This application claims priority from Japanese Patent Application No. 2009-128129, filed on May 27, 2009, the entire subject matter of which is incorporated herein by reference.
Aspects of the present invention relate to an image forming apparatus capable of duplex printing, and more particularly, to an image forming apparatus capable of duplex printing by printing a plurality of sheets on first sides thereof and subsequently printing the sheets on second sides thereof.
There has been proposed a technique for improving a speed of the duplex printing process by printing N sheets (N is a positive integer) on the first sides thereof and subsequently printing M sheets (M is an integer equal to or more than 0 and equal to or less than N) on the second sides thereof For example, for performing the duplex printing on 10 pages (5 sheets), an image forming apparatus prints them in the page order of 2 (even page), 4 (even page), 1 (odd page), 6 (even page), 3 (odd page), 8 (even page), 5 (odd page), 10 (even page), 7 (odd page) and 9 (odd page). Furthermore, an image forming apparatus that prints them in the page order of 1, 3, 5, 2, 7, 4, 9, 6, 8, and 10.
However, in the above-described duplex printing technique, there have been the following problems. That is, a time required for completing generation of print data for “one printing process unit” (for example, one page) is different for each copy setting. For example, a setting for printing a plurality of pages on one sheet or setting for reading both sides requires a longer time for completing a reading of an original image, as compared with other settings. Therefore, even though a printing speed is increased by increasing the number of sheets to be successively printed on the first sides thereof, generation of the print data for subsequent “one printing process unit” may not be completed before a certain printing operation of “one printing process unit” is completed. Therefore, the printing operation may be temporarily suspended. In that case, the advantage of printing successively on first sides can be not fully enjoyed. Additionally, as the plurality of sheets are printed on the first sides thereof, the number of sheets staying in the image forming apparatus increases. Therefore, there may be a disadvantage in that the number of defective print sheets increases, which are caused by a sheet jam.
Accordingly, it is an aspect of the present invention to provide an image forming apparatus capable of efficiently performing the duplex printing while reducing a possibility of the temporary suspension of the printing operation.
According to an illustrative embodiment of the present invention, there is provided an image forming apparatus comprising: a reading section configured to read an original document; a printing section configured to perform duplex printing including printing N sheets on first sides thereof and subsequently printing M sheets on second sides thereof when printing an image of the original document read by the reading section, wherein M is equal to or smaller than N; a determination section configured to calculate a preparation time required to generate print data based on a copy setting which affects the preparation time, and configured to determine the value of N, wherein the determination section determines a smaller value as the value of N, as the preparation time is longer; and a control section configured to control the printing section to perform the duplex printing in accordance with the value of N determined by the determination section.
According to another illustrative embodiment of the present invention, there is provided an image forming apparatus comprising: a reading section configured to read an original document; an operation section configured to allow a user input regarding an image reading setting of the reading section; a printing section configured to perform duplex printing including printing N sheets on first sides thereof and subsequently printing M sheets on second sides thereof when printing an image of the original document read by the reading section, wherein M is equal to or smaller than N; a determination section configured to determine the value of N based on the image reading setting; and a control section configured to control the printing section to perform the duplex printing in accordance with the value of N determined by the determination section.
According to a further illustrative embodiment of the present invention, there is provided an image forming apparatus comprising: a reading section configured to read an original document in a reading mode selected from a first mode of reading an image of the original document while conveying the original document and second mode of reading an image of the original document placed on a document placing table; a printing section configured to perform duplex printing including printing N sheets on first sides thereof and subsequently printing M sheets on second sides thereof when printing the image of the original document read by the reading section, wherein M is equal to or smaller than N; a determination section configured to determines the value of N at least based on the reading mode of the reading section; and a control section configured to control the printing section to perform the duplex printing in accordance with the value of N determined by the determination section.
According to the above-described illustrative embodiments, it is possible to provide the image forming apparatus which is capable of efficiently performing duplex printing while reducing the possibility of the temporary suspension of the printing operation.
The above and other aspects of the present invention will become more apparent and more readily appreciated from the following description of illustrative embodiments of the present invention taken in conjunction with the attached drawings, in which:
Hereinafter, an image forming apparatus according to an illustrative embodiment of the present invention will be described in detail with reference to the accompanying drawings. In the illustrative embodiment, there will be described an electrophotographic color printer as an example of the image forming apparatus. The color printer is capable of duplex printing by printing a plurality of sheets on the first sides thereof and subsequently printing the sheets on the second sides thereof.
As shown in
As shown in
The image reading section 20 has two modes of reading the original document, which include a flatbed mode, in which an original document is stationary during scanning and an ADF mode, in which an original document is moved during scanning. In the flatbed mode, the original document is placed one by one on the platen glass 24 (hereinafter referred to as a “FB glass 24”). In this sate, the image sensor 25 is moved in a sub-scanning direction, which is orthogonal to a main scanning direction, and which is shown as arrow A in
As shown in
The processing section 50 is capable of forming a color image, and includes four processing units corresponding to the respective colors of yellow (Y), magenta (M), cyan (C), and black (K) which are arranged in parallel. Specifically, the processing section 50 includes a processing unit 50Y that forms a yellow (Y) image, a processing unit 50M that forms a magenta (M) image, a processing unit 50C that forms a cyan (C) image, and a processing unit 50K that forms a black (K) image. The processing section 50 further includes an exposure unit 53 that illuminates light on the respective processing units 50Y, 50M, 50C, and 50K, and a conveying belt 7 that is looped between the rollers 73 and 74 and that conveys a sheet to the transfer positions of the respective processing units 50Y, 50M, 50C, and 50K. Each of the processing units 50K, 5OY, 50M, and 50C is configured to form a toner image by an electrophotographic method.
The image forming section 10 feeds the sheets accommodated on the sheet feeding cassette 91 one by one, conveys the fed sheet to the processing section 50, and transfers the toner images formed by the processing section 50 onto the sheet. Furthermore, the sheet onto which the toner images are transferred is conveyed into the fixing unit 8, and the toner images are thermally fixed on the sheet. Then, the fixed sheet is discharged to the sheet discharging tray 92.
Furthermore, the image forming section 10 has a duplex printing mechanism that prints both sides (first side and second side) of a sheet. As shown in
Specifically, in the duplex printing performed by the image forming section 10, the sheet is reversed in the following procedure. First, the sheet which is passed through the conveying path 11 (hereinafter referred to as a “forward conveying path 11”) and has an image formed on the first side thereof, is thermally fixed by the fixing unit 8, and is subsequently sent to the conveying path 12 (hereinafter referred to as a “reverse conveying path 12”). Then, the sheet is conveyed into the temporary staying path 121, and the conveyance of the sheet is temporarily suspended. Thereafter, by turning the rotation direction of the turning roller 75, the sheet conveying direction is reversed, and the sheet is conveyed into the returning path 122. Then, the sheet is returned to the forward conveying path 11 at an upstream side from the processing section 50. Accordingly, the sheet is reversed, and an image is formed on the second side.
The image forming section 10 has a function of successively printing N sheets (N is a positive integer) on the first sides thereof and subsequently printing M sheets (M is an integer equal to or more than 0 and equal to or less than N) on the second sides thereof at the time of performing the duplex printing. Furthermore, the image forming section 10 has a function of changing the number of sheets N and the number of sheets M to be successively printed. The change of N and M is performed by adjusting the timing of sheet conveyance and the conveying speed. The number of sheets N to be successively printed is appropriately set by the double-side copying process to be described later.
For example, when the number of sheets N to be successively printed is 2, the sheets are conveyed in the following procedure. First, as shown in
Further, for example, when the number of sheets N to be successively printed is 3, the sheets are conveyed in the following procedure. First, the first sheet S1 is conveyed into the forward conveying path 11, and is printed on the first side thereof. Next, while the sheet S1 is conveyed into the temporary staying path 121, the second sheet S2 is conveyed into the forward conveying path 11, and is printed on the first side thereof. Subsequently, as shown in
It is noted that the maximum number of sheets N to be successively printed is different depending on the number of sheets capable of staying in the reverse conveying path 12. The number of sheets capable of staying in the reverse conveying path 12 depends on the length of the reverse conveying path 12, the length of the sheet in the sheet conveying direction, and the like. That is, the number of sheets N to be successively printed is not limited to 2 or 3 described above, but may be 4 or more.
Subsequently, an electric configuration of the printer 100 will be described. As shown in
The ROM 32 stores various control programs and various settings for controlling the printer 100, initial values, and the like. The RAM 33 is used as a work area, from which the various control programs are read, or as a storage area which temporarily stores image data.
The CPU 31 stores the processing result in the RAM 33 or the NVRAM 34 according to signals transmitted from various sensors and the control program read from the ROM 32, and controls various elements of the printer 100 through the ASIC 35 (for example, lighting timing of the exposure device 53, drive motors (not shown) of the various rollers constituting the forward conveying path 11 and the reverse conveying path 12, and moving motors (not shown) of an image sensor unit constituting the image reading section 20).
The network interface 36 is connected to a network such as the Internet to enable a communication with an information processing apparatus in which a driver for the printer 100 is installed. A print job can be communicated through the network interface 36.
Next, the double-side copying process in the printer 100 will be described with reference to the flowchart of
First, a copy setting for the double-side copying is acquired (S101). The copy setting includes, for example, an n-up setting, a reading quality (reading resolution) setting, a double-side reading (reading side) setting, and a color reading setting. The copy setting affects preparation time required to generate the print data.
Next, it is determined whether the reading mode is the flatbed mode (S102). If the reading mode is the flatbed mode (S102: YES), the process proceeds to the operation S105. In the flatbed mode, it is assumed to take time to generate the print data corresponding to one page since the original document is manually set on a sheet by sheet basis. Therefore, it is not so expected that an increase in speed of the printing process is achieved by using a large number of sheets N to be successively printed on the first sides. Additionally, disadvantages may be caused by setting a larger value as the value of N. Accordingly, a same process for a case where the preparation time required to generate the print data is long (S104: NO), that is, the process of determining a smaller value of N is performed.
On the other hand, if the reading mode is not the flatbed mode, that is, if the reading mode is the ADF mode (S102: NO), the preparation time required to generate the print data is estimated (calculated) (S103). Specifically, the printer 100 stores a definition table 321 which includes coefficients for each copy setting and a threshold time as shown in
Herein, the preparation time estimation process of the operation S103 will be described with reference to the flowchart of
Next, it is determined whether a 2in1 setting for printing two original images on one sheet is made as the n-up setting (S132). If the 2in1 setting is made (S132: YES), the preparation time Tm is multiplied by a time coefficient R2 for the 2in1 reading (S142). If the 2in1 setting is not made (S132: NO), it is determined whether a 4in1 setting for printing four original images on one sheet is made (S133). If the 4in1 setting is made (S133: YES), the preparation time Tm is multiplied by a time coefficient R4 for the 4in1 reading (S143).
Next, it is determined whether a picture quality (high reading resolution) is set as an original document quality setting (S134). If the picture quality is set (S134: YES), the preparation time Tm is multiplied by a time coefficient Rp for the picture quality reading (S144).
Next, it is determined whether the double-side reading is set (S135). If the double-side reading is set (S135: YES), the preparation time Tm is multiplied by a time coefficient Rd for the double-side reading (S145).
Next, it is determined whether a color reading is set (S136). If the color reading is set (S136: YES), the preparation time Tm is multiplied by a time coefficient Rc for the color reading (S146).
As described above, in the preparation time estimation process in the operation S103, the preparation time Tm is multiplied by time coefficients according to the copy setting. Herein, it is noted that, the referred copy settings are not limited to the above. If a certain setting affects the generation time of the print data, more specifically, if a certain setting relates to the image reading time or the memory expansion time of the read data, a time coefficient corresponding to such setting may be multiplied.
Returning to the description of the flowchart of
If the preparation time Tm is equal to or longer than the threshold time Th (S104: NO), it is determined whether a setting for reusing data as a print setting is made (S105). The setting of reusing data is a setting for reusing the print data without deleting the print data even after the completion of the duplex printing performed on one sheet. The setting of reusing data corresponds to, for example, a sort printing setting or a reprinting setting. If the setting for reusing data is not made (S105: NO), it is determined that the value of N is 1 (S106).
Specifically, when the preparation time Tm is equal to or longer than the threshold time Th, it can be expected that a relatively long time is necessary for the reading of the original document and the memory expansion of data, and it takes time for completing the generation of the print data. Therefore, even though a larger value is set as the value of N, an increase in printing speed is not always expected, and additionally, disadvantages may be caused by setting a larger value as the value of N. Accordingly, the value of N is set to 1.
If the setting for reusing data is made (S105: YES), it is determined whether an available amount of the memory of the printer 100 is sufficient (greater than a value) (S121). If the available amount of the memory is sufficient, N is set to 2 (S122). That is, when the setting for reusing data is made, the print data is not immediately deleted from the memory even after the end of the printing. Therefore, even if the smaller value is set as the value of N, it is not expected to enjoy an effect of avoiding disadvantages caused by the larger value of N, that is, an effect of reducing the amount of the memory used. Accordingly, the larger value is set as the value of N, and priority is given to the increase in speed of the duplex printing process.
In contrast, if the preparation time is shorter than the threshold time Th (S104: YES), it is determined whether an available amount of the memory in the printer 100 is sufficient (S121). If the available amount of the memory is sufficient (S121: YES), it is determined that the value of N is 2 (S122).
That is, if the preparation time Tm is shorter than the threshold time Th, it can be expected that a long time is not necessary for the reading of the original document and the memory expansion of data, and the printing preparation is completed early. Therefore, by setting the value of N to 2, the duplex printing speed is increased.
If the available amount of the memory is not sufficient (S121:NO), it is not possible to perform the operation by setting the value of N to 2, and thus it is determined that the value of N is 1 (S106). That is, when the value of N is set to 2, in order to retry the printing after a paper jam, a larger memory area is necessary as compared with the case where the value of N is set to 1. For example, a memory area for storing the print data corresponding to 4 pages is necessary for the case where the value of N is set to 2. Accordingly, in the operation of S121, it is determined whether the available amount of the memory is sufficient for storing the print data corresponding to 4 pages. The determination as to the available amount of the memory is not limited to the physical memory capacity, and may be made based on whether the memory capacity required to allow the printer 100 to perform another process is reserved.
After the determination of the value of N, the memory area having a size corresponding to the value of N is reserved (S107). In other words, when the value of N is 1, the memory area corresponding to 2 pages is reserved, and when the value of N is 2, the memory area corresponding to 4 pages is reserved. Thereafter, the reading of the original document is started (S108).
Subsequently, the duplex printing is started (S109). Next, the procedure of the duplex printing execution process will be described with reference to the flowchart of
First, it is determined whether the reversing of the sheet, on which the first side printing has been performed, is completed and the preparation for conveying the sheet to the processing section 50 is completed (S151). In the operation S151, it is determined that the preparation for conveying the sheet is not completed when the sheet does not stay in the reverse conveying path 12, or when the sheet is positioned at a predetermined distance or more apart from a junction position between the forward conveying path 11 and the reverse conveying path 12 even when the sheet is staying therein.
If the preparation for conveying the sheet is not completed (S151: NO), it is determined whether the number of sheets staying in the reverse conveying path 12 is smaller than N (S161). If the number of sheets is smaller than N (S161: YES), one sheet is fed from the sheet feeding cassette 91, and the sheet is conveyed to the processing section 50, thereby printing the sheet on the first side thereof (S162). Thereafter, the sheet having been printed on the first side is conveyed to the reverse conveying path 12 (S163). If the number of sheets is equal to or greater than N (S161: NO), the number of sheets staying in the reverse conveying path 12 reaches a limit thereof. Therefore, printing is suspended until the sheet in the reverse conveying path 12 is prepared to be returned to the forward conveying path 11 (S171).
If the preparation for conveying the sheet having been printed on the first side is completed (S151: YES), the sheet in the reverse conveying path 12 is conveyed to the processing section 50, and is printed on the second side thereof (S152). Thereafter, the sheet printed on both sides thereof is discharged to the sheet discharging tray 92 (S153).
Next, it is determined whether the setting for reusing the print data is made (S154). If the setting for reusing the data is made (S154: YES), the duplex printing execution process ends without deleting the print data from the memory. In contrast, if the setting for reusing the data is not made (S154: NO), the deletable print data is deleted from the memory (S155). That is, when the print data of the sheet having been printed on both sides thereof remains, the data is deleted. Furthermore, after being deleted, print data of a new page is expanded in the memory. That is, the print data of the sheet having been printed on both sides thereof is deleted immediately after printing, thereby avoiding an increase in memory area used for the print data.
Returning to the description of the printing process of
It is noted that, in the above-described double-side copying process, the number of sheets N to be successively printed on the first sides is set to 1 or 2, but the value of N is not limited thereto. That is, in the conveyable range, the value of N may be set to 3 or more. In this case, the threshold times corresponding to the values of N are provided respectively, and the preparation time and the respective threshold times are compared to determine an appropriate value of N.
As described above, the printer 100 according to this illustrative embodiment is capable of performing the duplex printing including printing N sheets on first sides thereof and subsequently printing M sheets (M≦N) on second sides thereof, and is also capable of changing the value of N. In addition, in determining (setting) the value of N, the preparation time required to generate the print data is calculated based on at least a part of the copy setting, and it is determined whether the preparation time is shorter than the threshold time for the value of N. Then, if the preparation time is not shorter than the threshold time (that is, it is expected that the preparation time for printing of the print data is longer), the value of N is set to be smaller in order to perform duplex printing. Accordingly, it can be expected to avoid the temporary suspension due to the waiting for the generation of the print data, and it is possible to start printing early by using the print data in which the print preparation is completed. In addition, when the conveyance of the sheet is suspended because of the temporary suspension at a large value of N, a risk of disadvantages (the amount of the memory used increases, the number of sheets having print failure caused by paper jam increases, and the like) caused by a large value of N is accompanied. However, if the value of N is set to be small, it is possible to avoid such disadvantages. On the other hand, when the preparation time is less than the threshold time (that is, it is expected that it takes less time to prepare the printing of the print data), the duplex printing is performed with a large value of N. Thereby, it is possible to perform printing efficiently. As described above, in the illustrative embodiment, the preparation time required to complete the printing preparation is estimated (calculated) based on the copy setting, and the number of sheets to be printed successively (that is, the number of sheets staying in the reverse conveying path) is changed. Therefore, it is possible to perform printing efficiently while reducing the possibility of the temporary suspension of the printing operation due to the waiting for the generation of the print data.
While the present invention has been shown and described with reference to certain illustrative embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
For example, the present invention is not limited to the color printer, and may be applied to a multi function peripheral, a FAX device, and the like if it has the image forming function. Furthermore, the image formation method of the image forming section is not limited to the electrophotographic method, and may be an inkjet method. In addition, the image forming section may form a color image, or form only a monochrome image.
Further, in the above-described illustrative embodiment, a plurality of sheets are successively printed on first sides thereof, and subsequently the same number of sheets are printed on the second sides thereof. However, after the plurality of sheets are printed on the first sides thereof, printing may be performed alternately on the second sides and on the first sides. For example, when the number of sheets to be successively printed is 2, the first sheet is printed on the second side thereof (step S3), the first sheet is discharged to the sheet discharging tray 92, and the third sheet S3 is conveyed into the forward conveying path 11, and is printed on the first side (step S4′). At this time, the second sheet S2 is staying in the reverse conveying path 12, and is not returned to the forward conveying path 11. Thereafter, the sheet S3 is conveyed into the reverse conveying path 12, and the second sheet S2 is returned to the forward conveying path 11, and is printed on the second side (step S5). Then, steps S4′ and S5 are repeated. For example, in a case where four sheets are printed on both sides, the printing is performed in order of the first side of the first sheet, the first side of the second sheet, the second side of the first sheet, the first side of the third sheet, the second side of the second sheet, the first side of the fourth sheet, the second side of the third sheet, and the second side of the fourth sheet. In this conveying order, while the sheet is reversed, another sheet is printed, so that printing efficiency can be improved.
Furthermore, the number of sheets M to be successively printed on the second sides may be equal to or less than the number of sheets N to be successively printed on the first sides. For example, at first, the three sheets may be successively printed on the first sides. Thereafter, the second side printing and the first side printing may be alternately performed by two sheets by two sheets.
Further, in the above-described illustrative embodiment, when the print data is expanded in the memory of the printer 100, each data corresponding to 2N page is sequentially expanded in the memory. This process particularly effective in the case where the memory capacity in the printer 100 is intended to be minimized, but the timing of expanding the print data is not limited thereto. For example, when the printer 100 includes a memory having a capacity capable of expanding the print data corresponding to all pages therein, the print data corresponding to all pages may be expanded at once in the memory.
The present invention provided illustrative, non-limiting embodiments as follows:
(1) An image forming apparatus comprises: a reading section configured to read an original document; a printing section configured to perform duplex printing including printing N sheets on first sides thereof and subsequently printing M sheets on second sides thereof when printing an image of the original document read by the reading section, wherein M is equal to or smaller than N; a determination section configured to calculate a preparation time required to generate print data based on a copy setting which affects the preparation time, and configured to determine the value of N, wherein the determination section determines a smaller value as the value of N, as the preparation time is longer; and a control section configured to control the printing section to perform the duplex printing in accordance with the value of N determined by the determination section.
The above-described image forming apparatus is configured to perform the duplex printing including printing N sheets on first sides thereof and subsequently printing M sheets (M≦N) on second sides thereof, wherein “N” is a positive integer, and “M” is an integer equal to or more than 0 and equal to or less than N. Depending on the value of “N”, the number of sheets staying in the apparatus as the standby of the printing on the second sides after the printing of the first sides is determined. The printing section is configured to change the numbers of sheets N and M to be printed on their respective sides in the conveyable range. When determining the value of N, as the preparation time required to generate the print data is longer, the smaller value is determined as the value of N. The “preparation time” is calculated based on the copy setting (a setting relating to the reading time of an image and a setting relating to the memory expansion time of the read data) which affects the generation time of the print data.
That is, when it is expected that relatively long time is required to complete printing preparation in a copy process, the above-described image fowling apparatus performs the duplex printing by setting the value of N, which is the number of sheets to be successively printed on the first sides, to be small. Accordingly, it is possible to avoid the temporary suspension caused by waiting for completion of the printing preparation of the print data, and it can be expected that the printing is started early by using the print data in which the printing preparation is completed. Furthermore, it is possible to avoid disadvantages caused when N is large. In contrast, when it is expected that relatively not long time is required to prepare the printing of the print data, the duplex printing is performed by using the larger value of N. Accordingly, printing efficiently can be improved.
(2) In the above-described image forming apparatus, the determination section may calculate the preparation time based on, among the copy setting, at least one of a reading resolution setting, a reading side setting, a reading color setting, and an n-up setting. By calculating the preparation time based on these copy settings, the preparation time can be accurately calculated (estimated).
(3) The above-described image forming apparatus may further comprise a memory configured to store the print data. The determination section may determine, as the value of N, a value which is smaller than a value to be determined based on the preparation time when an available amount of the memory is smaller than a threshold value. That is, when the available amount of memory is small, the effect on processes other than printing is large if a large amount of memory is used with the larger value of N. Therefore, in order to avoid this situation, the determination section determines a smaller value as the value of N.
(4) The above-described image forming apparatus may further comprise: a memory configured to store the print data; and a deleting section configured to delete, in response to completion of print on the first and second sides of one sheet, the print data corresponding to the one sheet. The completion of the printing may be completion of image formation on the sheet or completion of discharge of the sheet to the outside of the apparatus. By deleting the print data as early as possible, load on other processes can be reduced.
(5) The above-described image forming apparatus may further comprise a setting section capable of making a setting of reusing print data after completion of print of the print data. When the setting of reusing print data is made, the deleting section may not delete the print data even when the print is completed, and the determination section determines, as the value of N, a value which is larger than a value to be determined based on the preparation time. The “setting of reusing the print data” includes, for example, the sort printing setting (which prints a plurality of sheets in the page order) and the reprinting setting (which reuses the print data by which printing is completed). The using of a small value of N is advantageous in, for example, reducing the amount of the memory used, but in the case of reusing the print data, the print data is not deleted, and therefore, this advantage can not be fully enjoyed. Accordingly, the larger N is used, and priority is given to an increase in printing speed.
(6) In the above-descried image forming apparatus, the reading section may have selectable reading modes including at least a first mode of reading an image of the original document while conveying the original document, and second mode of reading an image of the original document placed on a document placing table. The determination section may determine, as the value of N, a value which is smaller than a value to be determined based on the preparation time when the original document is to be read by the reading section in the second mode. In the second mode, it is expected that the reading takes relatively long time. Therefore, it is not expected that an increase in speed of the printing process is achieved by using a large number of sheets N to be successively printed on their first sides. Additionally, there may be a disadvantage caused by using the large value of N. Therefore, it is advantageous to use the small value of N to cause the amount of used memory to be small regardless of the calculation result of the preparation time.
Number | Date | Country | Kind |
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2009-128129 | May 2009 | JP | national |