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SQL Data & JavaScript - Best Practice

Let's say a website needs to pull information from a specific table in a database based on a user's menu selection. That table's data is then fed into some JS equations and thrown onto the page.
What is the best way to go about pulling that table's information? I've read that trying to access an SQL database via JavaScript is bad practice, so is there another way to do this? I know about PHP's json_encode, but I guess I'm not entirely sure
What the syntax is if I'm calling PHP from a JS script, and
If that's 'best' practice. Still relatively new to this, so I'd like to do this right.
Another option as far as I'm concerned is attempting to pull ALL of the possible tables (not a security concern) at once on page load. I expect that'd introduce a good deal of latency, though.

It looks to me that you are not really sure what technique to use. Here are some options. I'm not going to type them here because, there is enough to find about each one:
plain php: w3schools
pure ajax call: stackoverflow
jquery: jquery
Ajax calls are more user friendly and many times more efficient because, you don't have to refresh the page. I usually get all information at once( as long your mysql data is not to big). As for security: You use php either way so it doesn't matter if you use Ajax or not. Oh and don't select valuable data of users data (like password or their emails). I hope you get more overview after this :)

Filtering PDO and MySQL queries with JS/jQuery

Sorry for my ignorance on the lack of knowledge I have on this subject however I cannot find an answer to my question anywhere.
So I have this MySQL table:
Feed_ID Vehicle_ID FullRegistration Colour FuelType Year Mileage Bodytype Doors Make Model Variant EngineSize Price PreviousPrice Transmission PictureRefs ServiceHistory PreviousOwners Description FourWheelDrive Options Comments New Used Site Origin V5 Condition ExDemo FranchiseApproved TradePrice TradePriceExtra ServiceHistoryText Cap_ID
As you can see each column will contain vehicle data.
I have displayed all of the results in the database using PDO onto my front end, all data is displayed in a listing style similar to Ebay.
Now I need to filter these results however I have noticed that many result filter systems are using JS.
Here are some examples so you get a better idea of what I am talking about:
http://www.autotrader.co.uk/search/used/cars/
http://www.motors.co.uk/search/car/
As you can see all the filters are using JS however I am having a problem understanding how JS is filtering the MySQL query?
I know this question might be a little broad but can someone show me an example of how JS can filter PDO results just like the examples I have shown?
Thanks

The first one uses what I suspect to be a combined method of Javascript and a server-side language (it's hard to prove, because I can't see the server-side code involved). For simplicity, I'll assume this server-side language is PHP, though it could easily not be.
Basically, all Javascript is doing on the first website is setting cookies and telling you to refresh the page. Once you refresh, PHP fetches the cookies that Javascript set and filters the results from the MySQL query based on those cookies.
Now, the second one is actually filtering using Javascript, yet at the same time still using PHP (again, it could be any server-side language).
This is a method called AJAX. It is a function built into Javascript which allows you to fetch another page from Javascript (aka. send and receive an HTTP request).
The reason this is useful is because once you've changed an option on that page, Javascript can send an HTTP query using AJAX to something like "http://www.motors.co.uk/search/getcarinfo.php?transmission=manual", allowing PHP to fetch a new dataset from MySQL and return it to Javascript (this probably isn't the API entry point that they use, but it has to be somewhere in their Javascript).
Once Javascript receives the response from that page (usually in JSON or XML form), it can modify HTML to update what's shown on the page.
To answer your question directly, Javascript doesn't filter the data. MySQL filters the data based on a PHP query, which returns its response to the Javascript. Then, Javascript just puts it on the screen.

avoid mismatch between server side and client side result

I use PHP and Javascript. In my website some results are processed server side some client side.
Using javascript only, prevents your website from being crawled correctly by search engines and using PHP only prevents correct real time response.
The problem is how to grantee both js functions and PHP functions give the same result? for example suppose there is a function which gives relative time:
JS:
function relative_time(timestamp)
{
...
}
PHP:
function relative_time($timestamp)
{
...
}
Keeping both functions matched with each other is not easy since I want to edit both. For example if both give us:
one year ago
And I change PHP only, to give me:
a year ago
Then JS is not updated too. Is there any standard way to ensure both will act in the same way?
unfortunately js function cannot be called on server side.

If there is some complicated logic, you should implement it server-side and just pull the results via AJAX. That way you only need to maintain the PHP code and provide a kind of AJAX API for access via JS.

I think you just need to make a decision where it is to be done, because if they do vary which is to be dominant ? (that's the one that should be doing it)
Also, how are you saving server load by doing it in both locations ?
Avoid this by making a decision for which code is to do it, failing that, Put a note in you code at both locations reminding yourself to update both locations ?

Using math in browser using XML data

I'm trying to make pull XML or Csv data into a HTML file then I want to use math to add up the values and show the result on the page ( I'm basically trying to display invoices on a web browser)
My skill set is HTML/CSS and I understand a little JavaScript
I've managed to pull XML data into HTML using http request and style that information using xslt
Really what I'm asking is what is the best solution to my needs is it using the above method then using xquiry to add up values or would I need to learn a bit of Ajax, Json and calculate the values with JavaScript?

You really should learn AJAX in order to fetch and manipulate data instead of fetching presentation parts. That's the way everyone follows as it allows more responsive interactions with the user and a cleaner architecture in case of complex interactions.
But that doesn't mean you must abandon XML : originally AJAX was built on XML (the X in AJAX) and not JSON.
Personally I prefer JSON, and I think it will be easier to manage in the long term, but if the server side is hard to change, you can fetch the XML (look for example at jquery's ajax function), build javascript objects using it, and then change your screen using those data. If later you decide to use JSON instead of XML, you'll just have to change the "parsing" part of the client code.

"I'm trying to make pull XML or Csv data into a HTML file then I want to use math to add up the values and show the result on the page"
You can do this with either XSLT or javascript. However, with XSLT things can become pretty complicated, depending on what version you're using. XSLT 1.0 has pretty limited set of functions for aggregating results. For all XSLT, you can't reassign variables you'll have to solve many of these things with recursion. In my opinion, not really a comfortable method.
Regardless of the choice between XSLT and Javascript, I would also question the architecture that would put this kind of logic in the presentation layer in the browser. I think it would be better if the server side would perform all the calculations that are required, and limit the browser's tasks to styling the output.

Best Server-Side Data Storage Method for Simple Data

I'm coding a website that involves storing very simple data, just a very long list of names with no additional data, on the server. As this data is so simple, I don't really want to use MySQL (it would be a bit too clunky) so I'm asking what's the best way to store very simple data on the server.
I definitely would favour speed over anything else, and easy access to the data via javascript and AJAX would be very good too as the rest of the site is coded in javascript/jQuery. I don't really care if the data can be viewed freely (as it will be available anyway), as long as it can't be changed by unauthorised users.

There are a lot of things to think about with this.
Is the information the same for all users with just a single set that applies to all users out there? Or is there a separate set of data for each user?
How is the data going to be served to the client, my guess here is that you would be having a web service or otherwise that might return a JSON.
From a security standpoint, do you want someone to be able to just "grab" the data and run?
Personally I find that a database if often a better choice, but otherwise i would use an XML file. Keep in mind though that you have to be careful with loading/reading of XML files to serve web requests to prevent any potential file locking issues.

Use an XML file that is web-accessible. Then you can query the XML file from the browser if need be, and still parse/write it in PHP. You'll want to use the flock function in PHP to make sure that two instances of a page don't try to write to the file at the same time.

Write it to a file and save the data as a serialized object. This way when you read in the data it's instantly accessible as the variable type you need (array, obj, etc). This will be faster than XML parsing.