Multidimensional Array [][] VS [,]

Multidimensional Array [][] vs [,]

One is an array of arrays, and one is a 2d array. The former can be jagged, the latter is uniform.

That is, a double[][] can validly be:

double[][] x = new double[5][];

x[0] = new double[10];
x[1] = new double[5];
x[2] = new double[3];
x[3] = new double[100];
x[4] = new double[1];

Because each entry in the array is a reference to an array of double. With a jagged array, you can do an assignment to an array like you want in your second example:

x[0] = new double[13];

On the second item, because it is a uniform 2d array, you can't assign a 1d array to a row or column, because you must index both the row and column, which gets you down to a single double:

double[,] ServicePoint = new double[10,9];

ServicePoint[0]... // <-- meaningless, a 2d array can't use just one index.

UPDATE:

To clarify based on your question, the reason your #1 had a syntax error is because you had this:

double[][] ServicePoint = new double[10][9];

And you can't specify the second index at the time of construction. The key is that ServicePoint is not a 2d array, but an 1d array (of arrays) and thus since you are creating a 1d array (of arrays), you specify only one index:

double[][] ServicePoint = new double[10][];

Then, when you create each item in the array, each of those are also arrays, so then you can specify their dimensions (which can be different, hence the term jagged array):

ServicePoint[0] = new double[13];
ServicePoint[1] = new double[20];

Hope that helps!

What are the differences between a multidimensional array and an array of arrays in C#?

Array of arrays (jagged arrays) are faster than multi-dimensional arrays and can be used more effectively. Multidimensional arrays have nicer syntax.

If you write some simple code using jagged and multidimensional arrays and then inspect the compiled assembly with an IL disassembler you will see that the storage and retrieval from jagged (or single dimensional) arrays are simple IL instructions while the same operations for multidimensional arrays are method invocations which are always slower.

Consider the following methods:

static void SetElementAt(int[][] array, int i, int j, int value)
{
    array[i][j] = value;
}

static void SetElementAt(int[,] array, int i, int j, int value)
{
    array[i, j] = value;
}

Their IL will be the following:

.method private hidebysig static void  SetElementAt(int32[][] 'array',
                                                    int32 i,
                                                    int32 j,
                                                    int32 'value') cil managed
{
  // Code size       7 (0x7)
  .maxstack  8
  IL_0000:  ldarg.0
  IL_0001:  ldarg.1
  IL_0002:  ldelem.ref
  IL_0003:  ldarg.2
  IL_0004:  ldarg.3
  IL_0005:  stelem.i4
  IL_0006:  ret
} // end of method Program::SetElementAt

.method private hidebysig static void  SetElementAt(int32[0...,0...] 'array',
                                                    int32 i,
                                                    int32 j,
                                                    int32 'value') cil managed
{
  // Code size       10 (0xa)
  .maxstack  8
  IL_0000:  ldarg.0
  IL_0001:  ldarg.1
  IL_0002:  ldarg.2
  IL_0003:  ldarg.3
  IL_0004:  call       instance void int32[0...,0...]::Set(int32,
                                                           int32,
                                                           int32)
  IL_0009:  ret
} // end of method Program::SetElementAt

When using jagged arrays you can easily perform such operations as row swap and row resize. Maybe in some cases usage of multidimensional arrays will be more safe, but even Microsoft FxCop tells that jagged arrays should be used instead of multidimensional when you use it to analyse your projects.

Multidimensional array vs array of objects

You might use an array of objects so I can manipulate them using familiar verb functions; like a lookup. There are likely more "pure" Javascript methods to do some of this but I also tested the lookupfor speed and it is decent in this form.

This is copied from another answer with a more complex example here: Binding an array of objects to their specific form fields for updating/deleting

Note on that one for instance the hasDuplicates function - so you could easily then support that upon your object array - and if you have more than one object array you can re-use the functions on each one.

var myApp = myApp || {};
myApp.arrayObj = {
  indexOf: function(myArray, searchTerm, property) {
    for (var i = 0; i < myArray.length; i++) {
      if (myArray[i][property] === searchTerm) return i;
    }
    return -1;
  },
  indexAllOf: function(myArray, searchTerm, property) {
    var ai = [];
    for (var i = 0; i < myArray.length; i++) {
      if (myArray[i][property] === searchTerm) ai.push(i);
    }
    return ai;
  },
  lookup: function(myArray, searchTerm, property, firstOnly) {
    var found = [];
    var i = myArray.length;
    while (i--) {
      if (myArray[i][property] === searchTerm) {
        found.push(myArray[i]);
        if (firstOnly) break; //if only the first 
      }
    }
    return found;
  },
  lookupAll: function(myArray, searchTerm, property) {
    return this.lookup(myArray, searchTerm, property, false);
  },
  remove: function(myArray, searchTerm, property, firstOnly) {
    for (var i = myArray.length - 1; i >= 0; i--) {
      if (myArray[i][property] === searchTerm) {
        myArray.splice(i, 1);
        if (firstOnly) break; //if only the first term has to be removed
      }
    }
  },
  removeByIndex: function(myArray, index) {
    myArray.splice(index, 1);
  }
};

Performance between multidimensional array or arrays of objects in JavaScript

For the first part of your question regarding the GET request, I imagine the array would be slightly quicker to load, but depending on your data, it could very well be negligible. I'm basing that on the fact that, if you take out the white space, the example data you have for each member of the array is 12 bytes, while the example data for the similar object is 20 bytes. If that were true for your actual data, theoretically there would be only 3/5 of the data to transfer, but unless you're getting a lot of data it's probably not going to make a noticeable difference.

To answer the second part of your question: the performance of any code is going to depend significantly on the details of your specific use case. For most situations, I think the most important point is:

Objects are significantly more readable and user-friendly

That said, when performance/speed is an issue and/or high priority, which it sounds like could be the case for you, there are definitely things to consider. While it relates to writing data instead of reading it, I found this good comparison of the performance of arrays vs objects that brought up some interesting points. In running the tests above multiple times using Chrome 45.0.2454.101 32-bit on Windows 7 64-bit, I found these points to generally be true:

Arrays will always be close to the fastest, if not the fastest
If the length of the object is known/can be hard coded, it's possible to make their performance close to and sometimes better than arrays

In the test linked above, this code using objects ran at 225 ops/sec in one of my tests:

var sum = 0;
for (var x in obj) {
  sum += obj[x].payload;
}

Compared to this code using arrays that ran at 13,620 ops/sec in the same test:

var sum = 0;
for (var x = 0; x < arr.length; ++x) {
  sum += arr[x].payload
}

Important to note, however, is that this code using objects with a hard coded length ran at 14,698 ops/sec in the same test, beating each of the above:

var sum = 0;
for (var x = 0; x < 10000; ++x) {
  sum += obj[x].payload
}

All of that said, it probably depends on your specific use case what will have the best performance, but hopefully this gives you some things to consider.

What's the difference between arrays of arrays and multidimensional arrays?

Take .NET arrays which illustrate this nicely:

C# has a distinction between jagged arrays which are defined in a nested fashion:

int[][] jagged = new int[3][];

Each nested array can have a different length:

jagged[0] = new int[3];
jagged[1] = new int[4];

(And note that one of the nested arrays isn’t initialised at all, i.e. null.)

By contrast, a multidimensional array is defined as follows:

int[,] multidim = new int[3, 4];

Here, it doesn’t make sense to talk of nested arrays, and indeed trying to access multidim[0] would be a compile-time error – you need to access it providing all dimensions, i.e. multidim[0, 1].

Their types are different too, as the declarations above reveal.

Furthermore, their handling is totally different. For instance, you can iterate over the above jagged array with an object of type int[]:

foreach (int[] x in jagged) …

but iterating over a multidimensional array is done with items of type int:

foreach (int x in multidim) …

Conceptually, a jagged array is an array of arrays (… of arrays of arrays … ad infinitum) of T while a multidimensional array is an array of T with a set access pattern (i.e. the index is a tuple).

Performance comparison of array of arrays vs multidimensional arrays

Java and C# allocate memory in much different fashion that C++ does. In fact, in .NET for sure all the arrays of AoA will be close together if they are allocated one after another because memory there is just one continuous chunk without any fragmentation whatsoever.

But it is still true for C++ and still makes sense if you want maximum speed. Although you shouldn't follow that advise every time you want multidimensional array, you should write maintainable code first and then profile it if it is slow, premature optimization is root for all evil in this world.

Multi-dimensional array vs. One-dimensional

There are many advantages in C# to using jagged arrays (array[][]). They actually will often outperform multidimensional arrays.

That being said, I would personally use a multidimensional or jagged array instead of a single dimensional array, as this matches the problem space more closely. Using a one dimensional array is adding complexity to your implementation that does not provide real benefits, especially when compared to a 2D array, as internally, it's still a single block of memory.