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Range of Integers

C#. I would like to compare a random number to a guess.
If the guess is 3 more or 3 less than the random number , the program should show the statement
Console.WriteLine("Almost right");
Can I write like this?
If (randomnumber < guess+3 | randomnumber> guess-3);
Console.Writeln ("Almost right")
I am not using array.
Is there a more efficient way to write the code?

You are on the right track.
When you write code here, you can and should write it as code, read the markdown spec or get accustomed to the editor here at stackoverflow. code looks like:
If (randomnumber < guess+3 | randomnumber> guess-3); Console.Writeln ("Almost right")
You should then write real code because your code is more c# like pseudo code. Correctly you must write:
if (randomnumber < guess+3 || randomnumber> guess-3) {
Console.Writeln ("Almost right");
}
Check the logical operators in C#, its || not |
https://learn.microsoft.com/en-us/dotnet/csharp/language-reference/operators/boolean-logical-operators
Performance wise this is fine you could write a specific method like
bool IsRoughly (x, y) {
return x < y + 3 || y < x + 3;
}
This puts the esence of your logic more into light. Finally you have to think about the corner cases: Is 1 really almost the maximum value of an int? Probably not.

With C# 9 you can do in easy readable way. These are just alternative ways do to the the same thing in bit different way
if (randomnumber is < (guess+3) or randomnumber is > (guess-3))
{
Console.WriteLine("Almost right");
}
Another alternative way is to use
if(Enumerable.Range(guess - 2, guess + 2).Contains(randomnumber))

How to generalize my algorithm to detect if one string is a rotation of another

So I've been going through various problems to review for upcoming interviews and one I encountered is determining whether two strings are rotations of each other. Obviously, I'm hardly the first person to solve this problem. In fact, I did discover that my idea for solving this seems similar to the approach taken in this question.
Full disclosure: I do have a related question on Math SE that's focused on the properties from a more mathematical perspective (although it's worth noting that the way that I tried to formulate the ideas behind this there end up being incorrect for reasons that are explained there).
Here's the idea (and this is similar to the approach taken in the linked question): suppose you have a string abcd and the rotation cdab. Clearly, both cd and ab are substrings of cdab, but if you concatenate them together you get abcd.
So basically, a rotation simply entails moving a substring from the end of the string to the beginning (e.g. we constructed cdab from abcd by moving cd from the end of the string to the beginning of the string).
I came up with an approach that works in a very restricted case (if both of the substrings consist of consecutive letters, like they do in the example there), but it fails otherwise (and I give an example of passing and failing cases and inputs/outputs below the code). I'm trying to figure out if it's possible (or even worthwhile) to try to fix it to work in the general case.
public bool AreRotations(string a, string b)
{
if (a == null)
throw new ArgumentNullException("a");
else if (b == null)
throw new ArgumentNullException("b");
else if (a.Trim().Length == 0)
throw new ArgumentException("a is empty or consists only of whitespace");
else if (b.Trim().Length == 0)
throw new ArgumentException("b is empty or consists only of whitespace");
// Obviously, if the strings are of different lengths, they can't possibly be rotations of each other
if (a.Length != b.Length)
return false;
int[] rotationLengths = new int[a.Length];
/* For rotations of length -2, -2, -2, 2, 2, 2, the distinct rotation lengths are -2, 2
*
* In the example I give below of a non-working input, this contains -16, -23, 16, 23
*
* On the face of it, that would seem like a useful pattern, but it seems like this
* could quickly get out of hand as I discover more edge cases
*/
List<int> distinctRotationLengths = new List<int>();
for (int i = 0; i < a.Length; i++)
{
rotationLengths[i] = a[i] - b[i];
if (i == 0)
distinctRotationLengths.Add(rotationLengths[0]);
else if (rotationLengths[i] != rotationLengths[i - 1])
{
distinctRotationLengths.Add(rotationLengths[i]);
}
}
return distinctRotationLengths.Count == 2;
}
And now for the sample inputs/outputs:
StringIsRotation rot = new StringIsRotation();
// This is the case that doesn't work right - it gives "false" instead of "true"
bool success = rot.AreRotations("acqz", "qzac");
// True
success = rot.AreRotations("abcdef", "cdefab");
// True
success = rot.AreRotations("ablm", "lmab");
// False, but should be true - this is another illustration of the bug
success = rot.AreRotations("baby", "byba");
// True
success = rot.AreRotations("abcdef", "defabc");
//True
success = rot.AreRotations("abcd", "cdab");
// True
success = rot.AreRotations("abc", "cab");
// False
success = rot.AreRotations("abcd", "acbd");
// This is an odd situation - right now it returns "false" but you could
// argue about whether that's correct
success = rot.AreRotations("abcd", "abcd");
Is it possible/worthwhile to salvage this approach and have it still be O(n), or should I just go with one of the approaches described in the post I linked to? (Note that this isn't actually production code or homework, it's purely for my own learning).
Edit: For further clarification based on the comments, there are actually two questions here - first, is this algorithm fixable? Secondly, is it even worth fixing it (or should I just try another approach like one described in the answers or the other question I linked to)? I thought of a few potential fixes but they all involved either inelegant special-case reasoning or making this algorithm O(n^2), both of which would kill the point of the algorithm in the first place.

Let suppose the first string is S and the second is S', clearly if they have different length then we output they are not a rotation of each other. Create a string S''=SS. In fact concatenation of S to itself. Then if S,S' are rotation of each other we find a substring S' in S'' by KMP Algorithm in O(n), otherwise we output they are not a rotation of each other. BTW if you are looking for a fast practical algorithm then instead of KMP use Boyer Moore algorithm.
To address the question more explicit, I'd say that I don't expect an easy algorithm for this special case of string matching problem. So having this background in mind, I don't think an easy modification on your algorithm can work. In fact the field of string matching algorithms is very well developed. If there is a somewhat simpler algorithm than sth like KMP or suffix tree based algorithms, for this special case, then still I think studying those general algorithms can help.

Would something like this work?:
private bool IsRotation(string a, string b)
{
if (a.Length != b.Length) { return false; }
for (int i = 0; i < b.Length; ++i)
{
if (GetCharactersLooped(b, i).SequenceEqual(a))
{
return true;
}
}
return false;
}
private IEnumerable<char> GetCharactersLooped(string data, int startPos)
{
for (int i = startPos; i < data.Length; ++i)
{
yield return data[i];
}
for (int i = 0; i < startPos; ++i)
{
yield return data[i];
}
}
P.S. This will return true for abcd = abcd, since you could consider it a full rotation. If this is not desired, change the start of the loop from 0 to 1 in the first function.

If you're looking just for a method that will check if a string is a rotation of another string, this is a C# implementation of the function you linked (which as far as I know is about the fastest way to solve this particular problem):
bool IsRotation(string a, string b)
{
if (a == null || b == null || a.Length != b.Length)
return false;
return (a + a).Contains(b);
}
If you're asking for feedback on your algorithm, I'm not sure I understand what your algorithm is trying to do. It seems like you are trying to detect a rotation by storing the difference of the char values in the string and seeing if they sum to 0? Or if the list of unique differences contains mirror pairs (pairs (x,y) where x = -y)? Or simply if the number of unique differences is even? Or something else entirely that I am missing from your description?
I'm not sure if what you're doing can be generalized, simply because it depends so heavily on the characters within the words that it may not adequately check for the order in which they are presented. And even if you could, it would be a scholarly exercise only, as the above method will be far faster and more efficient than your method could ever be.

Fermat primality test

I have tried to write a code for Fermat primality test, but apparently failed.
So if I understood well: if p is prime then ((a^p)-a)%p=0 where p%a!=0.
My code seems to be OK, therefore most likely I misunderstood the basics. What am I missing here?
private bool IsPrime(int candidate)
{
//checking if candidate = 0 || 1 || 2
int a = candidate + 1; //candidate can't be divisor of candidate+1
if ((Math.Pow(a, candidate) - a) % candidate == 0) return true;
return false;
}

Reading the wikipedia article on the Fermat primality test, You must choose an a that is less than the candidate you are testing, not more.
Furthermore, as MattW commented, testing only a single a won't give you a conclusive answer as to whether the candidate is prime. You must test many possible as before you can decide that a number is probably prime. And even then, some numbers may appear to be prime but actually be composite.

Your basic algorithm is correct, though you will have to use a larger data type than int if you want to do this for non-trivial numbers.
You should not implement the modular exponentiation in the way that you did, because the intermediate result is huge. Here is the square-and-multiply algorithm for modular exponentiation:
function powerMod(b, e, m)
x := 1
while e > 0
if e%2 == 1
x, e := (x*b)%m, e-1
else b, e := (b*b)%m, e//2
return x
As an example, 437^13 (mod 1741) = 819. If you use the algorithm shown above, no intermediate result will be greater than 1740 * 1740 = 3027600. But if you perform the exponentiation first, the intermediate result of 437^13 is 21196232792890476235164446315006597, which you probably want to avoid.
Even with all of that, the Fermat test is imperfect. There are some composite numbers, the Carmichael numbers, that will always report prime no matter what witness you choose. Look for the Miller-Rabin test if you want something that will work better. I modestly recommend this essay on Programming with Prime Numbers at my blog.

You are dealing with very large numbers, and trying to store them in doubles, which is only 64 bits.
The double will do the best it can to hold your number, but you are going to loose some accuracy.
An alternative approach:
Remember that the mod operator can be applied multiple times, and still give the same result.
So, to avoid getting massive numbers you could apply the mod operator during the calculation of your power.
Something like:
private bool IsPrime(int candidate)
{
//checking if candidate = 0 || 1 || 2
int a = candidate - 1; //candidate can't be divisor of candidate - 1
int result = 1;
for(int i = 0; i < candidate; i++)
{
result = result * a;
//Notice that without the following line,
//this method is essentially the same as your own.
//All this line does is keeps the numbers small and manageable.
result = result % candidate;
}
result -= a;
return result == 0;
}

Off By One errors and Mutation Testing

In the process of writing an "Off By One" mutation tester for my favourite mutation testing framework (NinjaTurtles), I wrote the following code to provide an opportunity to check the correctness of my implementation:
public int SumTo(int max)
{
int sum = 0;
for (var i = 1; i <= max; i++)
{
sum += i;
}
return sum;
}
now this seems simple enough, and it didn't strike me that there would be a problem trying to mutate all the literal integer constants in the IL. After all, there are only 3 (the 0, the 1, and the ++).
WRONG!
It became very obvious on the first run that it was never going to work in this particular instance. Why? Because changing the code to
public int SumTo(int max)
{
int sum = 0;
for (var i = 0; i <= max; i++)
{
sum += i;
}
return sum;
}
only adds 0 (zero) to the sum, and this obviously has no effect. Different story if it was the multiple set, but in this instance it was not.
Now there's a fairly easy algorithm for working out the sum of integers
sum = max * (max + 1) / 2;
which I could have fail the mutations easily, since adding or subtracting 1 from either of the constants there will result in an error. (given that max >= 0)
So, problem solved for this particular case. Although it did not do what I wanted for the test of the mutation, which was to check what would happen when I lost the ++ - effectively an infinite loop. But that's another problem.
So - My Question: Are there any trivial or non-trivial cases where a loop starting from 0 or 1 may result in a "mutation off by one" test failure that cannot be refactored (code under test or test) in a similar way? (examples please)
Note: Mutation tests fail when the test suite passes after a mutation has been applied.
Update: an example of something less trivial, but something that could still have the test refactored so that it failed would be the following
public int SumArray(int[] array)
{
int sum = 0;
for (var i = 0; i < array.Length; i++)
{
sum += array[i];
}
return sum;
}
Mutation testing against this code would fail when changing the var i=0 to var i=1 if the test input you gave it was new[] {0,1,2,3,4,5,6,7,8,9}. However change the test input to new[] {9,8,7,6,5,4,3,2,1,0}, and the mutation testing will fail. So a successful refactor proves the testing.

I think with this particular method, there are two choices. You either admit that it's not suitable for mutation testing because of this mathematical anomaly, or you try to write it in a way that makes it safe for mutation testing, either by refactoring to the form you give, or some other way (possibly recursive?).
Your question really boils down to this: is there a real life situation where we care about whether the element 0 is included in or excluded from the operation of a loop, and for which we cannot write a test around that specific aspect? My instinct is to say no.
Your trivial example may be an example of lack of what I referred to as test-drivenness in my blog, writing about NinjaTurtles. Meaning in the case that you have not refactored this method as far as you should.

One natural case of "mutation test failure" is an algorithm for matrix transposition. To make it more suitable for a single for-loop, add some constraints to this task: let the matrix be non-square and require transposition to be in-place. These constraints make one-dimensional array most suitable place to store the matrix and a for-loop (starting, usually, from index '1') may be used to process it. If you start it from index '0', nothing changes, because top-left element of the matrix always transposes to itself.
For an example of such code, see answer to other question (not in C#, sorry).
Here "mutation off by one" test fails, refactoring the test does not change it. I don't know if the code itself may be refactored to avoid this. In theory it may be possible, but should be too difficult.
The code snippet I referenced earlier is not a perfect example. It still may be refactored if the for loop is substituted by two nested loops (as if for rows and columns) and then these rows and columns are recalculated back to one-dimensional index. Still it gives an idea how to make some algorithm, which cannot be refactored (though not very meaningful).
Iterate through an array of positive integers in the order of increasing indexes, for each index compute its pair as i + i % a[i], and if it's not outside the bounds, swap these elements:
for (var i = 1; i < a.Length; i++)
{
var j = i + i % a[i];
if (j < a.Length)
Swap(a[i], a[j]);
}
Here again a[0] is "unmovable", refactoring the test does not change this, and refactoring the code itself is practically impossible.
One more "meaningful" example. Let's implement an implicit Binary Heap. It is usually placed to some array, starting from index '1' (this simplifies many Binary Heap computations, compared to starting from index '0'). Now implement a copy method for this heap. "Off-by-one" problem in this copy method is undetectable because index zero is unused and C# zero-initializes all arrays. This is similar to OP's array summation, but cannot be refactored.
Strictly speaking, you can refactor the whole class and start everything from '0'. But changing only 'copy' method or the test does not prevent "mutation off by one" test failure. Binary Heap class may be treated just as a motivation to copy an array with unused first element.
int[] dst = new int[src.Length];
for (var i = 1; i < src.Length; i++)
{
dst[i] = src[i];
}

Yes, there are many, assuming I have understood your question.
One similar to your case is:
public int MultiplyTo(int max)
{
int product = 1;
for (var i = 1; i <= max; i++)
{
product *= i;
}
return product;
}
Here, if it starts from 0, the result will be 0, but if it starts from 1 the result should be correct. (Although it won't tell the difference between 1 and 2!).

Not quite sure what you are looking for exactly, but it seems to me that if you change/mutate the initial value of sum from 0 to 1, you should fail the test:
public int SumTo(int max)
{
int sum = 1; // Now we are off-by-one from the beginning!
for (var i = 0; i <= max; i++)
{
sum += i;
}
return sum;
}
Update based on comments:
The loop will only not fail after mutation when the loop invariant is violated in the processing of index 0 (or in the absence of it). Most such special cases can be refactored out of the loop, but consider a summation of 1/x:
for (var i = 1; i <= max; i++) {
sum += 1/i;
}
This works fine, but if you mutate the initial bundary from 1 to 0, the test will fail as 1/0 is invalid operation.

How to prevent creating intermediate objects in cascading operators?

I use a custom Matrix class in my application, and I frequently add multiple matrices:
Matrix result = a + b + c + d; // a, b, c and d are also Matrices
However, this creates an intermediate matrix for each addition operation. Since this is simple addition, it is possible to avoid the intermediate objects and create the result by adding the elements of all 4 matrices at once. How can I accomplish this?
NOTE: I know I can define multiple functions like Add3Matrices(a, b, c), Add4Matrices(a, b, c, d), etc. but I want to keep the elegancy of result = a + b + c + d.

You could limit yourself to a single small intermediate by using lazy evaluation. Something like
public class LazyMatrix
{
public static implicit operator Matrix(LazyMatrix l)
{
Matrix m = new Matrix();
foreach (Matrix x in l.Pending)
{
for (int i = 0; i < 2; ++i)
for (int j = 0; j < 2; ++j)
m.Contents[i, j] += x.Contents[i, j];
}
return m;
}
public List<Matrix> Pending = new List<Matrix>();
}
public class Matrix
{
public int[,] Contents = { { 0, 0 }, { 0, 0 } };
public static LazyMatrix operator+(Matrix a, Matrix b)
{
LazyMatrix l = new LazyMatrix();
l.Pending.Add(a);
l.Pending.Add(b);
return l;
}
public static LazyMatrix operator+(Matrix a, LazyMatrix b)
{
b.Pending.Add(a);
return b;
}
}
class Program
{
static void Main(string[] args)
{
Matrix a = new Matrix();
Matrix b = new Matrix();
Matrix c = new Matrix();
Matrix d = new Matrix();
a.Contents[0, 0] = 1;
b.Contents[1, 0] = 4;
c.Contents[0, 1] = 9;
d.Contents[1, 1] = 16;
Matrix m = a + b + c + d;
for (int i = 0; i < 2; ++i)
{
for (int j = 0; j < 2; ++j)
{
System.Console.Write(m.Contents[i, j]);
System.Console.Write(" ");
}
System.Console.WriteLine();
}
System.Console.ReadLine();
}
}

Something that would at least avoid the pain of
Matrix Add3Matrices(a,b,c) //and so on
would be
Matrix AddMatrices(Matrix[] matrices)

In C++ it is possible to use Template Metaprograms and also here, using templates to do exactly this. However, the template programing is non-trivial. I don't know if a similar technique is available in C#, quite possibly not.
This technique, in c++ does exactly what you want. The disadvantage is that if something is not quite right then the compiler error messages tend to run to several pages and are almost impossible to decipher.
Without such techniques I suspect you are limited to functions such as Add3Matrices.
But for C# this link might be exactly what you need: Efficient Matrix Programming in C# although it seems to work slightly differently to C++ template expressions.

You can't avoid creating intermediate objects.
However, you can use expression templates as described here to minimise them and do fancy lazy evaluation of the templates.
At the simplest level, the expression template could be an object that stores references to several matrices and calls an appropriate function like Add3Matrices() upon assignment. At the most advanced level, the expression templates will do things like calculate the minimum amount of information in a lazy fashion upon request.

This is not the cleanest solution, but if you know the evaluation order, you could do something like this:
result = MatrixAdditionCollector() << a + b + c + d
(or the same thing with different names). The MatrixCollector then implements + as +=, that is, starts with a 0-matrix of undefined size, takes a size once the first + is evaluated and adds everything together (or, copies the first matrix). This reduces the amount of intermediate objects to 1 (or even 0, if you implement assignment in a good way, because the MatrixCollector might be/contain the result immediately.)
I am not entirely sure if this is ugly as hell or one of the nicer hacks one might do. A certain advantage is that it is kind of obvious what's happening.

Might I suggest a MatrixAdder that behaves much like a StringBuilder. You add matrixes to the MatrixAdder and then call a ToMatrix() method that would do the additions for you in a lazy implementation. This would get you the result you want, could be expandable to any sort of LazyEvaluation, but also wouldn't introduce any clever implementations that could confuse other maintainers of the code.

I thought that you could just make the desired add-in-place behavior explicit:
Matrix result = a;
result += b;
result += c;
result += d;
But as pointed out by Doug in the Comments on this post, this code is treated by the compiler as if I had written:
Matrix result = a;
result = result + b;
result = result + c;
result = result + d;
so temporaries are still created.
I'd just delete this answer, but it seems others might have the same misconception, so consider this a counter example.

Bjarne Stroustrup has a short paper called Abstraction, libraries, and efficiency in C++ where he mentions techniques used to achieve what you're looking for. Specifically, he mentions the library Blitz++, a library for scientific calculations that also has efficient operations for matrices, along with some other interesting libraries. Also, I recommend reading a conversation with Bjarne Stroustrup on artima.com on that subject.

It is not possible, using operators.

My first solution would be something along this lines (to add in the Matrix class if possible) :
static Matrix AddMatrices(Matrix[] lMatrices) // or List<Matrix> lMatrices
{
// Check consistency of matrices
Matrix m = new Matrix(n, p);
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
foreach (Maxtrix mat in lMatrices)
m[i, j] += mat[i, j];
return m;
}
I'd had it in the Matrix class because you can rely on the private methods and properties that could be usefull for your function in case the implementation of the matrix change (linked list of non empty nodes instead of a big double array, for example).
Of course, you would loose the elegance of result = a + b + c + d. But you would have something along the lines of result = Matrix.AddMatrices(new Matrix[] { a, b, c, d });.

There are several ways to implement lazy evaluation to achieve that. But its important to remember that not always your compiler will be able to get the best code of all of them.
I already made implementations that worked great in GCC and even superceeded the performance of the traditional several For unreadable code because they lead the compiler to observe that there were no aliases between the data segments (somethign hard to grasp with arrays coming of nowhere). But some of those were a complete fail at MSVC and vice versa on other implementations. Unfortunately those are too long to post here (don't think several thousands lines of code fit here).
A very complex library with great embedded knowledge int he area is Blitz++ library for scientific computation.