KR101525895B1 - Device and method for calculating sequence number - Google Patents

Device and method for calculating sequence number Download PDF

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Publication number
KR101525895B1
KR101525895B1 KR1020130156726A KR20130156726A KR101525895B1 KR 101525895 B1 KR101525895 B1 KR 101525895B1 KR 1020130156726 A KR1020130156726 A KR 1020130156726A KR 20130156726 A KR20130156726 A KR 20130156726A KR 101525895 B1 KR101525895 B1 KR 101525895B1
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South Korea
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instance
permutation
combination
serial number
query
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KR1020130156726A
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Korean (ko)
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서창진
김영주
신재원
팜띠끼안
천명호
강혜진
임형민
장재수
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숭실대학교산학협력단
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/70—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer
    • G06F21/71—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer to assure secure computing or processing of information
    • G06F21/73—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer to assure secure computing or processing of information by creating or determining hardware identification, e.g. serial numbers

Abstract

The present invention provides a device for calculating a sequence number which comprises: a sequence number calculating unit which receives a combination instance or a permutation instance and calculates a sequence number of the combination instance or the permutation instance; an instance calculating unit which receives a combination sequence number or a permutation sequence number and calculates an instance corresponding to the combination sequence number or the permutation sequence number.

Description

TECHNICAL FIELD [0001] The present invention relates to a serial number calculator,

The present invention relates to a calculator and a method for assigning serial numbers to the results of combination and permutation problems.

The permutation problem P (m, n) and the combination problem C (m, n) used in various fields are not allowed to overlap but all the legal cases are listed. It is not easy to do.

In the prior art, only information on the degree of the next result in a given state can be known. On the other hand, I can not tell you what the 1000th result is from the beginning, and how many intermediate results there are between the two specific results.

Therefore, there is a need for a serial number calculator and method that can easily calculate a serial number corresponding to each result of a combination or permutation problem and easily calculate a corresponding result from each serial number.

Japanese Patent Publication No. 2007-179536 ("Method for issuing a control number for fluids and inanimate objects") discloses a configuration for assigning a control number to an object in connection with the present invention.

In addition, Japanese Patent Document No. 1996-029881 ("long-drift drifting device and long drift drifting method") discloses a configuration in which a serial number is used for long shift drift theorem.

The object of the present invention is to provide a serial number calculation device capable of easily calculating a serial number for a specific combination or permutation instance and a combination or permutation instance for a specific serial number, And a method thereof.

According to a first aspect of the present invention, there is provided a serial number calculator comprising: a serial number calculator that receives a combination instance or a permutation instance and calculates a serial number of the combination instance or permutation instance; And an instance calculation unit for calculating an instance corresponding to the combination serial number or the permutation serial number by receiving the combination serial number or the permutation serial number.

According to a second aspect of the present invention, there is provided a serial number calculating method including: (a) receiving a query; (b) if the query includes a combination instance or a permutation instance, calculating a combination serial number corresponding to the combination instance or a permutation sequence number corresponding to the permutation instance; (c) if the query includes a combination serial number or a permutation serial number, calculating a permutation instance corresponding to the combination instance corresponding to the combination serial number or the permutation serial number.

INDUSTRIAL APPLICABILITY The present invention has the effect that it is possible to easily calculate a serial number for a specific combination or permutation instance and a combination or permutation instance for a specific serial number irrespective of the kind of objects in the serial number calculator and method.

Effective distribution management is achieved by presenting the amount of work in numerical form when dispersing and processing a vast number of surveys.

It is possible to quickly calculate a serial number corresponding to an arbitrary instance and quickly calculate an instance corresponding to an arbitrary serial number.

A number of different numbers can be simplified and stored as a single number, which can shorten the search or comparison time.

1 shows a structure of a serial number calculator according to an embodiment of the present invention.
FIG. 2 shows a flow of a serial number calculation method according to an embodiment of the present invention.
FIG. 3 shows a flow of a combination serial number calculation method according to an embodiment of the present invention.
FIG. 4 shows a flow of a permutation serial number calculation method according to an embodiment of the present invention.
5 shows a flow of a combination instance calculation method according to an embodiment of the present invention.
FIG. 6 shows a flow of a permutation instance calculation method according to an embodiment of the present invention.
7 and 8 show an embodiment of a method for calculating serial number according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings, which will be readily apparent to those skilled in the art. The present invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. In order to clearly illustrate the present invention, parts not related to the description are omitted, and similar parts are denoted by like reference characters throughout the specification.

Throughout the specification, when a part is referred to as being "connected" to another part, it includes not only "directly connected" but also "electrically connected" with another part in between . Also, when an element is referred to as "comprising ", it means that it can include other elements as well, without departing from the other elements unless specifically stated otherwise.

1 shows a structure of a serial number calculator according to an embodiment of the present invention.

The serial number calculator 10 according to an embodiment of the present invention includes a query input unit 20 for receiving a query, a result output unit 40 for outputting a query processing result, a combination serial number An instance calculation unit 200 including a serial number calculation unit 100 and a combination instance calculation unit 210 and a permutation instance calculation unit 220 including a calculation unit 110 and a permutation serial number calculation unit 120, .

The serial number calculator 100 receives a combination instance or a permutation instance and calculates a serial number of the instance. The instance calculator 200 receives the combination serial number or the permutation serial number and conversely corresponds to the serial number Lt; / RTI > That is, the operations performed by the serial number calculator 100 and the instance calculator 200 are in inverse functions.

As used herein, the term instance or result refers to a specific result of a combination or permutation operation, and the term sequence number refers to a number assigned to each instance in order.

For example, the result of a combination problem that selects two of three objects a, b, and c without duplicates is ab, ac, bc. The present specification refers to each of these as a combination instance. When serial numbers of 0, 1, and 2 are sequentially assigned to each instance, the serial number calculator 10 according to an embodiment of the present invention calculates an serial number 1 by inputting an instance of ac, Entering number 1 yields instance ac.

Also, the term standardized combination or standardized permutation in this specification means to calculate a combination or permutation by using a number representing an object instead of an object. For example, if you use numbers 0, 1, and 2 in place of a, b, and c in the example above, each instance of the combination problem that selects two of the three objects without duplicates would be 01, 02, Accordingly, the serial number calculator 10 according to the embodiment of the present invention receives the instance 02 and calculates the input number 1 regardless of the object type. When the serial number 1 is input, Instance is calculated.

Therefore, the present invention is advantageous in that it is possible to easily calculate a serial number for a specific combination or permutation instance and a combination or permutation instance for a specific serial number irrespective of an object type.

The flow of the serial number calculation method according to an embodiment of the present invention will be described in detail with reference to FIG.

FIG. 2 shows a flow of a serial number calculation method according to an embodiment of the present invention.

If the query is to ask for the corresponding serial number for the combination or permutation instance (S100), the combination serial number corresponding to the combination instance is calculated (S400), depending on whether it is about the combination or the permutation (S200) A corresponding permutation serial number is calculated (S500).

On the other hand, if the query is to ask for a corresponding instance for a combination or a permutation serial number (S100), a combination instance corresponding to the combination serial number is calculated (S600) depending on whether it is about a combination or a permutation (S300) A permutation instance corresponding to the serial number is calculated (S700).

Each of the calculation steps S400, S500, S600, and S700 includes a combination serial number calculation unit 110 and a permutation serial number calculation unit 120 of the serial number calculator 10 according to an embodiment of the present invention, , And a combination instance calculation unit 210 and a permutation instance calculation unit 220. [

The standardization of combination and permutation problems is described in more detail below.

First, the combination problem, that is, C * (m, n) (m and n are positive integers having a relationship of m? N) are m different objects (i.e., object 0 , object 1 , ..., object m -1 ), we list all the results that pick n objects without considering the order of selection. In the combination problem, a total of m! / (N! (Mn)!) Results are generated.

The partial permutation problem, P * (m, n) (m> n), considers the order of selection when given m different objects (ie, object 0 , object 1 , ..., object m-1 ) And lists all the results that pick up n objects. In the permutation problem, m! / (Mn)! Results are generated.

The total permutation F * (m) is defined by switching to a P * (m, m-1) permutation or P * (m, m) where m = n-1 in the partial permutation P * . Since the full permutation can be simplified as an example of partial permutation, the present invention deals only with the C * (m, n) combination problem and the P * (m, n) permutation problem under the condition of m? N.

These general combination problems and permutation problems can be solved after they have been converted to standard combination problems and standard permutation problems that solve the problem in order to solve them.

Combination problem C * (m, n) and the permutation problem * P (m, n) is the m number including zero to select a different m of the object that is the object 0, object 1, ..., m-1, each object 1, ..., (m-1), the solution becomes simpler.

(M, n) and the permutation problem P * (m, n) in which m numbers are defined as {0, 1, ..., (m- (M, n) and the standard permutation problem P (m, n), respectively.

However, the combination problem ignores the order of selection, so you can rearrange the selected order. The present invention uses a permutation as a method of relocation. Using sorting prevents the disadvantage that one result in a combinatorial problem is expressed in several different forms.

For example, if the four numbers selected in the standard permutation problem C (5,4) are {4, 1, 2, 0} or {1, 4, 2, 0}, they are the same output, , 4).

The permutation problem, the combination problem, the standard permutation problem, and the standard combination problem are summarized in the following table.

Problem Given m Choose n How to express the result determined by n selected n The permutation problem P * (m, n) Object 0 , object 1 , ..., object m-1 Object k0 , object k1 , ..., object k (n-1) (Object k0 , object k1 , ..., object k (n-1) ), The combination problem C * (m, n) (Object ks0 , object ks1 , ..., object ks (n-1) ), The standard permutation problem P (m, n) 0, 1. ..., m-1. k0, k1, ..., k (n-1). (k0, k1, ..., k (n-1)), Standard combination problem C (m, n) (ks0, ks1, ..., ks (n-1)),
ks0 < ks1 < ks (n-1)

At this time, object 0 , object 1 , ..., object m-1 is an array in which forward m-ary objects are present. That is, m objects are arranged according to the order of object 0 <object 1 <... <object m-1 . (ks0, ks1, ..., ks (n-1)) are arrays obtained by forward alignment of (k0, k1, ..., k (n-1)). That is, the sets {k0, k1, ..., k (n-1)} and the sets {ks0, ks1, ..., ks (n-1)} represent the same sets in different orders.

This standardized combination or permutation problem is easier to solve than a normal combination or permutation problem, and the result of a standardized combination or permutation problem can be countered one-on-one with the result of a combination or permutation problem. Rather than solving the combination or permutation problem directly using these two properties, it can be solved indirectly by using a solution of the standardized combination or permutation problem as follows.

Step 1. Arrange m objects given in combination or permutation order in order. These are referred to as object 0 , object 1 , ..., object m-1 from the front.

Step 2. and stores the objects sorted in m constant matrices Mem [0: m-1].

Mem [k] = object k k = 0, 1, 2, ..., (m-1).

Step 3. The standard output (k0, k1, ..., k (m-1)) is extracted using the result of the standardized combination or permutation problem. Mem [k0], Mem [k1], ..., Mem [k (m-1)]) using these values. This output corresponds to (object k0 , object k1 , ..., object k (m-1) ).

Assign serial numbers one by one in a lexicographical order to the resulting series of generated results. Lexical ordering can apply the same rules for permutation problems and combinatorial problems.

When two standard output A and B (A ≠ B) are expressed as A: (a 0 a 1 ... a mn-1 ) and B: (b 0 b 1 ... b mn-1 ) The sequence is determined as follows in the case of the same place digits.

- When a 0 <b 0 : S (A) <S (B),

- (a 0 = b 0) , (a 1 = b 1), ... (a k-1 = b k-1), a k <b k be when: S (A) <S ( B).

In this case, S (A) <S (B) means that the result A precedes the result B.

That is, for two standard outputs of the same permutation problem or for two standard outputs of the same combination problem, A and B (A ≠ B), the numbers selected from the first left digit 0 to the rightmost digit n-1 are compared with each other, After finding a place with a value, the magnitude of the place value determines the magnitude of the overall result A and B.

The inverse function Sc -1 of the functions Sc and Sc for assigning the serial number qc according to the dictionary order to the standard result generated by the combination problem C * (m, n) or the standard combination problem C (m, n) Can be defined together.

The standard output Ac is expressed as (ac 0 ac 1 ... ac n-1 ) if all suitable outputs of C (m, n), ie, each instance is defined as Ac and the set of all instances is defined as {Ac} (Ac 0 &lt; ac 1 &lt; ac n-1 ). Also, | {Ac} |, which means the total number of standard outputs produced by C (m, n), is m! / (N!

The serial number calculation function Sc () allocates all the numbers from 0 to ({Ac} | -1) as a serial number without any delimitation and defines it as a function conforming to the dictionary order rule.

That is, a function that conforms to the following rules is defined as Sc (). (Sc (Ac) = qc)

- Any two outputs are assigned serial numbers based on dictionary order.

(Ac1 <Ac2) → (Sc (Ac1) <Sc (Ac2))

- Assigns the smallest serial number, 0, to the fastest result Ac (first) .

Let Ac (first) = min {Ac} = (0, 1, 2, ..., n-1).

Then Sc (Ac (first) ) = 0.

- Assign the largest serial number (| {Ac} | -1) to the last late result Ac (last) .

Let Ac (last) = max {Ac} = (mn, mn-1, mn-2, ..., m-1).

Then Sc (Ac (last) ) = (| {Ac} | -1) = m! / (N! (Mn)) -1.

The serial number calculation function Sc has an inverse function as follows, starting with 0 for all outputs {Vc}, and sequentially assigning | {Ac} | serial numbers qc using all the numbers without overlapping each other.

(Sc (Ac) = qc) ↔ (Sc -1 (qc) = Ac)

In addition, the permutation problem * P (m, n) or a standard permutation problem P (m, n) in the dictionary in order to create a standard output according to define the inverse function of the function Sp and Sp Sp -1 assigned to the serial number qp .

Any suitable product of P (m, n), that is, each instance to Ap, by defining a set of all the instances in {} Ap, Ap is the standard instances (ap 0, ap 1, ... ap n-1) Lt; / RTI &gt; Also, | {Ap} |, which means the total number of standard outputs produced by P (m, n), is m! / (Mn)! It is branch.

All numbers from 0 to (| {Ap} | -1) of the sequence number function Sp () are assigned to a sequence number without any delimitation and defined as a function conforming to the lexical ordering rule.

That is, a function that conforms to the following rules is defined as Sp (). (Sp (Ap) = qp)

- Any two outputs are assigned serial numbers based on dictionary order.

(Ap1 <Ap2) → (Sp (Ap1) <Sp (Ap2))

- Assigns the minimum serial number 0 to the ephemeral output Ap (first) .

Let Ap (first) = min {Ap} = (0, 1, 2, ..., n-1).

Then Sp (Ap (first) ) = 0.

- Assign the maximum sequence number | {Vp} | -1 to the last spontaneously result Vp (last) .

Let Ap (last) = max {Ap} = (m-1, m-2, m-3, ..., mn).

Then Sp (Ap (last) ) = (| {Ap} | -1) = m! / (Mn)! - One.

This serial number calculation function Sp has an inverse function as follows, starting from 0 for all outputs {Vp}, and assigning serial numbers qp of | {Ap} |

(Sp (Ap) = qp)? (Sp- 1 (qp) = Ap)

Each of the functions described above includes a combination serial number calculation step (S110), a permutation serial number calculation step (S120), and a combination instance calculation step (S210) and a permutation instance calculation step of the serial number calculation method according to an embodiment of the present invention (S220).

Hereinafter, one embodiment of the algorithm that each of the calculation steps S400, S500, S600, and S700 can use will be described with reference to FIGS. This is for illustrative purposes only and the algorithms that may be used are not limited thereto.

FIG. 3 shows a flow of a combination serial number calculation method according to an embodiment of the present invention.

The figure shows an embodiment of an algorithm that implements a function Sc () that yields a serial number for the result of a standard combination problem C (m, n).

The algorithm C (m, n) A legitimate instance of (a 0, a 1, ... a n-1) of using as an input variable, the internal variable (v 0, v 1, ... of v n- 1 ), and then generates the serial number qc.

FIG. 4 illustrates a flow of a permutation serial number calculation method according to an embodiment of the present invention.

Sc -1 (qc), which is an inverse function of Sc (), calculates a corresponding standard instance A for a given serial number qc.

The inverse function calculation proceeds according to the greedy algorithm to the right from the first digit of the first left digit to the number of digits of the right end digit (n-1). The variable q is calculated as a 0 , a 1 , a 2 sequentially after the input serial number qc is assigned as an initial value. When qc reaches 0 , the variable q is filled in. do.

5 shows a flow of a combination instance calculation method according to an embodiment of the present invention.

The figure shows an embodiment of an algorithm that implements a function Sc () that yields a serial number for the result of a standard combination problem C (m, n).

Algorithm is P (m, n) A legitimate instance of (a 0, a 1, ... a n-1) of using as an input variable, the internal variable (v 0, v 1, ... of v n- 1 ), and then generates the serial number qp.

The basic position value 1 of the internal variable v k corresponds to P (mk-1, nk-1). As you go to the internal variable k value matrix V is matrix A from the left to the right (k = 0,1,2, ..., n -1) a k the values of all the variables a right kj having a value greater than their Can be obtained by reducing by 1.

FIG. 6 shows a flow of a permutation instance calculation method according to an embodiment of the present invention.

The inverse function of Sp (Sp -1 ) (qp) yields the corresponding standard instance A for a given serial number qp.

The inverse function calculation is performed in the reverse order of Sp (). (v 0 , v 1 ,..., v n-1 ) having a base position 1 of digits k is P (mk-1, nk-1) m, n). &lt; / RTI &gt;

7 and 8 illustrate an embodiment of a method for calculating a serial number according to an embodiment of the present invention.

Figure 7 shows the overall list of standard output A p = (a 0 a 1 a 2 ) produced by the standard combination problem C (6,3) and the internal variable V p = (v 0 v 1 v 2) corresponding to each standard output ) And a serial number qc.

In other words, a total of 20 instances, a solution to the C (6,3) problem of selecting three numbers taking into account the order of six numbers {0,1,2,3,4,5}, are listed in lexicographic order .

Figure 8 shows a complete list of standard output A p = (a 0 a 1 a 2 ) generated by the standard permutation problem P (5,3) and an internal variable V p = (v 0 v 1 v 2) corresponding to each standard output ) And a serial number q p .

In other words, a total of 60 instances of the P (5,3) solution for selecting three numbers taking the order into account in the five numbers {0,1,2,3,4} are listed in a lexicographic order .

One embodiment of the present invention may also be embodied in the form of a recording medium including instructions executable by a computer, such as program modules, being executed by a computer. Computer readable media can be any available media that can be accessed by a computer and includes both volatile and nonvolatile media, removable and non-removable media. In addition, the computer-readable medium may include both computer storage media and communication media. Computer storage media includes both volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Communication media typically includes any information delivery media, including computer readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave, or other transport mechanism.

While the methods and systems of the present invention have been described in connection with specific embodiments, some or all of those elements or operations may be implemented using a computer system having a general purpose hardware architecture. In describing an example of a computer system architecture that may be used to implement one or more components or operations of an embodiment of the invention, a hardware system includes a processor, a cache, a memory, and one or more software applications and drivers associated with the functions described above can do.

It will be understood by those skilled in the art that the foregoing description of the present invention is for illustrative purposes only and that those of ordinary skill in the art can readily understand that various changes and modifications may be made without departing from the spirit or essential characteristics of the present invention. will be. It is therefore to be understood that the above-described embodiments are illustrative in all aspects and not restrictive. For example, each component described as a single entity may be distributed and implemented, and components described as being distributed may also be implemented in a combined form.

The scope of the present invention is defined by the appended claims rather than the detailed description and all changes or modifications derived from the meaning and scope of the claims and their equivalents are to be construed as being included within the scope of the present invention do.

10: Serial number calculator
100: serial number calculation unit
200: Instance calculation unit
110: Combination serial number calculation unit
120: permutation serial number calculating section
210: Combination instance calculation unit
220: permutation instance calculation unit

Claims (7)

In the serial number calculator,
An instance generation unit for generating a combination instance or a permutation instance based on a standardized combination problem or a standardized permutation problem;
A query input unit for receiving a query from a user;
A serial number calculation unit for receiving a combination instance or a permutation instance included in the query and calculating a serial number of the combination instance or the permutation instance;
An instance calculating unit that receives the combination serial number or the permutation serial number included in the query and calculates an instance corresponding to the combination serial number or the permutation serial number; And
And a result output unit for outputting the result of the instance calculation unit and the serial number calculation unit for the query,
The query input unit receives a query from a user and transfers the query to the serial number calculation unit or the instance calculation unit. The method according to claim 1,
Wherein the combination instance and the permutation instance are computed using a series of numbers instead of a series of objects, and represents a combination or permutation of the series of objects. The method according to claim 1,
Wherein the combination instance and the permutation instance are sorted in ascending order. delete In the serial number calculating method,
Generating a combination instance or permutation instance based on a standardized combination problem or a standardized permutation problem;
Receiving a query from a user;
If the query includes the combination instance or the permutation instance, calculating a combination serial number corresponding to the combination instance or a permutation sequence number corresponding to the permutation instance;
Calculating a permutation instance corresponding to the combination instance corresponding to the combination sequence number or the permutation sequence number if the query includes a combination sequence number or a permutation sequence number; And
And outputting the combination serial number or permutation serial number and combination instance or permutation instance calculated in the step. 6. The method of claim 5,
Wherein the combination instance and the permutation instance are computed using a series of numbers instead of a series of objects, and the combination number or the permutation result of the series of objects is calculated. 6. The method of claim 5,
Wherein the combination instance and the permutation instance are sorted in ascending order.
KR1020130156726A 2013-12-16 2013-12-16 Device and method for calculating sequence number KR101525895B1 (en)

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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH08227269A (en) * 1994-01-10 1996-09-03 Fujitsu Ltd Conversion pattern generation mechanism, cipher function mechanism and cipher device using it
KR20060056015A (en) * 2004-11-19 2006-05-24 엘지전자 주식회사 Method for searching call number on standby mode of mobile communication terminal
KR101089005B1 (en) * 2011-04-11 2011-12-01 이기범 Coupon creation apparatus and method for free gift

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH08227269A (en) * 1994-01-10 1996-09-03 Fujitsu Ltd Conversion pattern generation mechanism, cipher function mechanism and cipher device using it
KR20060056015A (en) * 2004-11-19 2006-05-24 엘지전자 주식회사 Method for searching call number on standby mode of mobile communication terminal
KR101089005B1 (en) * 2011-04-11 2011-12-01 이기범 Coupon creation apparatus and method for free gift

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