I would like to know if someone can help me designing a context free grammar
for a language where { w | |w|a=2|w|b }
for example w=aab , aaaabb , aaaaaabbb ,baa , aba , aabbaaaba ...
S-> aab | baa | aba | SS | abSa | baSa | aaSb | bSaa would not generate aaabba.
So my next question is , isn't it too ambiguous to have a grammar that looks like this ->
**
S-> aab | baa | aba | aSab | aSba | aaSb |abSa |aabS | abaS | Saab | Saba | Sbaa | SS | bSaa | baSa | baaS ?
**
Thank you in advance
None of the grammars you posted can product aaabba, you need something like this:
S-> HaSa | aHSa | aSHa | aSaH | HSaa | SHaa | SaHa | SaaH | HaaS | aHaS | aaHS | aaSH | epsilon
H -> b
It can probably be done with a shorter grammar, but I think this will do.
Try this one:
S -> ε | S1 S
S1 -> ε | aaS1bS1 | bS1aaS1 | aS1bS1a
Related
I don't know why it doesn't give me the answer for students enrolled in Database Systems but not in Operating System Design.
select student.snum, student.sname, enrolled.cname
-> from enrolled
-> inner join student ON enrolled.snum = student.snum
-> where enrolled.cname="Database Systems" AND enrolled.cname<>"Operating System Design";`
+-----------+--------------------+------------------+
| snum | sname | cname |
+-----------+--------------------+------------------+
| 112348546 | Joseph Thompson | Database Systems |
| 115987938 | Christopher Garcia | Database Systems |
| 348121549 | Paul Hall | Database Systems |
| 322654189 | Lisa Walker | Database Systems |
| 552455318 | Ana Lopez | Database Systems |
+-----------+--------------------+------------------+
My student table.
+-----------+--------------------+------------------------+-------+------+
| snum | sname | major | level | age |
+-----------+--------------------+------------------------+-------+------+
| 51135593 | Maria White | English | SR | 21 |
| 60839453 | Charles Harris | Architecture | SR | 22 |
| 99354543 | Susan Martin | Law | JR | 20 |
| 112348546 | Joseph Thompson | Computer Science | SO | 19 |
| 115987938 | Christopher Garcia | Computer Science | JR | 20 |
| 132977562 | Angela Martinez | History | SR | 20 |
| 269734834 | Thomas Robinson | Psychology | SO | 18 |
| 280158572 | Margaret Clark | Animal Science | FR | 18 |
| 301221823 | Juan Rodriguez | Psychology | JR | 20 |
| 318548912 | Dorthy Lewis | Finance | FR | 18 |
| 320874981 | Daniel Lee | Electrical Engineering | FR | 17 |
| 322654189 | Lisa Walker | Computer Science | SO | 17 |
| 348121549 | Paul Hall | Computer Science | JR | 18 |
| 351565322 | Nancy Allen | Accounting | JR | 19 |
| 451519864 | Mark Young | Finance | FR | 18 |
| 455798411 | Luis Hernandez | Electrical Engineering | FR | 17 |
| 462156489 | Donald King | Mechanical Engineering | SO | 19 |
| 550156548 | George Wright | Education | SR | 21 |
| 552455318 | Ana Lopez | Computer Engineering | SR | 19 |
| 556784565 | Kenneth Hill | Civil Engineering | SR | 21 |
| 567354612 | Karen Scott | Computer Engineering | FR | 18 |
| 573284895 | Steven Green | Kinesiology | SO | 19 |
| 574489456 | Betty Adams | Economics | JR | 20 |
| 578875478 | Edward Baker | Veterinary Medicine | SR | 21 |
+-----------+--------------------+------------------------+-------+------+
My enrolled table
+-----------+----------------------------+
| snum | cname |
+-----------+----------------------------+
| 112348546 | Database Systems |
| 115987938 | Database Systems |
| 348121549 | Database Systems |
| 322654189 | Database Systems |
| 552455318 | Database Systems |
| 455798411 | Operating System Design |
| 552455318 | Operating System Design |
| 567354612 | Operating System Design |
| 112348546 | Operating System Design |
| 115987938 | Operating System Design |
| 322654189 | Operating System Design |
| 567354612 | Data Structures |
| 552455318 | Communication Networks |
| 455798411 | Optical Electronics |
| 301221823 | Perception |
| 301221823 | Social Cognition |
| 301221823 | American Political Parties |
| 556784565 | Air Quality Engineering |
| 99354543 | Patent Law |
| 574489456 | Urban Economics |
+-----------+----------------------------+
You need to use the NOT EXISTS as follows:
select s.snum, s.sname, e.cname
from enrolled e
inner join student s ON e.snum = s.snum
where e.cname='Database Systems'
AND not exists
(select 1 from enrolled ee
where ee.snum = e.snum and e.cname = 'Operating System Design');
Compare string with single quotation mark(' ') than double quotation(" "). Your code seems ok to me.
Remember:
Single quotes are for strings.
Double quotes are for tables names and column names.
select student.snum, student.sname, enrolled.cname
from enrolled
inner join student ON enrolled.snum = student.snum
where enrolled.cname='Database Systems'
AND enrolled.cname<>'Operating System Design';
or try this
select student.snum, student.sname, enrolled.cname
from enrolled
inner join student ON enrolled.snum = student.snum
where enrolled.cname='Database Systems'
my google sheet excel document contain data like this
+---+---+---+---+---+---+
| | A | B | C | D | E |
+---+---+---+---+---+---+
| 1 | | c | | x | |
+---+---+---+---+---+---+
| 2 | | r | | 4 | |
+---+---+---+---+---+---+
| 3 | | | | m | |
+---+---+---+---+---+---+
| 4 | | | | | |
+---+---+---+---+---+---+
Column B and D contain data provided by IMPORTRANGE function, which are store in different files.
And i would like to fill column A with first not empty value in row, in other words: desired result must look like this:
+---+---+---+---+---+---+
| | A | B | C | D | E |
+---+---+---+---+---+---+
| 1 | c | c | | x | |
+---+---+---+---+---+---+
| 2 | r | r | | 4 | |
+---+---+---+---+---+---+
| 3 | m | | | m | |
+---+---+---+---+---+---+
| 4 | | | | | |
+---+---+---+---+---+---+
I tried ISBLANK function, but apperantly if column is imported then, even if the value is empty, is not blank, so this function dosn't work for my case. Then i tried QUERY function in 2 different variant:
1) =QUERY({B1;D1}; "select Col1 where Col1 is not null limit 1"; 0) but result in this case is wrong when row contain cells with numbers. Result with this query is following:
+---+---+---+---+---+---+
| | A | B | C | D | E |
+---+---+---+---+---+---+
| 1 | c | c | | x | |
+---+---+---+---+---+---+
| 2 | 4 | r | | 4 | |
+---+---+---+---+---+---+
| 3 | m | | | m | |
+---+---+---+---+---+---+
| 4 | | | | | |
+---+---+---+---+---+---+
2) =QUERY({B1;D1};"select Col1 where Col1 <> '' limit 1"; 0) / =QUERY({B1;D1};"select Col1 where Col1 != '' limit 1"; 0) and this dosn't work at all, result is always #N/A
Also i would like to avoid using nested IFs and javascript scripts, if possible, as solution with QUERY function suits for my case best due to easy expansion to another columns without any deeper knowladge about programming. Is there any way how to make it simply, just with QUERY, and i am just missing something, or i have to use IFs/javascript?
try:
=ARRAYFORMULA(SUBSTITUTE(INDEX(IFERROR(SPLIT(TRIM(TRANSPOSE(QUERY(
TRANSPOSE(SUBSTITUTE(B:G, " ", "♦")),,99^99))), " ")),,1), "♦", " "))
selective columns:
There is a really good explanation of multi-dimensional array here on stackoverflow which I have studied and researched but i have few follow up questions for anyone who wants to help out. This is not a HW question, it is out of my text book which I am trying to understand more so please confirm if I am looking at the below example correctly. Thank you in advance.
So if i had a 3 dimensional array such as this:
{{{'1','2'},{'3','4'}},
{{'5','6'},{'7','8'}},
{{'9','10'},{'11','12'}}};
Would the one dimensional outcome (using c compiler) simply be?:
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| | | | | | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
And the corresponding position as?
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| | | | | | | | | | | | |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+
Again I am using this link as my source.
The only thing I am looking for as a form of answer is, am I looking/doing this correctly? If not, I would appreciate it if you can tell me where I have made any mistakes. Thank you again.
1.
char [3][2][2] :
+-----+-----+ +-----+-----+
|+-----+-----+ |+-----+-----+
|| 1 | 3 | || 4 | 5 |
||1,0+-----+-----+ || +-----+-----+
|+---| a | b | |+---| 0 | 1 |
|| 2|0,0,0|0,0,1| || 6| | |
+|1,1+-----+-----+ => +| +-----+-----+
+---| x | y | +---| 2 | 3 |
|0,1,0|0,1,1| | | |
+-----+-----+ +-----+-----+
so your outcome seems ok, and thus (2.) t3[0] should be a.
2.
if t2 looks like this, t2[0][1] is b:
+-----+-----+-----+-----+ +-----+-----+-----+-----+
| a | b | x | y | | | | | |
|0,0,0|0,0,1|0,1,0|0,1,1| | 0,0 | 0,1 | 0,2 | 0,3 |
+-----+-----+-----+-----+ +-----+-----+-----+-----+
| 1 | 3 | 2 | 7 | => | | | | |
|1,0,0|1,0,1|1,1,0|1,1,1| | 1,0 | 1,1 | 1,2 | 1,3 |
+-----+-----+-----+-----+ +-----+-----+-----+-----+
| q | g | r | 4 | | | | | |
|2,0,0|2,0,1|2,1,0|2,1,1| | 2,0 | 2,1 | 2,2 | 2,3 |
+-----+-----+-----+-----+ +-----+-----+-----+-----+
As long you are converting them the right way(as it seems according to the link) it should work...
For conceptual understanding this is a good starting point.
But you should understand the difference between row vs column major. And technically it could vary between compilers and languages depending upon what they are designed for.
http://en.wikipedia.org/wiki/Row-major_order
I want to show what my UserControl/Control is doing when I plug a list of data in it, what happens when the user press certain keys, selecting text etc...
I feel somehow a sequence diagramm is not really suited for showing several loops and doing stuff within the loops.
Am I wrong or how can I cope with that case?
If you are talking about a loop, then you have a series of operations that take place for all elements in the loop.
I would model the operations done in the loop as a sequence diagram by itself, if the operation in the loop are fairly complex.
I don't think we can have rules of thumb here, but when the process with the loop itself is complex, and the loop is relatively less complex, we can have them in a single sequence diagram.
If the process that has the loop is not very complex, but the loop is complex, then I would draw a sequence diagram for the operations of the loop and have a note that this entire sequence is called by a loop.
You can also have both sequence diagrams if needed.
Update:
We have to add some notes to the diagram because it is not straightforward to denote a "condition" in a sequence diagram.
The validate is part is something like
do validation
if validation succeeds
proceed to next (business or other) logic
if validation fails
feedback to user (or some other logic)
+----+ +----+ +----------------+ +----------------+
|User| | UI | | Your Validator | | Business Logic |
+----+ +----+ +----------------+ +----------------+
| select | | |
|--------------->| doValidation | |
| |------------------>|----+ |
| | | | Validate |
| | |<---+ |
| | | |
| | | (validation fails: |
| | Validation Fail | feedback to client) |
| |<------------------| |
| | | |
| | | |
| | | (validation succeeds: |
| | | proceed to |
| | | business logic) |
| | | |
| | | someLogic |
| | |----------------------->|
| | | |
UPDATE 2
Why use sequence diagram in a case as mine?
Because you still have to show the sequence of operations, and the developer still needs this information for coding :-)
With UML, as you probably already know, nothing is imposed. You are at your freedom to denote something in some fashion, provided your team also understands it the way you intended. These notes are also helpful.
I should have mentioned this before, some use an "option" fragment to denote a if else. This is more or less a note (I see it this way) but is perhaps more evident. I use them only when both the IF and the ELSE parts are both complex.
+----+ +----+ +----------------+ +----------------+
|User| | UI | | UI - Backend | | Busines Logic |
+----+ +----+ +----------------+ +----------------+
| Add Record | | |
|--------------->| doinsertOrUpdate | |
| |------------------>| |
| | | exists(record) |
| | |----------------------->|
| | | |
____|________________|___________________|________________________|__________
|[Record exists] | | | |
| | | | Get Record | |
| | | |----------------------->| |
| | | | | |
| | | |--------+ | |
| | | | | Set UI Values | |
| | | |<-------+ | |
| | | | | |
| | | | Update Record | |
| | | |----------------------->| |
| | | | | |
| | | Send Message | | |
| | |<------------------| | |
| | | "Record found, | | |
| | | Updated" | | |
|___|________________|___________________|________________________|_________|
| | | |
| | | |
______|________________|___________________|________________________|_________
| [Record does not | | | |
| exist] | | | |
| | | |--------+ | |
| | | | | Generate | |
| | | | | Seqeuence | |
| | | |<-------+ | |
| | | | | |
| | | | Create New Record | |
| | | |----------------------->| |
| | | Send Message | | |
| | |<------------------| | |
| | | "New Record | | |
| | | Created" | | |
|_____|________________|___________________|________________________|_________|
| | | |
| | | |
| | | |
See this for an example using an alt block.
I have implemented the A* algorithm in AS3 and it works great except for one thing.
Often the resulting path does not take the most “natural” or smooth route to the target.
In my environment the object can move diagonally as inexpensively as it can move horizontally or vertically.
Here is a very simple example; the start point is marked by the S, and the end (or finish) point by the F.
| | | | | | | | | |
|S| | | | | | | | |
x| | | | | | | | | |
x| | | | | | | | | |
x| | | | | | | | | |
x| | | | | | | | | |
x| | | | | | | | | |
|F| | | | | | | | |
| | | | | | | | | |
| | | | | | | | | |
As you can see, during the 1st round of finding, nodes [0,2], [1,2], [2,2] will all be added to the list of possible node as they all have a score of N.
The issue I’m having comes at the next point when I’m trying to decide which node to proceed with. In the example above I am using possibleNodes[0] to choose the next node. If I change this to possibleNodes[possibleNodes.length-1] I get the following path.
| | | | | | | | | |
|S| | | | | | | | |
| |x| | | | | | | |
| | |x| | | | | | |
| | | |x| | | | | |
| | |x| | | | | | |
| |x| | | | | | | |
|F| | | | | | | | |
| | | | | | | | | |
| | | | | | | | | |
And then with possibleNextNodes[Math.round(possibleNextNodes.length / 2)-1]
| | | | | | | | | |
|S| | | | | | | | |
|x| | | | | | | | |
x| | | | | | | | | |
x| | | | | | | | | |
x| | | | | | | | | |
x| | | | | | | | | |
|F| | | | | | | | |
| | | | | | | | | |
| | | | | | | | | |
All these paths have the same cost as they all contain the same number of steps but, in this situation, the most sensible path would be as follows...
| | | | | | | | | |
|S| | | | | | | | |
|x| | | | | | | | |
|x| | | | | | | | |
|x| | | | | | | | |
|x| | | | | | | | |
|x| | | | | | | | |
|F| | | | | | | | |
| | | | | | | | | |
| | | | | | | | | |
Is there a formally accepted method of making the path appear more sensible rather than just mathematically correct?
You need to add a Tie-breaker to your heuristic function. The problem here is that there are many paths with the same costs.
For a simple Tie-breaker that favors the direct route you can use the cross-product. I.e. if S is the start and E is the end, and X is the current position in the algorithm, you could calculate the cross-products of S-E and X-E and add a penalty to the heuristic the further it deviates from 0 (= the direct route).
In code:
dx1 = current.x - goal.x
dy1 = current.y - goal.y
dx2 = start.x - goal.x
dy2 = start.y - goal.y
cross = abs(dx1*dy2 - dx2*dy1)
heuristic += cross*0.001
See also http://theory.stanford.edu/~amitp/GameProgramming/Heuristics.html#S12, which is an excellent tutorial about A* in general.
If you want paths that look natural, you need to make sure that your costs correspond to the length on a cartesian coordinate system. That means the cost of moving diagonally should be sqrt(2) times the cost of moving vertically or horizontally.
You can add 'control effort' to the cost calculations for each square. The actor will try not to turn or change direction too much as that will add a cost to the path:
http://angryee.blogspot.com/2009/03/better-pathfinding.html
If I remember correctly, the trick to this is to add an extra parameter to the cost function (for every step between adjacent nodes, or squares in your case) that penalises turns slightly more than normal (for example, having a relative cost of greater than sqrt(2) for digonal moves). Now, there's probably a fine line between smoothing out the path and actually decreasing the optimality of the route (elongating it), however, and you're not going to be able to avoid this in any way. There's a certain trade-off you'll need to discover specific to your own application, and this can only really be achieved by testing.
There was an article on a game dev site, I believe, that detailed exactly how this could be done, but I can't seem to find it at the moment. Have a play around with your cost function anyway and see what results you get - I'm pretty sure that's the way to go.
What is more 'sensible'? Straighter? You need to quantify it properly if the algorithm is going to do anything about it.
Since moving diagonally is as inexpensive as moving horizontally/vertically, all the paths are equivalent according to all the criterion available to A*. If you want a more 'sensible' path, you need to tell the algorithm that some paths are more desirable than others, effectively weighting horizontal/vertical as 'better' than diagonal. As far as I can see, that would be altering the parameters of your environment.