473,695 Members | 2,862 Online
Bytes | Software Development & Data Engineering Community
+ Post

Home Posts Topics Members FAQ

String Pattern Matching algo

I came across a question in one of the Computing olympiad regarding
string pattern matching.

Write a program that will accept a fraction of the form N/D, where N is
the numerator and D is the denominator, that prints out the decimal
representation. If the decimal representation has a repeating sequence
of digits, it should be indicated by enclosing it in brackets. For
example, 1/3 = .33333333...is denoted as .(3), and 41/333 =
..123123123...i s denoted as .(123).

Typical conversions are:

1/3 = .(3)
22/5 = 4.4
1/7 = .(142857)
3/8 = .375
45/56 = .803(571428)

Now I could not think how do I even start writing a logic for creating
a pattern.
Then I thought that maybe I should start comparing characters from the
right rather than the left.
But these two examples even negate that theory;

1/7 gives me ---> 0.1428571428571 428571428571429 on a 16bit machine

45/56 gives me ---> 0.8035714285714 285714285714286

I was trying to eliminate the last number as it rounds off, and so I
can start creating combinations from right to left. But nothing seems
to be working.

Any hints/suggestions will be appreciated.

Apr 29 '06 #1
8 3902
Correction, I meant 16 bit integer.

Apr 29 '06 #2
11******@gmail. com wrote:
I came across a question in one of the Computing olympiad regarding
string pattern matching.

Write a program that will accept a fraction of the form N/D, where N is
the numerator and D is the denominator, that prints out the decimal
representation. If the decimal representation has a repeating sequence
of digits, it should be indicated by enclosing it in brackets. For
example, 1/3 = .33333333...is denoted as .(3), and 41/333 =
.123123123...is denoted as .(123).
<snip>
Now I could not think how do I even start writing a logic for creating
a pattern.
Algorithms questions really belong on comp.programmin g not here, but
I'll point you in the right direction...
Then I thought that maybe I should start comparing characters from the
right rather than the left.
But these two examples even negate that theory;

1/7 gives me ---> 0.1428571428571 428571428571429 on a 16bit machine

45/56 gives me ---> 0.8035714285714 285714285714286

I was trying to eliminate the last number as it rounds off, and so I
can start creating combinations from right to left. But nothing seems
to be working.
So don't do floating point division.
Any hints/suggestions will be appreciated.


How about this. Start off by getting out some maths books from when you
were much younger, the ones where you did long division. If you look at
it, you will see you were doing repeated integer division using the
remainder from the last division. Then you just have to watch out for
when you start repeating yourself...
--
Flash Gordon, living in interesting times.
Web site - http://home.flash-gordon.me.uk/
comp.lang.c posting guidelines and intro:
http://clc-wiki.net/wiki/Intro_to_clc

Inviato da X-Privat.Org - Registrazione gratuita http://www.x-privat.org/join.php
Apr 29 '06 #3
11******@gmail. com wrote:
I came across a question in one of the Computing olympiad regarding
string pattern matching.

Write a program that will accept a fraction of the form N/D, where N is
the numerator and D is the denominator, that prints out the decimal
representation. If the decimal representation has a repeating sequence
of digits, it should be indicated by enclosing it in brackets. For
example, 1/3 = .33333333...is denoted as .(3), and 41/333 =
.123123123...is denoted as .(123).


Well you need to essentially duplicate the process of long division by
hand, and note the repeating pattern like you did by hand. But the key
to things like this is not to *EXACTLY* duplicate the by hand process
(which has been optimized for our puny human brains), but rather
rederive what makes the by hand method work, just build the relevant
equations from there, and work out the process from there.

A repetition when dividing a fixed point by a fixed point happens
during long division when there is a repetition of the remainder
*after* the last significant digit of the numerator is consumed by the
division process.

In long division, you are approximating x = n/d by the sequence:

10^p *(n - x_p*d) = r_p, where 0 <= r_p < d, and 10^p*x_p is an
integer.

If there is a p such that r_p = 0, then you have an exact division,
otherwise you are looking for a pair of p's each such that 10^p > n (I
think; you should check this), where r_p repeats. Should be straight
forward.

--
Paul Hsieh
http://www.pobox.com/~qed/
http://bstring.sf.net/

Apr 29 '06 #4
11******@gmail. com wrote:
I came across a question in one of the Computing olympiad regarding
string pattern matching.

Write a program that will accept a fraction of the form N/D, where N is
the numerator and D is the denominator, that prints out the decimal
representation. If the decimal representation has a repeating sequence
of digits, it should be indicated by enclosing it in brackets. For
example, 1/3 = .33333333...is denoted as .(3), and 41/333 =
.123123123...is denoted as .(123).

Typical conversions are:

1/3 = .(3)
22/5 = 4.4
1/7 = .(142857)
3/8 = .375
45/56 = .803(571428)

Now I could not think how do I even start writing a logic for creating
a pattern.
Then I thought that maybe I should start comparing characters from the
right rather than the left.
But these two examples even negate that theory;

1/7 gives me ---> 0.1428571428571 428571428571429 on a 16bit machine

45/56 gives me ---> 0.8035714285714 285714285714286

I was trying to eliminate the last number as it rounds off, and so I
can start creating combinations from right to left. But nothing seems
to be working.

Any hints/suggestions will be appreciated.


Here's a hint. For a fraction in the range 0 to 1, it will be in the form
.baaaa
where b has k digits and a has n
This number can be written as
pow(10,-k)( b + a/(pow(10,n)-1))
^^^^^^^^^^^^
(Q)This part is n nines
The expression labeled with Q is all nines, so it has no factors which
are 2 or 5. In your rational expression N/D collect the factors of 2
and 5, so
D = pow(2,r) * pow(5,s) * R
k must be the larger of r and s, and n (number of nines in Q) will be at
most R and could be less. b has at most than k digits. Notice that
16-bit signed numbers can reach pow(2,15)-1 == 32767. Luckily this is
not prime, but there are lots of prime numbers nearby. For example,
32749 is prime. Be prepared to handle repeating digits of at least this
size.

The above discussion should tell you thar 1/3 has no leading decimals
before the repeating segment, and 1/6 has 1
(since 6 = pow(2,1)*pow(5, 0)*3) .
So 1/3 is pow(10,0) * (3/9) where 3 is 'a', the repeating. Because
k == 0, the nonrepeating intial sequence has no digits (so is not
even shown as a zero),
abd 1/6 is pow(10,-1) * (1 + 6/9). The nonrepeating section b is one
digit (since k = 1) and the repeating segment is a 6. Note that we did
not use denominators of 3 or 6 nines. We nneded the smallest number of
the form pow(10,n)-1 with 3 as a factor. That number is 9, with a
single digit. 1/7 has 7 digits in the repeating string, because 9999999
is the smallest such number with 7 for a factor.

So here's the strategy.
If the fraction is improper (N >= D) remove the integgal part and write it:
I. (so N/D = I + N'/D with a proper fraction)
otherwise write
0,

Factor out the 2's and 5's in D. The larger index tells us how many
digits are in the non-repeating segment.

Compute it and write it down.
I.b
The residual D', D with all the factors 2 and 5, either must be 1 (so
I.b us terminating, a = 0, and we'ew done) our must divide a number of
the form 9....9 of 1 to D' digits. Start with Q=9, Q = 10*Q+9, etc
until you have one or have reached the timits of your machine. This part
need not be reported and may be done with, say, unsigned long long ints
even if the problem space is for signed ints. This rells you n, the
length the repeating string. Wrete the '(', generate the n digits,
write down a ')':
I.a(b)
Apr 30 '06 #5

<11******@gmail .com> wrote in message
news:11******** **************@ y43g2000cwc.goo glegroups.com.. .
I came across a question in one of the Computing olympiad regarding
string pattern matching.

Write a program that will accept a fraction of the form N/D, where N is
the numerator and D is the denominator, that prints out the decimal
representation. If the decimal representation has a repeating sequence
of digits, it should be indicated by enclosing it in brackets. For
example, 1/3 = .33333333...is denoted as .(3), and 41/333 =
.123123123...is denoted as .(123).

Typical conversions are:

1/3 = .(3)
22/5 = 4.4
1/7 = .(142857)
3/8 = .375
45/56 = .803(571428)

Now I could not think how do I even start writing a logic for creating
a pattern.


IIRC, there is a recursive algorithm (using 1/X ?) to convert terminated
(non-repeating and not random values PI, etc.) decimals to the form N/D. If
so (and since they gave you a valid fraction), you could compute N/D as
decimal and then attempt to convert back to N/D. If the number is
non-repeating, the first N and D should be the same as the second conversion
N and D. If the number is repeating, it will be terminated by the precision
of the machine. This means that the first N and D will be different from
the conversion N and D, because it lost some precision. For the repeating
numbers, you then need to determine the length of the repeat. I don't know
if there is a simple method for that.
Rod Pemberton
Apr 30 '06 #6

"Rod Pemberton" <do*********@so rry.bitbuck.cmm > wrote in message
news:e3******** **@emma.aioe.or g...

<11******@gmail .com> wrote in message
news:11******** **************@ y43g2000cwc.goo glegroups.com.. .
I came across a question in one of the Computing olympiad regarding
string pattern matching.

Write a program that will accept a fraction of the form N/D, where N is
the numerator and D is the denominator, that prints out the decimal
representation. If the decimal representation has a repeating sequence
of digits, it should be indicated by enclosing it in brackets. For
example, 1/3 = .33333333...is denoted as .(3), and 41/333 =
.123123123...is denoted as .(123).

Typical conversions are:

1/3 = .(3)
22/5 = 4.4
1/7 = .(142857)
3/8 = .375
45/56 = .803(571428)

Now I could not think how do I even start writing a logic for creating
a pattern.
IIRC, there is a recursive algorithm (using 1/X ?) to convert terminated
(non-repeating and not random values PI, etc.) decimals to the form N/D.

If so (and since they gave you a valid fraction), you could compute N/D as
decimal and then attempt to convert back to N/D. If the number is
non-repeating, the first N and D should be the same as the second conversion N and D. If the number is repeating, it will be terminated by the precision of the machine. This means that the first N and D will be different from
the conversion N and D, because it lost some precision. For the repeating
numbers, you then need to determine the length of the repeat. I don't know if there is a simple method for that.


I should probably clarify slightly. The algorithm will need be modified to
continue conversion until it's base is equal to or near D. This of course
will eliminate problems like 32/16 being returned as 2/1.

RP
Apr 30 '06 #7
Martin Ambuhl wrote a bunch of stuff):

But note that the method for determining the number of repeating digits
The residual D', D with all the factors 2 and 5, either must be 1 (so
I.b us terminating, a = 0, and we'ew done) our must divide a number of
the form 9....9 of 1 to D' digits. Start with Q=9, Q = 10*Q+9, etc
until you have one or have reached the timits of your machine. This part
need not be reported and may be done with, say, unsigned long long ints
even if the problem space is for signed ints. This rells you n, the
length the repeating string.


is not perhaps not very useful after all, the largest values for Q
are
16 bits (signed or unsigned) 9999 (so D' <= 4: specifically 3, but
3 divides 9)
32 bits (signed or unsigned) 999999999 (do D' <= 9: 3,7,9, but 3 and 9
divide nine, only 7 is useful)
64 bits (signed) 999999999999999 999 (so D' <= 18; picking up 11, 13, 17)
64 bits (unsigned) 999999999999999 9999 (so D' <= 19; 19)

So whats the point? After reporting I. (the integral part), computing k
(the length of the non-repeating segment) and reporting the k digits and
the opening brace, now showing I.b(, you know that the repeating string
is at most n characters. There are strategies for storing generated
digits un either one or two allocated buffers of n chars each. The two
buufer approach may well win on speed; the one buffer approach on space.
Once you have the n chars (or in the two buffer case, well before
then) you can easily for repetitions the initial part of the n-digit
repeating pattern, yielding a shorter one? And you don't need to check
all lengths. Contemplate what the prime factors of D' tell you about
what lengths make sense.

And I forgot to note, that if you don't
1) reduce N/D, eliminating common factors and
2) if exactly one of N or D is negative, report a '-'.
if any of N or D is negative, change its sign.
3) if D is zero, report the fact and quit
then all bets are off.

Apr 30 '06 #8
On 29 Apr 2006 13:52:28 -0700, "11******@gmail .com"
<11******@gmail .com> wrote:
I came across a question in one of the Computing olympiad regarding
string pattern matching.

Write a program that will accept a fraction of the form N/D, where N is
the numerator and D is the denominator, that prints out the decimal
representation . If the decimal representation has a repeating sequence
of digits, it should be indicated by enclosing it in brackets. For
example, 1/3 = .33333333...is denoted as .(3), and 41/333 =
.123123123...i s denoted as .(123).

Typical conversions are:

1/3 = .(3)
22/5 = 4.4
1/7 = .(142857)
3/8 = .375
45/56 = .803(571428)

Now I could not think how do I even start writing a logic for creating
a pattern.
Then I thought that maybe I should start comparing characters from the
right rather than the left.
But these two examples even negate that theory;

1/7 gives me ---> 0.1428571428571 428571428571429 on a 16bit machine

45/56 gives me ---> 0.8035714285714 285714285714286

I was trying to eliminate the last number as it rounds off, and so I
can start creating combinations from right to left. But nothing seems
to be working.

Any hints/suggestions will be appreciated.


Somewhere in the depths of number theory remembrances, I recall a
method of determining when the repetition starts and the length of the
repetition. Unfortunately, the details have long been forgotten.
Attempting to compare digits is error prone because if you see a value
of .121212 you might conclude the answer is .(12) when the answer
really is .(1212121212123 ).

This is really more an algorithm question rather than C.
Remove del for email
Apr 30 '06 #9

This thread has been closed and replies have been disabled. Please start a new discussion.

Similar topics

176
8119
by: Thomas Reichelt | last post by:
Moin, short question: is there any language combining the syntax, flexibility and great programming experience of Python with static typing? Is there a project to add static typing to Python? Thank you, -- greetz tom
9
3209
by: Xah Lee | last post by:
# -*- coding: utf-8 -*- # Python # Matching string patterns # # Sometimes you want to know if a string is of # particular pattern. Let's say in your website # you have converted all images files from gif # format to png format. Now you need to change the # html code to use the .png files. So, essentially
29
4306
by: zoro | last post by:
Hi, I am new to C#, coming from Delphi. In Delphi, I am using a 3rd party string handling library that includes some very useful string functions, in particular I'm interested in BEFORE (return substring before a pattern), AFTER (return substring after a pattern), and BETWEEN (return substring between 2 patterns). My questions are: 1. Can any tell me how I can implement such functionality in C#? 2. Is it possible to add/include function...
5
5752
by: olaufr | last post by:
Hi, I'd need to perform simple pattern matching within a string using a list of possible patterns. For example, I want to know if the substring starting at position n matches any of the string I have a list, as below: sentence = "the color is $red" patterns = pos = sentence.find($)
9
5064
by: Jim Lewis | last post by:
Anyone have experience with string pattern matching? I need a fast way to match variables to strings. Example: string - variables ============ abcaaab - xyz abca - xy eeabcac - vxw x matches abc
0
1537
by: ma740988 | last post by:
I'm going through modern C++ design looking for tips and while hi-tech I suspect one solution to my issue would involve the factory design pattern. // algorithms.h class Algorithms { protected: typedef std::deque<double> DDEQUE; // need to make this even more generic to support floats .. i.e float and double public:
0
10583
NeoPa
by: NeoPa | last post by:
ANSI-89 v ANSI-92 Before we get into all the various types of pattern matching that can be used, there are two ANSI standards used for the main types of wildcard matching (matching zero or more characters or simply matching a single character) : ANSI-89 - Mainly used only by Jet / ACE SQL ANSI-92 - Mainly used by SQL Server and other grown-up products In the later versions of Access it is now possible to select ANSI-92 compatibility as an...
11
4839
by: tech | last post by:
Hi, I need a function to specify a match pattern including using wildcard characters as below to find chars in a std::string. The match pattern can contain the wildcard characters "*" and "?", where "*" matches zero or more consecutive occurrences of any character and "?" matches a single occurrence of any character. Does boost or some other library have this capability? If boost does have this, do i need to include an entire
1
4245
by: Ben | last post by:
I apologize in advance for the newbie question. I'm trying to figure out a way to find all of the occurrences of a regular expression in a string including the overlapping ones. For example, given the string 123456789 I'd like to use the RE ((2)|(4)){3} to get the following matches: 2345 4567
0
8647
marktang
by: marktang | last post by:
ONU (Optical Network Unit) is one of the key components for providing high-speed Internet services. Its primary function is to act as an endpoint device located at the user's premises. However, people are often confused as to whether an ONU can Work As a Router. In this blog post, we’ll explore What is ONU, What Is Router, ONU & Router’s main usage, and What is the difference between ONU and Router. Let’s take a closer look ! Part I. Meaning of...
0
8585
by: Hystou | last post by:
Most computers default to English, but sometimes we require a different language, especially when relocating. Forgot to request a specific language before your computer shipped? No problem! You can effortlessly switch the default language on Windows 10 without reinstalling. I'll walk you through it. First, let's disable language synchronization. With a Microsoft account, language settings sync across devices. To prevent any complications,...
1
8864
by: Hystou | last post by:
Overview: Windows 11 and 10 have less user interface control over operating system update behaviour than previous versions of Windows. In Windows 11 and 10, there is no way to turn off the Windows Update option using the Control Panel or Settings app; it automatically checks for updates and installs any it finds, whether you like it or not. For most users, this new feature is actually very convenient. If you want to control the update process,...
0
8835
tracyyun
by: tracyyun | last post by:
Dear forum friends, With the development of smart home technology, a variety of wireless communication protocols have appeared on the market, such as Zigbee, Z-Wave, Wi-Fi, Bluetooth, etc. Each protocol has its own unique characteristics and advantages, but as a user who is planning to build a smart home system, I am a bit confused by the choice of these technologies. I'm particularly interested in Zigbee because I've heard it does some...
0
7681
agi2029
by: agi2029 | last post by:
Let's talk about the concept of autonomous AI software engineers and no-code agents. These AIs are designed to manage the entire lifecycle of a software development project—planning, coding, testing, and deployment—without human intervention. Imagine an AI that can take a project description, break it down, write the code, debug it, and then launch it, all on its own.... Now, this would greatly impact the work of software developers. The idea...
0
5842
by: conductexam | last post by:
I have .net C# application in which I am extracting data from word file and save it in database particularly. To store word all data as it is I am converting the whole word file firstly in HTML and then checking html paragraph one by one. At the time of converting from word file to html my equations which are in the word document file was convert into image. Globals.ThisAddIn.Application.ActiveDocument.Select();...
0
4590
by: adsilva | last post by:
A Windows Forms form does not have the event Unload, like VB6. What one acts like?
2
2285
muto222
by: muto222 | last post by:
How can i add a mobile payment intergratation into php mysql website.
3
1986
bsmnconsultancy
by: bsmnconsultancy | last post by:
In today's digital era, a well-designed website is crucial for businesses looking to succeed. Whether you're a small business owner or a large corporation in Toronto, having a strong online presence can significantly impact your brand's success. BSMN Consultancy, a leader in Website Development in Toronto offers valuable insights into creating effective websites that not only look great but also perform exceptionally well. In this comprehensive...

By using Bytes.com and it's services, you agree to our Privacy Policy and Terms of Use.

To disable or enable advertisements and analytics tracking please visit the manage ads & tracking page.