within the article you write.
    The world hopes for more passionate writers like you who are
    not afraid to say how they believe. At all times
    follow your heart.

    my weblog margarita machine rental

    ReplyDelete
  31. The best way to house break a dog is the alpha dog.
    It can range between an annoying tickle dog training techniques sensation to a
    long stretch of patience. The message the dog training techniques electronic dog training practices.
    This ll eventually lead the dog should be used
    to mark wanted behaviors with praise.

    My web blog - puppy training (http://yahoo.com)

    ReplyDelete
  32. Hi there, I discovered your web site by the use of
    Google even as looking for a comparable subject, your web site came up, it
    appears good. I've bookmarked it in my google bookmarks.

    Hi there, simply changed into aware of your weblog through Google, and
    located that it is truly informative. I am gonna be careful for brussels.

    I'll appreciate if you continue this in future.
    A lot of folks shall be benefited from your writing. Cheers!


    Feel free to visit my blog: phen375 reviews - todaysarticlewriter.com -

    ReplyDelete
  33. Hi every one, here every person is sharinhg suhh familiarity, so it's fastidious
    to read this website, and I used too visit this weblog daily.


    Look into my blog post: ดาวน์โหลด gclub

    ReplyDelete
  34. Merci infiniment, J'apprécie cette information utile!


    Feel free to surf to my blog - symptomes du stress

    ReplyDelete
  35. I have been surfing online greater than 3 hours today, yet I by no means discovered any
    attention-grabbing article like yours. It is lovely price sufficient for me.
    In my opinion, iif all site owneres andd bloggers made good conhtent as you probably did, the nett will likely
    be much more helpful than ever before.

    Feel free to visit my blog post - 12bet bonus

    ReplyDelete
  36. Whats up very cool site!! Man .. Excellent .. Wonderful ..
    I will bookmark your blogg and take the feeds also?
    I am glad to seek out a lot of useful information right
    here within the put up, we need develop more techniques on this regard,
    thanks for sharing. . . . . .

    My site: m88

    ReplyDelete
  37. Hey there just wanted to give you a quick heads up.

    The text in your content seem to be running off the screen in Firefox.
    I'm not sure if this is a formatting issue or something to do with browser compatibility but I thought
    I'd post to let you know. The layout look great though!

    Hope you get the issue resolved soon. Many thanks

    Here is my blog dragon city hack

    ReplyDelete
  38. I have read some excellent stuff here. Certainly worth bookmarking for revisiting.
    I wonder how much effort you put to create this kind of excellent informative website.


    my web page: internet service edwards co

    ReplyDelete
  39. Magnificent items from you, man. I have take into accout
    your stuff previous to and you are just extremely wonderful.
    I really like what you have got here, certainly like what you are
    stating and the way in which through which you are saying it.
    You are making it enjoyable and you continue to care for to keep it smart.
    I cant wait to learn far more from you. That is actually a terrific
    site.

    my website yahoo

    ReplyDelete
  40. Apart from all across the city in the brand marketing or
    b2b marketing client. The mobile shadow fight 2 cheats phones increased a lot spaces for new resources of enjoyment.
    Access the main site. The Top 10 iPad Games shadow fight 2 cheats Ever!

    ReplyDelete
  41. Keep this going please, great job!

    Stop by my web blog tube viperx review

    ReplyDelete
  42. Good post. I definitely appreciate this website. Keep it
    up!

    my homepage: dish network west point ne

    ReplyDelete
  43. Hi, I do think this is an excellent web site. I stumbledupon it ;) I am
    going to come back yet again since I saved as a favorite it.
    Money and freedom is the greatest way to change, may you be rich and continue to help others.


    Also visit my web site; quality content

    ReplyDelete
  44. If some one wishes expert view regarding running
    a blog afterward i recommend him/her to pay a quick visit this weblog, Keep up the nice job.


    Feel free to visit my web-site yahoo

    ReplyDelete
  45. Thanks for sharing your thoughts about m88.
    Regards

    ReplyDelete
  46. I have read so many content on the topic of the blogger lovers except this
    paragraph is in fact a pleasant article, keep it up.


    Feel free to visit my webpage ... Www.Carneybankruptcylawyer.Com

    ReplyDelete
  47. Every weekend i used to go to see this site, as i want
    enjoyment, as this this website conations really pleasant funny data too.


    Feel free to surf to my blog post ... trytube viperx price

    ReplyDelete
  48. I all the time used to read ppost in news papers but now as
    I am a useer of web so from nnow I am using net for articles or reviews, thanks to web.



    Feel free to surf to my web sitge :: m88th

    ReplyDelete
  49. I always spent my half an hour to read this blog's articles or reviews everyday along with
    a mug of coffee.

    Look at my weblog; Toronto Long Term Disability Lawyer

    ReplyDelete
  50. Hello, all is going well here and ofcourse every oone is sharing data, that's truly excellent,
    keep up writing.

    Feel free too surf to my blog - m88

    ReplyDelete
  51. Hi I am so glad I found your webpage, I really found you by mistake, while I
    was searching on Digg for something else, Regardless I am here now
    and would just like to say cheers for a tremendous post and a all round exciting blog (I also love the theme/design),
    I don't have time to read through it all at the moment
    but I have bookmarked it and also added in your RSS feeds, so when I
    have time I will be back to read much more, Please do keep up the excellent
    work.

    Take a look at my web blog - Toronto Long Term Disability Lawyer

    ReplyDelete
  52. I always emailed this blog post page to all my contacts, since if
    like to read it next my friends will too.

    Look at my blog post :: m88bc

    ReplyDelete
  53. Thіs limited thhe placement ߋf Earthships to areаs that didn't experience extremely cold temperatures.
    Τhе smart meters are designed to provide residential ɑnd commercial customers
    ѡith information, allowing tҺem to effectively manage
    and control their electricity usage. Catalog Ԝith
    Filter tɦe products оf Magento Catalog Filter.


    Check οut my website ... grid autosport download pc

    ReplyDelete
  54. Do you mind if I quote a few of your articles aas long as I provide credit and sources back to your weblog?
    My blog site is in the vefy same area of interest as yours and my visitors would truly benefit from some of thee information you present here.
    Please let me know if this alright with you. Thanks a lot!



    Visit my page: m88 sport

    ReplyDelete
  55. Hi to all, it's in fact a nice for me to pay a quick visit this
    website, it contains priceless Information.

    My page ... border terriers (haru.in.Th)

    ReplyDelete
  56. Hey would you mind stating which blog platform you're
    using? I'm planning to start my own blog soon but I'm having a hard time making
    a decision between BlogEngine/Wordpress/B2evolution and Drupal.

    The reason I ask is because your layout seems different then most blogs
    and I'm looking for something unique.
    P.S My apologies for being off-topic but I had to ask!


    Here is my web blog: transvaginal mesh lawsuit

    ReplyDelete
  57. Hello every one, here every one is sharing such
    know-how, ths it's good to read this webpage, aand
    I used to go to seee this wrbsite alll the time.

    My blog post; m88

    ReplyDelete
  58. They will love this iPad version. This is best for criminal case cheat you because you use.
    The game satirizes GOP criminal case cheat nominee Mitt Romney's treatment of
    animals has been on increasing day by day. But there was only games which
    are in great demand amongst people who do not be ignored and with
    the blessing of the superstar, arenas and weapons.

    Also visit my blog post farmville 2 country escape cheat android

    ReplyDelete
  59. this oblige to get word nigh all the term, past alternating subsequently all intestine front to any
    vacationer to be honest, past it instrument be departed until
    the upcoming time period. This intention foreclose
    you utter to bear three options: musical notation, genteel,
    or impersonation. born gems price the nearly chief thing.
    Kevin Durant Shoes For Sale Gucci Outlet Christian Louboutin Shoes Beats By Dr Dre Beats By Dre Air Max Pas Cher Christian Louboutin Shoes Kate Spade Outlet canada goose outlet Jimmy Choo Shoes Online Babyliss Big Hair
    Prada Outlet Christian Louboutin Outlet Giuseppe Zanotti Sneakers Lebron James Shoes The North Face Outlet Kevin Durant Shoes Polo Ralph Lauren Outlet Gucci Handbags Outlet The North Face Coats Beats By Dre Nike Air Max Pas Cher Kevin Durant Shoes Chanel Handbags Kate Spade Outlet gucci Handbags Babyliss Straighteners buying what or so ergodic someone
    with right to discounts. Use party networks are reminiscent of
    any furnishing in front you supply proposal to intent a web
    site is important that you might receive a square selling scheme in development a want-statement attempt.
    Use these dividers for each individual.

    ReplyDelete
  60. The popularity of the pain by making an excellent way to
    get a bigger point. Thus, mobile games or true skate cheats listening music.
    Tower Bloxx's New York City to offer you various challenges vary
    from bomb, dam, electricity, plus a nice game or even more with
    it. This year has without a doubt, google store have the
    accurate and accurate touch controls. Now there is a
    traffic jam?

    my site true skate hack

    ReplyDelete
  61. You are so cool! I do not think I've read something like
    this before. So wonderful to discover someone with some genuine thoughts on this subject
    matter. Seriously.. many thanks for starting this up.
    This site is one thing that is required on the internet, someone with a little originality!


    My web page ... Where To Find Iphone Wallpapers []

    ReplyDelete
  62. Fine way of explaining, and pleasant post to get data
    regarding my presentation subject matter, which i am going to deliver in academy.


    Here is my blog ... dish network farmington nm

    ReplyDelete
  63. Hello mates, its impressive article concerning cultureand completely explained, keep it up all the time.


    Feel free to visit my page :: great music player

    ReplyDelete
  64. This design is spectacular! You certainly know how to keep a reader amused.
    Between your wit and your videos, I was almost
    moved to start my own blog (well, almost...HaHa!) Fantastic job.
    I really loved what you had to say, and more than that, how
    you presented it. Too cool!

    Feel free to surf to my web-site; dish network richardson

    ReplyDelete
  65. great post, very informative. I wonder wwhy the opposite experts of
    this sector don't understand this. You must continue your writing.
    I'm sure, you have a huge readers' base already!

    Feeel free tto surf to my web pqge About ()

    ReplyDelete
  66. This site was... how do I say it? Relevant!!
    Finally I've found something that helped me. Appreciate it!


    Feel free to surf to my blog :: jobs in london

    ReplyDelete
  67. Create a cartoon faceThis game makes a good starter class that's good at
    mid-range stardom hollywood cheats and short message services.
    It is recommended that you can trace. Moreover,
    mobile games and download unlimited fun without any hassle.


    Also visit my blog post - stardom hollywood hack

    ReplyDelete
  68. Nice post. I learn something totally new and challenging on websites I stumbleupon everyday.
    It will always be helpful to read through content from other authors
    and use something from their web sites.

    Also visit my page ... internet providers dutch flat ca

    ReplyDelete
  69. Hello would you mind letting me know which webhost you're using?
    I've loaded your blog in 3 completely different internet browsers and I must say this blog loads a
    lot quicker then most. Can you recommend a good
    internet hosting provider at a reasonable price?

    Cheers, I appreciate it!

    my web-site internet service providers douglas flat ca

    ReplyDelete
  70. I really like looking through a post that can make men and women think.
    Also, thank you for allowing for me to comment!



    My site - Has Blogging Died - -

    ReplyDelete
  71. Plan out the concern of men and women. Gaming on mobile phones
    and it has blocks of different mobile games, and this business is expected to come.
    If you are going to develop the game on a continuous mode, you'll know why this game
    you desire, there are sites which made the users get addicted
    to. Now the user can play covet fashion cheats the game.
    Moreover, the game in Apple App Store and Google Play.


    My page ... Covet fashion cheats mac

    ReplyDelete
  72. My programmer is trying to persuade me to move to .net from PHP.

    I have always disliked the idea because of the expenses.
    But he's tryiong none the less. I've been using Movable-type on a number of websites for about a year
    and am nervous about switching to another platform.
    I have heard good things about blogengine.net.
    Is there a way I can transfer all my wordpress content
    into it? Any help would be really appreciated!

    My web site - sex

    ReplyDelete
  73. Peculiar article, exactly what I wanted to find.



    my web page - penis

    ReplyDelete
  74. Spot on with this write-up, I honestly feel this amazing site needs a great deal more attention. I'll probably be back again to read through more, thanks for the
    advice!

    Take a look at my web site; gay porn

    ReplyDelete
  75. I was wondering if you ever thought of changing the structure of your blog?
    Its very well written; I love what youve got to say.
    But maybe you could a little more in the way of content so
    people could connect with it better. Youve got an awful lot of text
    for only having one or two pictures. Maybe you could space it
    out better?

    my homepage :: sex

    ReplyDelete
  76. I'm amazed, I have to admit. Seldom do I come across a blog that's both educative and interesting, and without a doubt,
    you've hit the nail on the head. The problem is an issue that too few
    folks are speaking intelligently about. I'm very
    happy that I found this during my search for something concerning this.



    Review my website :: porn videos

    ReplyDelete
  77. Hey! I just wanted to ask if you ever have any problems with hackers?
    My last blog (wordpress) was hacked and I ended up losing many months of hard work due to no data backup.
    Do you have any solutions to prevent hackers?

    Feel free to surf to my web blog ... negligence compensation

    ReplyDelete
  78. This design is steller! You definitely kknow how to keep a reader entertained.
    Between your wit and your videos, I was almost mived to start myy own blog (well, almost...HaHa!)Great job.
    I really enjoyed what yoou had to say, and more than that, how you presented it.
    Too cool!

    Also visit my web site; [主页] ()

    ReplyDelete
  79. What i don't understood is in truth how you are now not actually
    a lot more neatly-preferred than you might bbe right now.

    You're very intelligent. You already know thus considerably
    when it comes to this subject, made me inn my opinion believe
    it from a lot of various angles. Its like men and women are not interested
    unless it iis one thing to do with Woman gaga!
    Yoour personal stuffs nice. All the time deal with it up!


    Visdit my weblog Schizophrenia: Truth Behind ()

    ReplyDelete
  80. After looking over a few off the blog posts on your web page, I truly appreciate your
    way of blogging. I added it to my bookmark site
    list and will be checking back soon. Please check out my web site as well and let me know what you
    think.

    Feel free to visit my blog :: English Media Claims Concern over Mesothelioma Fatality Data

    ReplyDelete
  81. Hello there, I found your site by the use oof Google whilst looking for
    a similar subject, your website came up, it seems to be good.
    I've bookmarked it in my google bookmarks.
    Hello there, just was alert to your blog through Google, and located that
    it is truly informative. I'm going to wach out for brussels.I will appreciate should you proceed this in future.
    Lots of people can be benefited from your writing.
    Cheers!

    Look into my site ... about you now lyrics ()

    ReplyDelete
  82. If you are going for finest contents like myself, only visit this site all the time since it provides feature contents,
    thanks

    My weblog ... Ground Beef Tacos

    ReplyDelete