JP3573671B2 - Euler square creation device - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention creates Euler squaresapparatusIn particular, the creation of Euler squares used for code conversion conversion tables, cipher tables, and experimental design methods, etc.apparatusAbout.
[0002]
[Prior art]
Before describing the conventional Euler square creation method, the Latin square will be described first. A set of n symbols A = {a1,. . . , An} using each element n times, for a total of n²Each element is arranged in a matrix having n elements, and each element of A appears once in each direction is called a Latin square on A or an nth-order Latin square.
[0003]
In addition, those in which the first row and the first column are both natural permutations are called irreducible or standard Latin squares. When the number of irreducible or standard Latin squares is represented by L (n), the total number of n-th Latin squares is n! (N-1)! L (n). The value of L (n) is as follows when n is 9 or less, that is, when n = 1 to 9.
L (1) = 1
L (2) = 1
L (3) = 1
L (4) = 4
L (5) = 56
L (6) = 9408
L (7) = 16942040
L (8) = 535281401856
L (9) = 377579570964258816
[0004]
Here, when the two Latin squares L = (A, ○) and L ′ = (A, ●) are overlapped, the character pairs that appear are all different, that is, x ○ y = x ′ ○ y. ′, X ● y = x ′ ● y′x = x ′, y = y ′, L and L ′ are said to be orthogonal to each other, and a square formed by superimposing these two Latin squares L and L ′ Is called orthogonal Latin square, Euler square, or Greco Latin square. The name of the Greco-Latin square is derived from the first letter of the element in Greek letters and the second letter in Latin letters.
[0005]
If n is a number other than 2 and 6, there is an nth order Euler square. It can be easily understood that there is no Euler square when n is 2, but when n is 6, it depends on the problem of 36 known Euler officers. This problem is disclosed in detail in the literature (Koichi Yamamoto: “Combinatorial Mathematics”, page 39, Asakura Shoten). This is “6 regiments from 6 regiments (College, Lieutenant Colonel, Major, Lieutenant, Lieutenant, Lieutenant), each with a total of 36 people in a row of 6 rows and 6 columns, each regimen in each row. Can the officers of each class be represented? "
[0006]
The present inventor has shown that the number of Euler squares is 1 in the first order, 0 in the second order, 72 in the third order, 6912 in the fourth order, 6220800 in the fifth order. Confirmed by
[0007]
FIG. 11A shows the basic form of the Euler square of the fourth-order element A = {0, 1, 2, 3}, and FIG. 11B shows the fourth-order element A = {1, 2, 3, 4}. The basic form of the Euler square is shown. FIG. 11C shows the basic form of the Euler square of the fourth order lower element A = {a, b, c, d} and the upper element A = {α, β, γ, δ}.
[0008]
[Problems to be solved by the invention]
In the conventional Euler square creation method, it is difficult to regularly create Euler squares, and they are created on a trial and error basis. For example, when obtaining a fourth-order Euler square shown in FIG. (B) and two orthogonal squares of the same order are overlapped to check whether the resulting symbols are identical, and the Euler square shown in (c) is created. ing. Here, among the two-digit symbols (here, numbers) of each square of the Euler square shown in FIG. 13 (c), the symbol on the left is the corresponding square number of the Latin square shown in FIG. The symbol on the right is the corresponding square number of the Latin square shown in FIG.
[0009]
For this reason, not only is it difficult and cumbersome to create Euler squares with the conventional creation method, but the number of Euler squares that can be created is limited, which increases the utility value and effectiveness of Euler squares. There is a problem that it is not possible.
[0010]
Therefore, the present invention has been made to solve the above-mentioned problems of the prior art, and it is possible to create an Euler square that can be easily and regularly created according to a certain method.apparatusThe purpose is to provide.
[0011]
Another object of the present invention is to create an Euler square that can broaden the range of use of the Euler square and can dramatically increase the utility value and effect of the Euler square.apparatusIs to provide.
[0012]
[Means for Solving the Problems]
In order to achieve the above object, the invention according to claim 1n in total in n rows and n columns (n is an integer of 3 or more excluding 6) ² Each of the memory elements stores a symbol m in which two symbols m1 and m2 arbitrarily selected from n different symbols are allowed to overlap. Euler square memory array and Euler square memory array n ² Among the storage elements, a designation means for designating a storage element at a set position, a readout means for reading a memory symbol from the storage element at a position designated by the designation means, and a storage element at a position designated by the designation means The writing means for storing the input symbols, the symbol comparison unit for comparing the symbols read by the reading means with the input symbols, the order n of the Euler square to be created, and the symbols m1 and m2 are n A selection order for selecting from among the symbols, a position where the symbol m of the Euler square memory array is first arranged, and an order in which the symbol m is arranged along the row direction or the column direction of the Euler square memory array, , The first value of the symbol m is set, the comparison result from the symbol comparison unit is received, and the designation means, the reading means and the writing means are controlled, and n is stored in the Euler square memory array. It is obtained by a structure having a calculation unit for storing the Euler square.
Here, the calculation unit sets the symbol m of the first set value in the storage element set as the first array position of the Euler square storage array, and then the next of the first array position. After the first value of the symbol m is stored in the storage element at the position via the writing means and the specifying means, the symbol m to be stored in the storage element is determined from the position based on the output comparison result of the symbol comparison unit. In the selection order until the same symbol as the symbol stored in the memory element at the previous position disappears, the same symbol as the symbol stored in the memory element at the previous position does not exist, and the same row After storing the symbol m having no symbol m1 or m2 of the same value in each storage element at the previous position in the column, the symbol m of the first value is further written to the storage element at the next position via the writing means and the specifying means. And then store the next location Based on the output comparison result of the symbol comparison unit, the child symbol m is placed at the previous position in the same row and column without the same symbol in each storage element at the position before the storage element at the next position. Until the symbol m without the symbol m1 or m2 of the same value appears, it is repeatedly changed and stored in the selection order until the memory element at the last position in the n-th row and the n-th column is repeated according to the set order. The Euler square is created such that a pair of two symbols m1 and m2 constituting the symbol m is not stored more than once in all the memory elements of the Euler square memory array.
[0013]
In the present invention, the order n of the Euler square to be created is set, and the symbol m for the order n is set by setting the permutation and permutation selection order. For example, when the order is 3rd and (0, 1, 2) is set as the symbol m, the pair of two symbols m1 and m2 constituting the symbol m is 00 → 01 → 02 → 10 → 11 → 12 → 20 → 21 → 22 is defined as a permutation (natural permutation), and selection is defined in the order of 00 → 01 → 02 → 10 → 11 → 12 → 20 → 21 → 22.
[0014]
In the present invention, the previous selection of the symbol m as an array element for each position of the Euler square is performed in the column direction of FIG. 6A or the row direction of FIG. 6B from the first position. , When selecting the symbol m, select a symbol different from the array element of the other already set position at that position, and further, the upper m1 and the lower rank of the symbol m at the previous position of the same row and column at that position Since m2 selects a value different from each other position in the matrix, Euler square creation is achieved by repeating this.
[0015]
In order to achieve the above object, the invention described in claim 2 is the same as the invention described in claim 1.The arithmetic unit isFor each position of n rows and n columns, the symbols m1 and m2 are set so that the pair of the two symbols m1 and m2 of the symbol m and the already determined array element at the previous position in the same row and column are not the same. When m2 is changed one after another in the selection order, if there is no symbol m that can be selected and decided after the last symbol is checked, the position K_IJPrevious position K_{I (J-1)}Or K_{(I-1) J} The first value of the symbol m is stored in the memory element via the writing means and the specifying means, and the position K is stored. _{I (J-1)} Or K _{(I-1) J} The symbol m to be stored in the storage element is determined based on the output comparison result of the symbol comparison unit. _{I (J-1)} Or K _{(I-1) J} Until there is no longer the same symbol as the symbol stored in the memory element at the previous position, and there is no symbol the same as the symbol stored in the memory element at the previous position, and Storing the symbol m without the symbol m1 or m2 of the same value in each storage element at the previous position in the same row and columnIt is characterized by.
[0016]
In the present invention, when there is no symbol m that can be selected and determined at an intermediate position, the position K_IJPrevious position K_{I (J-1)}Or K_{(I-1) J}To replace the symbol m of the array element already determinedProcessingSince there is no symbol m that can be selected, the previous position K_{I (J-1)}Or K_{(I-1) J}Thus, it is possible to obtain the possibility of selecting and determining the symbol m changed at least at the previous position.
[0024]
In order to achieve the above object, the claims3The described invention has n rows and n columns.(N is an integer of 3 or more excluding 6)N in all²N storage elements, each of which has n different symbolsForgive duplicationAn Euler square memory array in which a symbol m in which two arbitrarily selected symbols m1 and m2 are paired is stored, and n of the Euler square memory array²Among the storage elements, a designation means for designating a storage element at a set position, a readout means for reading a memory symbol from the storage element at a position designated by the designation means, and a storage element at a position designated by the designation means A writing means for storing the input symbol, a symbol comparison unit for comparing the symbol read by the reading means with the input symbol, the order n of the Euler square to be created,Select symbols m1 and m2 from n symbolsSelection order and symbolsmAre arranged in the row direction or the column direction of the Euler square storage arrangement, and the existing first Euler square prepared in advance are respectively set, receiving the comparison result from the symbol comparison unit, specifying means, and reading And an arithmetic unit for controlling the means and the writing means to store the second Euler square in the Euler square memory array.
[0025]
Here, the arithmetic unit isAfter storing the first Euler square in the Euler square memory array by controlling the specifying means, the reading means and the writing means,The symbol of the specified position at the specified position of the set first Euler squaremIs replaced with the symbol of the next selection order to check if there is the same symbol in the position before the specified position, and the symbol at the specified position until the same symbol disappearsmSpecify the Euler square storage array for symbols that do not have the same symbol at the previous position and do not have the same value of the symbol m1 or m2 at the previous position in the same row and column. Even if it is stored in the memory element corresponding to the position and the selection order is changed and the last symbol is checked, the same symbol is used until the previous position.mThere is a symbol m1 or m2 of the same value at the previous position in the same row and column, so that the symbol that can be selected and determinedmWhen there is no specified position K_IJPrevious position K_{I (J-1)}Or K_{(I-1) J}Return to the specified position andAndPosition K_{I (J-1)}Or K_{(I-1) J}Is replaced by the symbol of the next selection order after the symbol of_{I (J-1)}Or K_{(I-1) J}The specified position in the Euler square storage array is the symbol m that does not have the same symbol m in the previous position and does not have the same value m1 or m2 in the previous position in the same row and column.K _{I (J-1)} Or K _{(I-1) J} The process of storing in the storage element corresponding to is repeated, and the symbol m without the same symbol m at the previous position and without the symbol m1 or m2 having the same value at the previous position in the same row and column If it can be placed, the final position of the first Euler square from the position after the position where the symbol m can be placedUp toContinue processing in the order of arrangement.
[0026]
This inventionThe pair of two symbols m1 and m2 constituting the symbol m of the already determined array element at the previous position in the same row and column is prevented from appearing more than once in all the positions of n rows and n columns, Creates a second Euler square different from the first Euler square. By repeating the setting of the second Euler square created as the first Euler square, the Euler square of the same order and the same symbol can be obtained. Everything can be created.
[0027]
DETAILED DESCRIPTION OF THE INVENTION
Next, embodiments of the present invention will be described with reference to the drawings. In the following description, for convenience of explanation, the order n is 4, the symbol m is a natural number (0, 1, 2, 3), and the permutation and selection order are natural permutations. Here, as described above with reference to FIG. 13, the symbol m of each square of the Euler square is composed of a pair of two symbols m1 and m2, and the natural permutation is a pair (m1, m2) composed of the symbols m1 and m2. (0,0) → (0,1) → (0,2) → (0,3) → (1,0) → (1,1) → (1,2) → (1,3) → (2 , 0) → (2,1) → (2,2) → (2,3) → (3,0) → (3,1) → (3,2) → (3,3) That is.
[0028]
FIG. 1 shows a block diagram of an embodiment of an Euler square creation apparatus according to the present invention. In the figure, the arithmetic unit 1 performs arithmetic processing by software, and also performs a permutation of the order n and the symbol m and the order of selection, first the array element E_IJPosition K to select_IJ, Array element E_IJIn the circuit section for setting the order of selecting and determining each of the Euler squares created in the present embodiment, various operations are executed according to a predetermined control program, and the Euler square R data to be created Specify the matrix position, compare judgment, set, and read.
[0029]
The Euler square R to be created is composed of n rows and n columns when the degree is n, as shown in FIG._IJAnd its position K_IJThe array elements (symbols m1, m2) arranged in_IJIt is represented by In the Euler square storage array 9 in FIG. 1, when creating an n-th order Euler square, n rows and n columns in total, n, in the same way as the Euler square R shown in FIG.²Position K of I rows and J columns, consisting of array elements (memory elements)_IJThe array of is 9_IJIt is represented by Here, each array element 9_IJStores two symbols m1 and m2, respectively. As described above, n = 4 here.
[0030]
The row position setting storage unit 2 designates the row position of the symbol m (that is, m1 and m2) selected and determined based on the output signal of the calculation unit 1 to the Euler square storage array 9. The column position setting storage unit 3 designates the column position of the symbol m (that is, m1 and m2) selected and determined based on the output signal of the calculation unit 1 to the Euler square storage array 9. The row position comparison storage unit 4 determines the row position of the symbol m ′ (which consists of two symbols m1 ′ and m2 ′) to be compared with the symbol m selected and determined based on the output signal of the arithmetic unit 1. Further, the column position comparison storage unit 5 stores the column positions of the symbols m ′ (that is, the symbols m1 ′ and m2 ′) to be compared with the symbol m selected and determined based on the output signal of the calculation unit 1, respectively. This is specified for the Euler square storage array 9.
[0031]
The setting symbol storage unit 6 stores a symbol m (that is, m1 and m2) that is selected and determined based on the output signal of the arithmetic unit 1, or a symbol m (that is, the symbol m from the Euler square storage array 9 (that is, Store m1 and m2). The comparison symbol storage unit 7 stores the symbol m ′ to be compared (that is, the symbols m1 ′ and m2 ′) read from the Euler square storage array 9. The symbol comparison unit 8 compares the symbol m set by the calculation unit 1 and stored in the setting symbol storage unit 6 with the symbol m ′ to be compared stored in the comparison symbol storage unit 7. The comparison result is output to the calculation unit 1.
[0032]
The Euler square creation apparatus shown in FIG. 1 has almost the same basic configuration as the creation apparatus previously disclosed by the present inventor in Japanese Patent Laid-Open No. 10-105544 (invention name “Latin square creation method”). Although the same, the control program set in the arithmetic unit 1 is different, and the creation method and the square to be created are completely different. That is, in the publication, a Latin square that is an n × n matrix with n types of elements is set in the storage array, whereas in this embodiment, the storage array 9 has n × n types. The Euler square that is a matrix of elements of is set. That is, the element symbol is A = {1, 2,. . . , N} in the Latin square, the element symbol m is 1, 2,. . . , N are set, but in the Euler square of this embodiment, as element symbols m (m1, m2), 11,. . . , Nn are set.
[0033]
In addition, in the Latin square, the symbol m (m1, m2) was compared up to the previous position in the matrix direction, but in the Euler square, the symbol m (m1, m2) is one of the positions. Compare and judge whether or not it has been used twice before, so that the pair of two symbols m1 and m2 constituting the symbol m is not duplicated in the previous row and column of that position. It is different in the point of comparison.
[0034]
Next, the Euler square creation method of the present invention created using the above-described Euler square creation apparatus will be described. FIG. 3 is a flowchart for explaining a first embodiment of the Euler square creation method according to the present invention. The embodiment of FIG. 3 will be specifically described with reference to FIGS. First, the order n, symbols m1 and m2 are set for the computing unit 1, and the selection order of symbols is set (step S1 in FIG. 3). Here, as described above, the order n is set to 4, the symbols m1 and m2 are set to natural numbers (0, 1, 2, 3), and the selection order of the symbols m1 and m2 is set to the natural permutation.
[0035]
Subsequently, an initial position is set for the calculation unit 1 and a traveling direction of the position is set (step S2 in FIG. 3). The traveling direction of the position includes a column direction that proceeds in the direction indicated by the arrow in FIG. 6A and a row direction that proceeds in the direction indicated by the arrow in FIG. Here, the first position is K₁₁And the traveling direction of the position is the column direction. As a result, the position is K₁₁→ K₁₂→ K₁₃→ K₁₄→ K₂₁→ ・ ・ ・ → K₄₂→ K₄₃→ K₄₄Proceed in order.
[0036]
Subsequently, the calculation unit 1 sets the first position K set.₁₁Is set to the first symbol (step S3 in FIG. 3). Here, the calculation unit 1 uses the column position setting storage unit 3 and the row position setting storage unit 4 to arrange the first row and first column array 9 of the Euler square storage array 9.₁₁And “00” (m1 = 0, m2 = 0) is stored as the first symbol via the setting symbol storage unit 6. As a result, the stored contents of the Euler square storage array 9 are in the state shown in FIG.
[0037]
Subsequently, the calculation unit 1 determines whether or not the current designated position is the head (step S4 in FIG. 3). This determination is made based on whether I = 1 and J = 1. Here, the designated position is K₁₁Therefore, it is determined to be the head, and the process proceeds to step S11 in FIG. In step S11, it is determined whether or not the current designated position is the last. This determination is made based on whether I = 4 and J = 4. Here, the designated position is K₁₁Therefore, it is determined that it is not the last, and the next designated position is set and the first symbol is set (step S12 in FIG. 3).
[0038]
Here, since the traveling direction of the position is the column direction, the next designated position is K₁₂Is set, and the first symbol “00” is set. That is, in this step S12, the arithmetic unit 1 uses the column position setting storage unit 3 and the row position setting storage unit 4 to arrange the array element 9 in the first row and second column of the Euler square storage array 9.₁₂And the symbol “00” (m1 = 0, m2 = 0) is stored via the setting symbol storage unit 6.
[0039]
Subsequently, the calculation unit 1 proceeds to step S4 in FIG. 3 and determines again whether or not the designated position is the head. Here the designated position is K₁₂Therefore, it is determined that it is not the head, and the process proceeds to step S5, where symbols up to the previous position are examined, and it is determined whether or not there is the same symbol in the examined symbols (step S6 in FIG. 3). Here, since there is the same symbol, the calculation unit 1 sets the symbol “01” (m1 = 0, m2 = 1) in the next selection order (step S14 in FIG. 3).
[0040]
That is, the calculation unit 1 reads the symbol m ′ (m1 ′ and m2 ′) read from the Euler square storage array 9 and the symbol “01” (m1 = 0, m2 = 1) stored in the setting symbol storage unit 6. ) Are compared with each other by the symbol comparison unit 8 and it is determined from the comparison result whether there is a match. In this case, since there is the same symbol, the column position setting storage unit 3 and the row position setting An array element 9 in the first row and the second column of the Euler square storage array 9 via the storage unit 4₁₂And the symbol “01” (m1 = 0, m2 = 1) is stored via the setting symbol storage unit 6.
[0041]
Subsequently, the calculation unit 1 determines whether or not the symbol has been checked up to the symbol “33” (m1 = 3, m2 = 3) in the last selection order (step S15 in FIG. 3), and has not been checked at this stage. Therefore, the process returns to step S4 to determine again whether or not the designated position is the head. Here, the designated position is K₁₂Therefore, it is determined not to be the head, and the process proceeds to step S5, where the symbols up to the previous position are examined, and it is determined whether or not there is the same symbol among the symbols examined in step S5.
[0042]
Here, since there is no same symbol, the subordinate symbol m2 of the symbol m at the previous position in the row is checked (step S7 in FIG. 3), and it is determined whether there is the same symbol as the current subordinate symbol m2. (Step S8 in FIG. 3). Here, since the current lower symbol m2 is “1”, it is different from “0” of the lower symbol m2 at the head position. The upper symbol m1 of the symbols m at the positions up to is checked (step S9 in FIG. 3), and it is determined whether there is the same symbol as the current upper symbol m1 (step S10 in FIG. 3).
[0043]
Here, since it is determined that there is the same, the calculation unit 1 proceeds to step S14 to set the next selection order symbol “02” (m1 = 0, m2 = 2), that is, Euler square memory. Array 9 in the first row and second column of array 9 for use₁₂After storing the symbol “02” (m1 = 0, m2 = 2) in step S15, it is determined in step S15 whether or not the symbol has been checked up to the symbol “33” in the last selection order. Returning to S4, it is determined again whether or not the designated position is the head. Thereafter, the processes from step S4 to step S10, steps S14, and S15 are repeated again in sequence.
[0044]
Thus, the selection order symbol is set to “11” (m1 = 1, m2 = 1), and the array element 9 in the first row and the second column of the Euler square storage array 9₁₂When the symbol “11” is stored in (m1 = 1, m2 = 1), the symbol m is not the same in the previous position, and the symbol m2 lower than the symbol m is the same in the row. There is no state up to the previous position, and the same symbol m1 that is higher than the symbol m does not exist up to the previous position in the row. As a result, the stored contents of the Euler square storage array 9 are in the state shown in FIG.
[0045]
Next, proceeding to step S11, the last position K₄₄Since it is not the last position, the next position K is determined in step S12.₁₃Is set to the first symbol “00” (the array element 9 in the first row and the third column of the Euler square storage array 9).₁₃After the symbol “00” is stored in step S4), the process proceeds to step S4, and it is determined again whether or not the designated position is the head. Here the designated position is K₁₃Therefore, it is determined that it is not the head, and in the same manner as described above, the array element 9 in the first row and the third column of the Euler square storage array 9 in step S14.₁₃In FIG. 4C, the symbol “22” is stored.
[0046]
Hereinafter, in the same manner as described above, the next position K₁₄Is specified, and the array element 9 in the first row and the fourth column of the Euler square storage array 9 is selected in step S14.₁₄The symbol “33” is stored in FIG. 4 (d). Subsequently, the process proceeds to steps S12 through steps S15 and S4 to S11. Here, since the designated position is the last column, the position K of the first column in the next row is set as the next position.₂₁Is specified, and the first symbol “00” is set here.
[0047]
The calculation unit 1 performs the same operation as described above, so that the stored contents of the Euler square storage array 9 are the same as those shown in FIGS. 4D, 4E, 4F, 4G, 5H, and 4H. i), FIG. 5 (j), (k), (l), (m), (n), (o), and (p). In step S14, the last position K of the Euler square storage array 9₄₄Array of 9₄₄As shown in FIG. 5 (p), when the symbol “02” (m1 = 0, m2 = 2) is stored, it is determined in the subsequent step S11 that the designated position is the last, so the processing ends. (Step S13 in FIG. 3).
[0048]
When it is determined in step S15 that the symbol has been checked up to the last symbol “33”, it is determined in the next step S16 whether the position is the first position. Since the arrangement does not exist (has been exhausted), the process proceeds to step S18 and the process is terminated. Set the selection order symbol.
[0049]
As described above, in this embodiment, the Euler square of degree 4 can be created easily and accurately according to a regular processing procedure, and the creation work can be automatically performed. It is good and can be created in a short time, and the certainty of creation can be improved.
[0050]
Next, a second embodiment of the present invention will be described. In the first embodiment described above, a new Euler square is created from a state where nothing exists. In the second embodiment, another Euler square is created based on the Euler square already created. It is. FIG. 7 is a flowchart for explaining a second embodiment of the Euler square creation method according to the present invention. In the figure, the same processing steps as those in FIG. 3 are denoted by the same reference numerals.
[0051]
The embodiment of FIG. 7 will be specifically described with reference to FIGS. First, the order n, symbols m1 and m2 are set for the calculation unit 1, and the selection order of symbols is set (step S1 in FIG. 7). Here, as described above, the order n is set to 4, the symbols m1 and m2 are set to natural numbers (0, 1, 2, 3), and the selection order of the symbols m1 and m2 is set to the natural permutation.
[0052]
Subsequently, an initial position is set for the calculation unit 1 and a traveling direction of the position is set (step S2 in FIG. 7). Here, the first position is K₄₄And the traveling direction of the position is the column direction. As a result, the position is K₁₁→ K₁₂→ K₁₃→ K₁₄→ K₂₁→ ・ ・ ・ → K₄₂→ K₄₃→ K₄₄Proceed in order.
[0053]
Subsequently, the calculation unit 1 sets an existing Euler square in the Euler square storage array 9 (step S21 in FIG. 7). Thereby, the stored contents of the Euler square storage array 9 become, for example, the Euler square shown in FIG. Incidentally, this Euler square is the same as the Euler square shown in FIG.
[0054]
Subsequently, the calculation unit 1 selects the designated position K₄₄Is set to the symbol “03” in the selection order next to the symbol “02” set in (step S22 in FIG. 7). That is, the calculation unit 1 uses the column position setting storage unit 3 and the row position setting storage unit 4 of FIG.₄₄And the symbol “03” (m1 = 0, m2 = 3) is stored through the setting symbol storage unit 6.
[0055]
Subsequently, the calculation unit 1 determines whether or not the set symbol has been finished up to the last symbol (step S23 in FIG. 7). Since the examination has not been completed yet, the process proceeds to step S4. Hereinafter, as described with reference to FIG. 3, it is determined in step S4 that the current position is not the first position, and the process proceeds to step S5 to check whether there is the same symbol up to the previous position. That is, the calculation unit 1 reads the symbol m ′ (m1 ′ and m2 ′) read from the Euler square storage array 9 and the symbol “03” (m1 = 0, m2 = 3) stored in the setting symbol storage unit 6. ) Are compared by the symbol comparison unit 8, and it is determined from the comparison result whether or not they match.
[0056]
Here, since the symbol “03” exists in the second row and the second column in FIG. 8A, it is determined in step S6 that the same symbol is present, and the process returns to step S22 to return to the next symbol “10” in the selection order. (The symbol “10” (m1 = 1, m2 = 0) is set to the array 9 through the setting symbol storage unit 6.₄₄To store).
[0057]
Thereafter, the processes of steps S22, S23, S4, S5, and S6 are repeated until a different symbol is found. At this time, if the comparison is completed up to the symbol “33”, the next symbol does not exist, so it is determined in step S23 that the comparison has been completed up to the last symbol, and in the subsequent step S24, the current position becomes the first position K.₁₁And check if the first position K₁₁In step S25, the designated position is returned to the previous one. Here, the position is K in step S25.₄₄Previous position K₄₃Returned to
[0058]
Subsequently, at step S22, the position K₄₃Is set to the symbol “20” (m 1 = 2, m 2 = 0) via the setting symbol storage unit 6.₄₃To store). Thereafter, in the same manner as described above, the processes in steps S22, S23, S4, S5, S6, S24, and S25 are repeated until a different symbol is found. If a different symbol is found, there is no same symbol up to the previous position, and the same symbol (m1, m2) as the lower m2 of the symbol and the upper m1 of the symbol is not in the previous position in the same row and column Check (steps S7 to S10 in FIG. 7).
[0059]
In the case of the Euler square of FIG.₃₁When the position symbol is changed to “31”, it is determined in step S10 that the above condition is satisfied. Thereby, the storage contents of the Euler square storage array 9 are determined as shown in FIG. 8B, and the calculation unit 1 determines whether or not the designated position is the last in step S11. Here, since it is not the last position, in the following step S12, the next position K₃₂At the first position K₁₁The symbol “00” is set. Further, the processes of steps S4 to S10 and steps S22 and S23 are performed, and the symbol “20” that satisfies the above condition is displayed at the position K as shown in FIG.₃₂To place.
[0060]
Subsequently, the calculation unit 1 determines whether or not the designated position is the last in step S11. Here, since it is not the last position, in the following step S12, the next position K₃₃At the first position K₁₁The symbol “00” is set. Further, the processes of steps S4 to S10 and steps S22 and S23 are performed, and the symbol “13” that satisfies the above condition is displayed at the position K as shown in FIG.₃₃To place. Hereinafter, in the same manner as described above, the position K₃₄The symbol “02” is arranged at the position (FIG. 8E), and the next position K₄₁The symbol “23” is placed at (FIG. 8F), and the next position K₄₂The symbol “32” is arranged at (FIG. 8G), and the next position K₄₃The symbol “01” is arranged at the end position K (FIG. 8H), and the last position K₄₄The symbol “10” is arranged in FIG. 8 (i). Last position K₄₄If a symbol is placed in the position, it is determined in step S11 that it is the last position, and the process ends (step S13 in FIG. 7).
[0061]
Thus, according to the present embodiment, another Euler square shown in FIG. 8 (i) can be automatically created from the Euler square shown in FIG. 8 (a). Further, according to this embodiment, the first Euler square set in step S21 of FIG. 7 can be created, or another new Euler square can be created instead.
[0062]
9 and 10 show the Euler square creation procedure created by the second embodiment when the first Euler square set in step S21 of FIG. 7 is the Euler square shown in FIG. 9A. Show. That is, when the Euler square shown in FIG. 9A is set in step S21, FIG. 9B → FIG. 9C → FIG. 9D → FIG. 9E according to the second embodiment. ) → FIG. 9 (f) → FIG. 9 (g) → FIG. 9 (h) → FIG. 9 (i) → FIG. 10 (j) → FIG. 10 (k) → FIG. The new Euler squares shown in) can be created automatically.
[0063]
This means that you can automatically create all Euler squares of the same order and symbol by repeating the creation of another Euler square as the first Euler square to set up. To do. Therefore, according to this embodiment, since all Euler squares of the same order and symbol can be created easily and reliably, the range of use of Euler squares can be expanded, and the utility value and utilization of Euler squares can be increased. The effect can be dramatically increased.
[0064]
The present invention is not limited to the above embodiment. For example, as shown in FIG. 6B, each array element E of the Euler square in the column direction._IJOf course, Euler squares of orders other than the fourth order can be created in the same manner. Moreover, the symbol m to be set is not particularly limited,
Although the above embodiments have been described with numerals, it is possible to distinguish between alphabets, Greek letters, combinations thereof as shown in FIG. 11C, combinations of these with numerals, colors, and shapes. Anything can be set arbitrarily. The Euler squares created according to these symbols m are, for example, as shown in FIGS.
[0065]
【The invention's effect】
As explained above, the claims1According to the described invention, an Euler square of a desired order n composed of a desired symbol m can be automatically created, so that the Euler square can be surely and easily operated efficiently and accurately in a short time. Can be created.
[0066]
In addition, according to the invention described in claim 2, since it is possible to obtain the possibility of selecting and determining the symbol m changed at least in the previous position, the certainty of regular creation of the Euler square is further improved. it can.
[0068]
Claims3According to the described invention, the second Euler square of the same order and symbol is created based on the existing first Euler square, so that all of the many different Euler squares of the same order and symbol are ensured, In addition, it can be easily created, so that the range of use of the Euler square can be expanded, and the use value and use effect of the Euler square can be dramatically increased.
[Brief description of the drawings]
FIG. 1 is a block diagram of an embodiment of a creation apparatus of the present invention.
FIG. 2 is a diagram showing a configuration of an Euler square created according to the present invention.
FIG. 3 is a flowchart illustrating a first embodiment of a method for creating the present invention.
FIG. 4 is a specific explanatory diagram (No. 1) of a procedure for creating an Euler square according to the flowchart of FIG. 3;
FIG. 5 is a specific explanatory diagram (part 2) of the Euler square creation procedure according to the flowchart of FIG. 3;
FIG. 6 is an explanatory diagram of the creation direction of the Euler square created according to the present invention.
FIG. 7 is a flowchart for explaining a second embodiment of the method for creating the present invention;
FIG. 8 is a specific explanatory diagram of an example of the Euler square creation procedure according to the flowchart of FIG. 7;
FIG. 9 is a specific explanatory diagram (part 1) of another example of the Euler square creation procedure according to the flowchart of FIG. 7;
FIG. 10 is a specific explanatory diagram (No. 2) of another example of the Euler square creation procedure according to the flowchart of FIG. 7;
FIG. 11 is an explanatory diagram of each example of the Euler square.
FIG. 12 is an explanatory diagram of a basic configuration of the Euler square.
FIG. 13 is an explanatory diagram of an example of a conventional Euler square creation method.
[Explanation of symbols]
1 Calculation unit
2-line position setting memory
3 Column position setting memory
4 Line position comparison memory
5 Column position comparison storage unit
6 Setting symbol storage
7 Symbol storage unit for comparison
8 Symbol comparison section
9 Euler square memory array
9_IJ  Array (memory element)
R Euler Square

Claims (3)

There are n ² storage elements in total in n rows and n columns (n is an integer of 3 or more excluding 6) , and each of the storage elements is arbitrarily allowed to overlap among n different symbols. An Euler square memory array in which a symbol m in which the two symbols m1 and m2 selected in FIG.
Designating means for designating a memory element at a set position among n ² memory elements of the Euler square memory array;
Reading means for reading out the memory symbol from the storage element at the position specified by the specifying means;
Writing means for storing the inputted symbol in the storage element at the position designated by the designation means;
A symbol comparison unit that compares the symbol read by the reading means with the input symbol;
And the order n of the Euler square to be created, a selection order for selecting said symbols m1 and m2 from among said n symbols, the position of the symbol m of the Euler square storing sequence is first array, The order in which the symbol m is arranged in the row direction or the column direction of the Euler square storage array and the first value of the symbol m are set, and the comparison result from the symbol comparison unit is received, and the designation is made. And an arithmetic unit for controlling the reading means and the writing means to store the n-th order Euler square in the Euler square memory array , wherein the arithmetic part is used as the first array position of the Euler square memory array. to set the memory element, set the symbol m of the set the first value, followed by the memory element at the next position of the first array location, wherein the writing the first value of said symbol m Included After stored via the means and specifying means, the symbol m to be stored in the storage device, based on the output comparison result of said symbol comparison unit, and is stored in the storage element before the position than the location Until the same symbol as the symbol disappears, the selection order is changed one after the other, there is no symbol same as the symbol stored in the storage element at the previous position, and each memory at the previous position in the same row and column After storing the symbol m without the symbol m1 or m2 of the same value in the element, the symbol m of the first value is further stored in the storage element in the next position via the writing means and the specifying means, Based on the output comparison result of the symbol comparison unit, the symbol m of the storage element at the next position has no same symbol in each storage element at a position before the storage element at the next position, and the same row The same value in the previous position in the column that it would store changed one after another in the selection order until m1 or m2 appears no symbols m, the n to the memory element in the last position of the rows and n columns, to repeat according to the setting arrangement order, the same value The Euler square is formed so that the pair of two symbols m1 and m2 constituting the symbol m is not stored more than once in all the memory elements of the Euler square memory array. Creation device. The arithmetic unit, for each storage element of the Euler square storage array, the symbol m stored in the storage element, based on the output comparison result of the symbol comparison unit, the position of the position before the position If there is no symbol m that can be selected and decided after the last symbol has been checked, the position K is changed when the selection order is changed one after another until the same symbol as that stored in the storage element disappears. _IJ Previous position K _{I (J-1)} Or K _{(I-1) J} The first value of the symbol m is stored in the memory element through the writing means and the specifying means, and the position K is stored. _{I (J-1)} Or K _{(I-1) J} The symbol m to be stored in the storage element is determined based on the output comparison result of the symbol comparison unit at the position K. _{I (J-1)} Or K _{(I-1) J} Until the same symbol as that stored in the memory element at the previous position disappears, the selection order is changed one after another, and there is no same symbol as the symbol stored in the memory element at the previous position. 2. The Euler square creation apparatus according to claim 1, wherein a symbol m without the symbol m1 or m2 having the same value is stored in each storage element at the previous position in the same row and column. There are n ² storage elements in total in n rows and n columns (n is an integer of 3 or more excluding 6) , and each of the storage elements is arbitrarily allowed to overlap among n different symbols. An Euler square memory array in which a symbol m in which the two symbols m1 and m2 selected in FIG.
Designating means for designating a memory element at a set position among n ² memory elements of the Euler square memory array;
Reading means for reading out the memory symbol from the storage element at the position specified by the specifying means;
Writing means for storing the inputted symbol in the storage element at the position designated by the designation means;
A symbol comparison unit that compares the symbol read by the reading means with the input symbol;
The order n of the Euler square to be created, the selection order for selecting the symbols m1 and m2 from the n symbols, and the symbol m along the row or column direction of the Euler square storage array. An order of arrangement and an existing first Euler square prepared in advance are set, respectively, and upon receiving the comparison result from the symbol comparison unit, the designation means, the reading means and the writing means are controlled to store the Euler square An arithmetic unit for storing the second Euler square in the array, and the arithmetic unit stores the first Euler square in the Euler square memory array by controlling the specifying means, the reading means, and the writing means. after, in the set specified position of the first Euler square, the symbol m of the designated position is replaced by a symbol next selection order, the on position before the said specified position Checked whether the symbol, it will change one after another symbol m of the location specified by the selection order to the same symbol disappears, no same sign in front position, and the same in the position until its same row and column Even if the symbol without the symbol m1 or m2 of the value is stored in the storage element corresponding to the designated position of the Euler square storage array and the selection order is changed to the last symbol, If there is no symbol m that can be selected because there is the same symbol m up to the position or the symbol m1 or m2 of the same value in the previous position in the same row and column, the one before the specified position K _IJ position K _{I (J-1)} or K _(I-1) back to the _J and the designated position, following selection order symbol of the position K _{I (J-1)} or K _{(I-1) J} of after replacing the symbols, the positions K _{I (J-1)} or K _(I-1) without the same sign m in front of the position than _J, and its the same row and column Stored at the location until the symbol m1 or m2 is no symbol m of the same value, the storage element corresponding to the Euler the designated position of the square for storing sequence K I _(J-1) or K _{(I-1) J} When the symbol m without the same symbol m at the previous position and the symbol m1 or m2 having the same value at the previous position in the same row and column can be arranged, An Euler square creation apparatus, wherein the processing is continued in a set arrangement order from a position next to the position where the symbol m can be arranged to a final position of the first Euler square.

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