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Finding All Combinations of a Multidimention Array with a Max Value in C#

Let's say I have an int[8,6] array which can have the maximum value of 255 per cell and I want to find all combinations of this array.
What is the most efficient way to accomplish this?

For array size N (1D array for simpliciry, 2D case works similar) and maximum value M there are M^N possible combinations. Every combination corresponds to value in range 0..M^N-1, so we can just walk throug this range and get combination for every value. Of course, it is possible for reasonable small values of N and M.
Python-like pseudocode:
int A[N]
P = M**N #math.intpower(M, N)
for i in range(P):
t = i
for k in range(N): #number of cells, number of digits in counter value
A[k] = t % M # value in k-th cells of result for variant number i
t = t // M #integer division
Note that for base M=256 you perhaps don't need to use division - needed values are just bytes of multibyte representation of big number in base 256

prefer high index number than lower one in an array

Assuming that I have these two sorted arrays with 5 cells:
The numbers in the array are between 2 and 14 ( 2 and 14 included and they are integers )
Now, I need to give a rank to each array from [0,100] when the lowest array will be:
[2,2,2,2,2] and the highest will be [14,14,14,14,14]
Now the thing is: the index is important so for example if we take a look at this these arrays:
1) [2,2,2,2,10]
2) [8,8,8,8,9]
So the 1st one is better than the the 2nd and will get an higher score.
And if there's a tie in the index ( from right to left ) for example:
1) [3,4,5,10,13]
2) [3,4,7,10,13]
So index numbers: 3 and 4 are the same, but since 7 is higher than 5. so in that case the 2nd array will have an higher score.
I'm struggling with the math, I mean I want to do it efficient, now I can do something like:
2^array[i] but it won't be efficient, so the main thing I managed to do is
double rank = 0;
for (int i = 0; i < 5; i++)
{
rank += (double)array[i] / 14 + i;
}
because if array[i] can be between 2 and 14, so 1/7 <= array[i]/14 <= 1
so I thought that if I'll add + i each iteration, the next iteration will be greater than all the previous ones, but it's mistake.
I'll be glad for some help in here.

You are essentially describing a base-13 number. Each "digit" (array position) represents one of 13 distinct, ordered values.
You can calculate a ranking by converting the array to a 5 digit, base 13 value:
Subtract 2 from each array element's value to normalize the element value to the range 0..12.
Give each array element a score = (normalized element value) * (13 raised to the array index power). 1)
Add up the scores.
1) Or raised to Array.Length - array index, depending on which side of the array should be the least significant.

Role of subscript operator in arrays

We declare multi-dimension array in C# as
Datatype[,] <arrayname> = new Datatype[size,size];
I was just wondering what's the role of subscript operator[,] here. Can someone explain above syntax how it works exactly?

Datatype[,] identifier;
delclares a two-dimensional array of Datatype. The general syntax is, for n dimensions you put n - 1 commas (,) between the square brackets. For example for a four-dimensional array, put three commas:
Datatype[,,,] identifier;
When you instantiate the array you have to set the size of each dimension, e.g.:
int sizeDimOne = 5, sizeDimTwo = 10, sizeDimThree = 10;
Datatype[,,] identifier = new Datatype[sizeDimOne, sizeDimTwo, sizeDimThree];

As part of a declaration, this part:
[,]
means "2-dimensional array", a rectangular array that will have 2 dimensions. You can call them "width" and "height" or whatever you wish, but 2 there is.
The number of commas denote the number of dimensions, minus 1, meaning that to declare a 3-dimensional array you would use 2 commas:
Datatype[,,] = ...

Object initialization in C# occurs in two step:
1)Create reference to the required type i.e int []num
2)Allocating physical memory of that object type i.e new num[2]
The subscript operator on the left-hand side gives an indication to the CLR that object that is currently being allocated to memory is fully compatible with the type of physical object that is being allocated memory.
For multidimensional array, each comma adds a dimension to array
For 1-D array []
2-D Array [,]
3-D Array[,,]

Fastest way to zero out a 2D array in C#

I have a 2D array that I want to clear and reset to 0 values. I know how to clear a vector (1D array) using Array.Clear() but I don't know the best way to clear a 2D matrix.
double D = new double[10];
Array.Clear(D, 0, D.Length);
How does one clear a 2D N x M array
double D[,] = new double[N,M];
Thank you for any help you may be able to provide.

Array.Clear works with multidimensional arrays, too:
double[,] D = new double[M,N];
Array.Clear(D, 0, D.Length);
Note, there's no need to compute the length yourself, since the Length property returns the total number of elements, regardless of the number of dimensions:
A 32-bit integer that represents the total number of elements in all the dimensions of the Array; zero if there are no elements in the array.

You can use the same method, but you may have to calculate your real length parameter value:
double D[,] = new double[N,M];
Array.Clear(D, 0, M*N);
I would use M*N because it's more readable, and I don't know what Length property returns for 2-dimmentional array.

Just reallocate it.
double D[,] = new double[N,M];
creates a empty 2D array.

Array.BinarySearch() return value

I have the following array:
double[] list = new double[] {0,0,100,100}
Why if I search for 29.6 I get -3?
Array.BinarySearch(list, 29.6)
I expected +1 or -1.
The Array.BinarySearch() documentation for the return parameter says:
The index of the specified value in the specified array, if value is found. If value is not found and value is less than one or more elements in array, a negative number which is the bitwise complement of the index of the first element that is larger than value. If value is not found and value is greater than any of the elements in array, a negative number which is the bitwise complement of (the index of the last element plus 1).
But it does not says too much to me.

If value is not found and value is less than one or more elements in array, a negative number which is the bitwise complement of the index of the first element that is larger than value.
The first element which is larger than 29.6 is 100, which has index of 2.
~2 is -3.

You can use the '~' to take the bitwise complement which will give you the index of the first item larger than the search item.
If the Array does not contain the specified value, the method returns
a negative integer. You can apply the bitwise complement operator (~)
to the negative result (in Visual Basic, Xor the negative result with
-1) to produce an index. If this index is greater than or equal to the size of the array, there are no elements larger than value in the
array. Otherwise, it is the index of the first element that is larger
than value.
From the MSDN
Thus if you had:
var pos = Array.BinarySearch(list, 29.6);
You can check:
if (pos < 0)
{
Console.WriteLine("Not found, the result was {0} which is index {1}", pos, ~pos);
}
Which, in your case, means your -3 would indicate the index 2 is the first item larger than your search target.

Here is your answer:
"a negative number which is the bitwise complement of the index of the first element that is larger than value."
So in your case, your searched value (29.6) is less then 100 which is the 3rd element in your array list, the complement of 3 is -3, which is the answer you got.
Here I extended your example and created another array list (list2) with some different values then I searched same value like you 29.6, now this 29.6 value is smaller then 100 but greater then 25, and in my array list 100 is on position 4 and its complement is -4.
So I get the result -4, if I have searched 20 in my array list I would have get answer -3.
double[] list = new double[] { 0, 0, 100, 100 };
double[] list2 = new double[] { 10, 15, 25, 100 };
int result = Array.BinarySearch(list, 29.6);
int result2 = Array.BinarySearch(list2, 29.6);
Response.Write("Your answer result:" + result.ToString() + "<br/>");
Response.Write("Your answer result2:" + result2.ToString());
My Code result:
Your answer result : -3
Your answer result2: -4
I hope this helps.