KR20030089934A - Range search binary method in integer type data structure and apparatus thereof - Google Patents

Abstract

PURPOSE: A method for a binary detection by a section search in a data structure having integer type data and a method thereof are provided to detect wanted data rapidly by sensing a section capable of including data to be searched instead of selecting the whole sections, detecting the data within the reduced range, thereby reducing the number of detecting comparison times in the case that massive data comprising integers are searched. CONSTITUTION: A record sorting unit receives data from an input unit(110) and sorts the received data(records) in descending powers or in ascending powers according to key values(120). A group of the sorted records is stored in a storage. A section setting unit comprises the upper/lower limit range calculation unit and a section calculation unit. The upper/lower limit range calculation unit receives a key value of data to be searched(130) and calculates the upper value and the lower value as to the key value(143). The section calculation unit calculates a range or an area of a key value to be searched(145). A key search unit decides a range as to an array number of a record having a key value to be searched out of the sorted records(153) and searches a record having a key value to be searched out of the decided range(155). If the record is searched, searched data are output through an output unit(160).

Description

Range detection binary method in integer type data structure and apparatus according to interval search in data structure with integer data

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to the field of detecting data stored in a computer, and the like, and in particular, to detect binary data by interval search for further improving the detection speed of data consisting of integers by a binary search algorithm to reduce the detection time. A method and apparatus therefor.

Conventional dichotomy detects a record whose desired key is K in a set R of integers in which records R ₁ , R ₂ , ..., R _n are arranged in ascending or descending order with keys K ₁ , K ₂ , ..., K _n . Assuming a search, first, the key K _m (m ≦ n) located in the middle of the order of the records is selected and repeated by repeating the comparison with a given key K. In the binary detection method, since the location of a given key is unknown, the first search section is selected as the search section from the record R ₁ to R _n . However, if we can find out in advance that the key K we are looking for is within a certain range in the set R, we can narrow the search range and reduce the average number of comparisons if the range is reduced, so a binary search over that range Detection speed will be faster than when.

The following is a binary detection algorithm that is one of several methods of data detection.

Binary_Search (x, v, n)

Int x, v [], n;

{

int low, mid, high;

low = 0; --------------- (One)

high = n-1; ---------- (2)

while (low <= high) {

mid = (low + high) / 2;

if (x <v [mid])

high = mid-1;

else if (x> v [mid])

low = mid + 1;

else return (mid);

}

return (0);

}

In the above binary detection method, x is a key value to be searched and is a variable whose value is a given key K, n is the number of records, which represents the size of set R, and v [] is a set of records and arranged in the order of key values. It is assumed that the records are sorted in ascending order. mid is a variable representing the intermediate record to be compared, and low and high are variables representing the lower and upper bounds of the records to be compared in the set R, v []. The function value immediately after the execution ends is the number of the record found or the value 0 indicating that the record to be found is not in the set R. If K> K _{mid, the} comparison target is R _{mid + 1} , R _{mid + 2} , ..., R _n, so the variable low in the lower limit is mid + 1, and if K <K _mid , R ₁ , R ₂ , ... Since the records in R _mid-1 are compared, the variable high in the upper range becomes mid-1. If the desired record is not found, low> high during the algorithm execution is violated by the low = high condition. As shown in equations (1) and (2), when the low and high values are specified, the binary detection method does not know where the given key is located. There is a problem that the entire set R from record R ₁ to R _n can be selected as a search section.

The technical problem to be solved by the present invention is to find out the section in which the data to be searched can be found in advance without selecting the first search section as the entire section when searching for a large amount of integer data to solve the above problems. The present invention provides a method and apparatus for dividing detection by section searching in order to detect desired data at a faster speed by reducing the number of detection comparisons by narrowing the range and detecting the result in a reduced range.

Another object of the present invention is to provide a computer-readable recording medium having recorded thereon a program for executing the method on a computer.

1 is a view showing a flow for the dichotomous detection method according to the section search according to the present invention.

2 is a block diagram of a binary search apparatus for searching data by section search according to the present invention.

FIG. 3 is a diagram illustrating a lower limit range (FIG. 3A), an upper limit range (FIG. 3B), and a range of key values (FIG. 3C) that each record may have in the sorted set of records.

4 is a diagram illustrating an equation for obtaining an upper limit value and a lower limit value of a record in order to determine a search section according to the present invention.

FIG. 5 is a diagram illustrating a distribution type of key values that each record may have, and a distribution having a type in which the key value has a larger size than the number of records (FIG. 5A). Type distribution (FIG. 5B), distribution having a type whose key size is smaller than the number of records (FIG. 5C) and distribution having a type whose key size is 1 (FIG. 5D).

The binary detection method according to the section search according to the present invention for achieving the above object, (a) sequentially sorting records having an integer key value; (b) in the records arranged in step (a) Receiving a key value of a record to be searched and determining a range of the key value; (c) determining a sequence range of records located within the range of the key value and having a record having the input key value within the sequence range Searching for;

In accordance with an aspect of the present invention, there is provided a binary detection apparatus for detecting a segment, comprising: a record sorting unit for sequentially arranging records having an integer key value; receiving a key value of a record to be searched from the sorted records An interval setting unit for determining a range of the key value; a key search unit for determining an order range of records located within the range of the key value and searching for a record having the input key value within the order range.

Hereinafter, with reference to the accompanying drawings will be described in detail a preferred embodiment of the present invention.

1 is a view showing a flow for a dichotomous detection method according to the section search according to the present invention, and receives the data in an integer type, sorts according to a key, and sets a section of a record to be searched.

2 is a block diagram of a binary search apparatus for searching data by section search according to the present invention.

1 and 2 will be described together.

Receiving data from the input unit 210 (step 110), the record sorting unit 220 sorts the records in descending or ascending order according to the key value (step 120). This section describes a set of records sorted in ascending order.

When the set of records is sorted, the sorted set of records is stored in the storage unit 270. The interval setting unit 240 includes an upper and lower range calculation unit 243 and an interval calculation unit 245, and the upper and lower range calculation unit 243 receives a key value of a material to be searched (step 130). The lower limit value and the upper limit value are calculated (step 143), and the interval calculator 245 calculates a range or region of key values to be searched (step 145). A description of the process of calculating the lower limit, the upper limit, and the range of the key value of the key value will be described in detail with reference to FIG. 3.

The key search unit 250 determines a range of an array number of records having a key value to be searched among the sorted records (step 153) and searches for a record having a key value to be searched within the determined range (step 155). )do. A process of calculating the range of the record, which is a search section, will be described in detail with reference to FIG. 4. When the record is found, the searched data is output through the output unit 260.

FIG. 3 is a diagram illustrating a lower limit range (FIG. 3A), an upper limit range (FIG. 3B), and a range of key values (FIG. 3C) that each record may have in the sorted set of records.

3A is a diagram illustrating a lower limit of a key value that a record may have. First, the records R ₁ , R ₂ , ..., R _n with keys K ₁ , K ₂ , ..., K _n are given, and they are arranged in ascending order by key and the values of the keys are all integers. Suppose we want to find a record, R _k , whose value is K, and we look at how to find out in advance which interval K is given in an integer set R.

Compute the lower and upper bounds (values) that each record can have in set R. First, as the least significant key value key of a record R ₁ in Fig. 3a K _1, and when the highest key value of the record R _n that K _n value of K that can be in the record R _2, so is arranged in ascending order greater than K ₁ K _n Will have a smaller value. That is, R ₂ is can enter a value from greater than K ₁ K ₁ +1, is, like R ₃ will have a value from greater than K ₁ +2 K ₁ +1. Applying this process to the R _n -1 R _n -1 will have a K ₁ + _(N-1) larger value K ₁ + _(N-1) from the value of -1 than -2. So the last record, R _{n, will} contain the value of K _n . Therefore, the lower limit of record R _k is K ₁ + (k-1). Where 1 <k <N and N represents the total number of records.

3B shows an upper limit range that each record can have. Since the records R ₁ and R _n are already determined in the set R, the values of the lower and upper ranges R ₁ are K ₁ and R _n is K _n . The upper limit range in which the R _n -1 R _n may have the upper limit of K, so _n R _n -1 is the _n -1 K. In the same principle, the upper limit of R _n -2 will be K _n -2 and R _n -3 will be K _n -3. Applying this process up to R _n , the upper limit of the record R _n is K _n- (N-2). Therefore, generalizing this, the upper limit of the record R _k is K _n- (Nk).

Summarizing the above result, the lower limit of record R _k in set R is K ₁ + (k-1) and the upper limit is K _n- (Nk). In other words, if K is the key value that can be taken by the kth record, the range of values that K can have is K ₁ + (k-1) ≤ K ≤ K _n- (Nk) (where k is 1). <k <N).

In a set R with N records, the range of key values that each record from R ₂ to R _n -1 excluding the first record and the last record can have (Key Range Size, hereinafter referred to as H) H is {K _n- (Nk)}-{(K ₁ + (k-1))} + 1 (i.e., upper limit-lower limit + 1), summed up, H = K _n -K ₁ -N + 2 All have the same size range. If this is shown as a picture, it can be seen that the shape always has a distribution of parallelograms as shown in FIG. 3C.

4 is a diagram illustrating an equation for obtaining an upper limit value and a lower limit value of a record in order to determine a search section according to the present invention.

In the case of finding a record having a key value K in a set R, in order to find out which interval K is in a given set R, the x-axis is the record number (n) and the y-axis is the key value (K) as shown in FIG. If the lower limit is K ₁ and the upper limit is K _n , two linear equations can be generated. That is, one is an equation of a straight line y = x, which can be expressed as K = (K ₁ -1) + n, and the other is a linear equation of the form y = x + b. It can be expressed by the equation ₁ -2) + n + H. Looking at the above two equations, if K is given, two n values are obtained. N obtained from K = (K ₁ -1) + n is called high and K = (K ₁ -2) + n + H When the value of n is determined to be low, low denotes the first starting term where K can exist, that is, the variable low, and high denotes the last term where K can exist, that is, the variable high.

Of course, depending on the distribution of N and key, the low and high values can also vary. When N starts from 0 (ie, when n> 0), the two equations are represented by K = K ₁ + n and K = (K ₁ -1) + n + H, respectively.

FIG. 5 is a diagram illustrating a distribution type of key values that each record may have, and a distribution having a type in which the key value has a larger size than the number of records (FIG. 5A). Type distribution (FIG. 5B), distribution having a type whose key size is smaller than the number of records (FIG. 5C) and distribution having a type whose key size is 1 (FIG. 5D).

The distribution types of key values that each record can have in the set R can be classified into four types as follows. First, FIG. 5A is a distribution type in which H> N, and a type having a large area range (H) of keys compared to the number N of records. In this case, the K value to be found is between K ₁ and K ₁ + N values (K ₁ ≤ K ≤ K ₁ + N) or between K ₁ + H and K _n (K ₁ + H <K ≤ K _n ), which means that the search interval is narrower than the conventional dichotomy detection algorithm. Decreases and therefore the search speed is relatively fast. However, when the K value is between K ₁ + N and K _n + H (that is, K ₁ + N ≤ K ≤ K ₁ + H), which is the same interval as the conventional binary detection algorithm, it is almost identical to the conventional binary detection algorithm. Will search at speed. In this case, the area where the search interval is the same as the conventional binary detection algorithm is K _n -K ₁ -2N (513), and the ratio is (K _n -K ₁ -2N) / (K _n -K ₁ ) as K _n- Assuming that K ₁ is infinitely larger than N, that is, when K _n -K ₁ >> N, the ratio approaches 1. In this extreme case, this technique will have almost the same search time as the conventional binary detection algorithm. The worst case example is where N is 1 (because N can't be 0) and the key values are distributed very broadly, with the same number of comparisons.

5b is a distribution type in which H = N, and only when the key value K is N, the search interval is the same as that of the conventional dichotomy detection algorithm, and the key value K is K _n <K <N and the interval N <K <K ₁ In the section, since the search section is reduced, that is, the N value is small, the number of comparisons is reduced. The characteristic of this distribution is that as the key value approaches the lowest value, K _1, or the highest value, K _n , the interval narrows and the number of comparisons decreases gradually, eventually reaching K ₁ or K _n . Is the case. At this time, since the maximum number of comparisons becomes 1 by log (1) +1, detection is completed by only one comparison. This feature appears the same in any distribution.

5c is a distribution type where H <N, and since the search interval is always a small area compared to the conventional dichotomy detection algorithm, the average number of comparisons will be reduced by log ₂ N-log ₂ R (where R represents the determined search interval). Since the decreasing average number of comparisons is log ₂ (N / R), when R is constant, the relative difference in comparisons increases proportionally as N increases. In other words, a larger value of N indicates that the average detection speed is relatively faster.

Figure 5d is a distribution type of H = 1, H value is 1 to have a uniform distribution of the type y = x, so under this distribution the low and high values are the same, so to find the record for any key value K The maximum number of comparisons is always one. In this case, even when N is infinitely large regardless of the number of N, the maximum number of comparisons is always 1, so only one comparison finds a record having a key value of K. Comparing the four types of distributions listed above in terms of average search speed, the speed increases from FIGS. 5A to 5D to FIG. 5D. Therefore, in case of any distribution, the search speed is faster when compared with the conventional binary search, and in particular, the larger N, the greater the comparison.

Summarizing the above, an improved bipartite detection algorithm can be described as follows.

Range_Search (x, v, n)

Int x, v [], n;

{

int low, mid, high;

high = x v [0]; ---------- (3)

if (high> = n-1) high = n-1;

low = x v [n-1] + n-1; ----------- (4)

if (low <= 0) low = 0;

while (low <= high) {

mid = (low + high) / 2;

if (x <v [mid])

high = mid-1;

else if (x> v [mid])

low = mid + 1;

else return (mid);

}

return (0);

}

In the above binary detection method, x is a variable having the key K as a value to find, n is the number of records, the size of the set R, and v [] is a set of records and arranged in the order of the key values. It is assumed that the records are arranged in ascending order. mid is a variable representing the intermediate record to be compared, and low and high are variables representing the lower and upper bounds of the records to be compared in the set R, v []. The function value immediately after the execution ends is the number of the record found or the value 0 indicating that the record to be found is not in the set R. If K> K _{mid, the} target of comparison is R _{mid + 1} , R _{mid + 2} , ..., R _n, so the variable low in the lower limit is mid + 1, and if K <K _mid , R ₁ , R ₂ , ... The records in R _mid-1 are compared, so the variable high in the upper range is mid-1. If the desired record is not found, low> high during the algorithm execution is violated by the condition of low ≤ high, and the process ends.

Equation (3) and equation (4) of the above-described algorithm to determine the low and high values are the same as already described in FIG. That is, the equation for determining the high value of _{K = (K 1 -1) +} n equation K = (K ₁ - 2) for n represents a high value, determines the low value in the n + a low value in the n + H Indicates. That is, high = K-K ₁ + 1, low = K-K ₁ -H + 2. When starting from n to 0 as described in Fig. _{4, K = (K 1 -1} ) + n , and _{K = (K 1 - 2)} + n + H each _{K = K 1 + n, K} = (K _1-1 ) + n + H, so high = K-K ₁ , low = K-K ₁ -H + 1.

In addition, as described in FIG. 3C, since H has a value of K _n -K ₁ -n + 2, it is represented by low = K-K _n + n-1. As above, it is possible to know the section in which the key is found by the low (lower limit) value and the high (higher limit value) in advance, so the detection is started within this interval rather than the entire interval. Therefore, the entire set R is selected as the detection interval. Detection is possible faster than conventional methods.

The following describes, for example, a process of finding a position section of a record having a key value K of 35 when N is 12 and arranged in the following array.

Arrangement One 2 3 4 5 6 7 8 9 10 11 12 Key value 27 28 30 31 32 35 36 37 39 40 41 42

By the arrangement of the records starting from _{1, H = K 12 - K} 1 - 12 + 2, high = K - K 1 + 1, low = K - K 1 - when calculated by using the H + 2, as in the arrangement Similarly, if we calculate the range of the position of the record having the key value K of 35, we can see that it is located in the 5th and 9th intervals of the array because H is 5, low is 5, and high is 9. Therefore, start a binary search in this interval to find the location of the record with the key value 35.

The invention can also be embodied as computer readable code on a computer readable recording medium. The computer-readable recording medium includes all kinds of recording devices in which data that can be read by a computer system is stored. Examples of computer-readable recording media include ROM, RAM, CD-ROM, magnetic tape, hard disk, floppy disk, flash memory, optical data storage device, and also carrier waves (for example, transmission over the Internet). It also includes the implementation in the form of. The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion.

As described above, according to the present invention, when detecting a given key in an integer type data set, the key K is found in advance in a certain range in the set R, and then data is detected in a reduced section. Therefore, compared with the conventional binary detection method, the number of comparisons is relatively reduced, which can reduce the time to detect desired data in a faster way.

Claims (12)

(a) sequentially sorting records having an integer key value; (b) receiving a key value of a record to be searched from the records sorted in step (a) and determining a range of the key value; And and (c) determining an order range of records located within a range of the key value and searching for a record having the input key value within the order range. The method of claim 1, wherein step (a) And dividing the records in ascending or descending order according to the size of the key value. The method of claim 1, wherein step (b) (b1) calculating a lower limit range and an upper limit range of a key value of the record having the predetermined number; And (b2) calculating an area of key values each record except for the first record and the last record in a set of records consisting of a predetermined number of records; Binary detection method. The method of claim 3, wherein in step (b1), The lower limit and the upper limit are obtained from the following equations, [Equation] Where K ₁ is the key value of the first record, K is the key value of the kth record, and K _n is the key value of the nth record, k is an integer greater than 1, and n is Divided detection method according to the section search, characterized in that the integer in the range of. The method of claim 3, wherein in step (b2), The area of the key value is obtained by the following equation, [Equation] Where K ₁ represents the kit value of the first record and K _n represents the key value of the nth record, and n is Divided detection method according to the section search, characterized in that the integer in the range of. The method of claim 1, wherein in step (c), The order range determines the lower limit and the upper limit of the record by the following equation, [Equation] Wherein K ₁ is the key value of the first record, K _n is the key value of the nth record, and H is a range of key values. A record sorting unit for sequentially ordering records having an integer key value; An interval setting unit which receives a key value of a record to be searched from the sorted records and determines a range of the key value; And And a key searching unit for determining an order range of records located within a range of the key value and searching for a record having the input key value within the order range. The method of claim 7, wherein And a input unit for receiving a key value of the records or the record to be searched. The method of claim 8, wherein the record sorting unit And dividing the records having an integer key input into the input unit in ascending or descending order. The method of claim 7, wherein the section setting unit An upper and lower range calculation unit configured to calculate a lower limit range and an upper limit range of the input key value; And Binary detection by edge searching, comprising: an interval calculating unit for calculating an area of key values each record except for the first and last records in a set of records consisting of a predetermined number of records Device. The method of claim 7, wherein And a storage unit for storing the sorted records or the records of the retrieved key values. A computer-readable recording medium having recorded thereon a program for executing the method of any one of claims 1 to 6.