How to prefix a positive number with plus sign in PHP

You can use regex as:

function formatNum($num){
    return preg_replace('/^(d+)$/',"+$1",$num);
}

But I would suggest not using regex for such a trivial thing. Its better to make use of sprintf here as:

function formatNum($num){
    return sprintf("%+d",$num);
}

From PHP Manual for sprintf:

An optional sign specifier that forces a sign (- or +) to be used on a number. By default, only the - sign is used on a number if it's negative. This specifier forces positive numbers to have the + sign attached as well, and was added in PHP 4.3.0.

I agree with the comments about not using a numbering scheme like this if the numbers are going to be used for anything other than a simple ordered display of items with numbers. If the numbers are actually going to be tied to something, then this is a really bad idea!

Use a variable, and increment it in the SELECT statement:

SELECT
    id,
    (@row:=@row+1) AS row
FROM table,
(SELECT @row:=0) AS row_count;

Example:

CREATE TABLE `table1` (
    `id` int(11) NOT NULL auto_increment,
    PRIMARY KEY  (`id`)
) ENGINE=InnoDB

INSERT INTO table1 VALUES (24), (87), (112);

SELECT
    id,
    (@row:=@row+1) AS row
FROM table1,
(SELECT @row:=0) AS row_count;

+-----+------+
| id  | row  |
+-----+------+
|  24 |    1 |
|  87 |    2 |
| 112 |    3 |
+-----+------+

How it works

@row is a user defined variable. It is necessary to set it to zero before the main SELECT statement runs. This can be done like this:

SELECT @row:=0;

or like this:

SET @row:=0

But it is handy to tie the two statements together. This can be done by creating a derived table, which is what happens here:

FROM table,
(SELECT @row:=0) AS row_count;

The the second SELECT actually gets run first. Once that's done, it's just a case of incrementing the value of @row for every row retrieved:

@row:=@row+1

The @row value is incremented every time a row is retrieved. It will always generate a sequential list of numbers, no matter what order the rows are accessed. So it's handy for some things, and dangerous for other things...

New answer

Re your revised question: foreach actually works with properties as well as with many-valued items (arrays), details here. So for instance, with the JSON string in your question:

$data = json_decode($json);
foreach ($data as $name => $value) {
    // This will loop three times:
    //     $name = inbox
    //     $name = sent
    //     $name = draft
    // ...with $value as the value of that property
}

Within your main loop over the properties, you can use an inner loop to go over the array entries each property points to. So for instance, if you know that each of the top-level properties has an array value, and that each array entry has a "firstName" property, this code:

$data = json_decode($json);
foreach ($data as $name => $value) {
    echo $name . ':'
    foreach ($value as $entry) {
        echo '  ' . $entry->firstName;
    }
}

...will show:

inbox:
  Brett
  Jason
  Elliotte
sent:
  Issac
  Tad
  Frank
draft:
  Eric
  Sergei

Old answer(s)

Begin edit Re your comment:

Now I would like to know how to decode JSON string with several objects!

The example you posted does have several objects, they're just all contained within one wrapper object. This is a requirement of JSON; you cannot (for example) do this:

{"name": "I'm the first object"},
{"name": "I'm the second object"}

That JSON is not valid. There has to be a single top-level object. It might just contain an array:

{"objects": [
    {"name": "I'm the first object"},
    {"name": "I'm the second object"}
]}

...or of course you can give the individual objects names:

{
    "obj0": {"name": "I'm the first object"},
    "obj1": {"name": "I'm the second object"}
}

End edit

Your example is one object containing three properties, the value of each of which is an array of objects. In fact, it's not much different from the example in the question you linked (which also has an object with properties that have array values).

So:

$data = json_decode($json);
foreach ($data->programmers as $programmer) {
    // ...use $programmer for something...
}
foreach ($data->authors as $author) {
    // ...use $author for something...
}
foreach ($data->musicians as $musician) {
    // ...use $musician for something...
}