Say I have
static System::Numerics::BigInteger MinimoNumero; int16_t Uno = 1;
static System::Numerics::BigInteger MaximoNumero;
static const std::string MaximoNumeroString = "91389681247993671255432112333333333333333333333333333333333333333333333333333333333333333333333333333333";
MaximoNumero = System::Numerics::BigInteger::Parse(marshal_as<String^>(MaximoNumeroString));
MinimoNumero = System::Numerics::BigInteger::Parse("1");
How can I SUM 1 to MaximoNumero so I want a result as BigInteger as 91389681247993671255432112333333333333333333333333333333333333333333333333333333333333333333333333333334
If I use
System::Numerics::BigInteger NUM = MinimoNumero + MaximoNumero;
then I got error "more than one operator "+" matches these operands.."
You can't (generally) use the plain arithmetic operators on the BigInteger type. Instead, call the relevant member function(s) of the BigInteger type – in this case, the Add function:
System::Numerics::BigInteger NUM = System::Numerics::BigInteger::Add(MinimoNumero, MaximoNumero);
Related
Very new to C#, so this could be a silly question.
I am working with alot of UInt64's. These are expressed as hex right? If we look at its binary representation, can we return such an array that if we apply the 'or' operation to, we will arrive back at the original UInt64?
For example, let's say
x = 1011
Then, I am looking for an efficient way to arrive at,
f(x) = {1000, 0010, 0001}
Where these numbers are in hex, rather than binary. Sorry, I am new to hex too.
I have a method already, but it feels inefficient. I first convert to a binary string, and loop over that string to find each '1'. I then add the corresponding binary number to an array.
Any thoughts?
Here is a better example. I have a hexadecimal number x, in the form of,
UInt64 x = 0x00000000000000FF
Where the binary representation of x is
0000000000000000000000000000000000000000000000000000000011111111
I wish to find an array consisting of hexadecimal numbers (UInt64??) such that the or operation applied to all members of that array would result in x again. For example,
f(x) = {0x0000000000000080, // 00000....10000000
0x0000000000000040, // 00000....01000000
0x0000000000000020, // 00000....00100000
0x0000000000000010, // 00000....00010000
0x0000000000000008, // 00000....00001000
0x0000000000000004, // 00000....00000100
0x0000000000000002, // 00000....00000010
0x0000000000000001 // 00000....00000001
}
I think the question comes down to finding an efficient way to find the index of the '1's in the binary expansion...
public static UInt64[] findOccupiedSquares(UInt64 pieces){
UInt64[] toReturn = new UInt64[BitOperations.PopCount(pieces)];
if (BitOperations.PopCount(pieces) == 1){
toReturn[0] = pieces;
}
else{
int i = 0;
int index = 0;
while (pieces != 0){
i += 1;
pieces = pieces >> 1;
if (BitOperations.TrailingZeroCount(pieces) == 0){ // One
int rank = (int)(i / 8);
int file = i - (rank * 8);
toReturn[index] = LUTable.MaskRank[rank] & LUTable.MaskFile[file];
index += 1;
}
}
}
return toReturn;
}
Your question still confuses me as you seem to be mixing the concepts of numbers and number representations. i.e. There is an integer and then there is a hexadecimal representation of that integer.
You can very simply break any integer into its base-2 components.
ulong input = 16094009876; // example input
ulong x = 1;
var bits = new List<ulong>();
do
{
if ((input & x) == x)
{
bits.Add(x);
}
x <<= 1;
} while (x != 0);
bits is now a list of integers which each represent one of the binary 1 bits within the input. This can be verified by adding (or ORing - same thing) all the values. So this expression is true:
bits.Aggregate((a, b) => a | b) == input
If you want hexadecimal representations of those integers in the list, you can simply use ToString():
var hexBits = bits.Select(b => b.ToString("X16"));
If you want the binary representations of the integers, you can use Convert:
var binaryBits = bits.Select(b => Convert.ToString((long)b, 2).PadLeft(64, '0'));
Is this possible? Get_type_name is a string. Can't I have an int array and use the name to index in? I get index expression type of illegal.
Obj n1;
int number[100];
n1 = new();
number[n1.get_type_name] = 1;
Long day. Should have declared int number[string]
I've searched for an hour for the methods doing numerical integration. I'm new to Rcpp and rewriting my old programs now. What I have done in R was:
x=smpl.x(n,theta.true)
joint=function(theta){# the joint dist for
#all random variable
d=c()
for(i in 1:n){
d[i]=den(x[i],theta)
}
return(prod(d)*dbeta(theta,a,b)) }
joint.vec=Vectorize(joint)##vectorize the function, as required when
##using integrate()
margin=integrate(joint.vec,0,1)$value # the
##normalizeing constant at the donominator
area=integrate(joint.vec,0,theta.true)$value # the values at the
## numeritor
The integrate() function in R will be slow, and since I am doing the integration for a posterior distribution of a sample of size n, the value of the integration will be huge with large error.
I am trying to rewrite my code with the help of Rcpp, but I don't know how to deal with the integrate. Should I include a c++ h file? Or any suggestions?
You can code your function in C and call it, for instance, via the sourceCpp function and then integrate it in R. In alternative, you can call the integrate function of R within your C code by using the Function macro of Rcpp. See Dirk's book (Seamless R and C++ Integration with Rcpp) on page 56 for an example of how to call R functions from C. Another alternative (which I believe is the best for most cases) is to integrate your function written in C , directly in C, using the RcppGSL package.
As about the huge normalizing constant, sometimes it is better to scale the function at the mode before integrating it (you can find modes with, e.g., nlminb, optim, etc.). Then, you integrate the rescaled function and to recover the original nroming constant multiply the resulting normalizing constant by the rescaling factor. Hope this may help!
after reading your #utobi advice, I felt programming by my own maybe easier. I simply use Simpson formula to approximate the integral:
// [[Rcpp::export]]
double den_cpp (double x, double theta){
return(2*x/theta*(x<=theta)+2*(1-x)/(1-theta)*(theta<x));
}
// [[Rcpp::export]]
double joint_cpp ( double theta,int n,NumericVector x, double a, double b){
double val = 1.0;
NumericVector d(n);
for (int i = 0; i < n; i++){
double tmp = den_cpp(x[i],theta);
val = val*tmp;
}
val=val*R::dbeta(theta,a,b,0);
return(val);
}
// [[Rcpp::export]]
List Cov_rate_raw ( double theta_true, int n, double a, double b,NumericVector x){
//This function is used to test, not used in the fanal one
int steps = 1000;
double s = 0;
double start = 1.0e-4;
std::cout<<start<<" ";
double end = 1-start;
std::cout<<end<<" ";
double h = (end-start)/steps;
std::cout<<"1st h ="<<h<<" ";
double area = 0;
double margin = 0;
for (int i = 0; i < steps ; i++){
double at_x = start+h*i;
double f_val = (joint_cpp(at_x,n,x,a,b)+4*joint_cpp(at_x+h/2,n,x,a,b)+joint_cpp(at_x+h,n,x,a,b))/6;
s = s + f_val;
}
margin = h*s;
s=0;
h=(theta_true-start)/steps;
std::cout<<"2nd h ="<<h<<" ";
for (int i = 0; i < steps ; i++){
double at_x = start+h*i;
double f_val = (joint_cpp(at_x,n,x,a,b)+4*joint_cpp(at_x+h/2,n,x,a,b)+joint_cpp(at_x+h,n,x,a,b))/6;
s = s + f_val;
}
area = h * s;
double r = area/margin;
int cover = (r>=0.025)&&(r<=0.975);
List ret;
ret["s"] = s;
ret["margin"] = margin;
ret["area"] = area;
ret["ratio"] = r;
ret["if_cover"] = cover;
return(ret);
}
I'm not that good at c++, so the two for loops like kind of silly.
It generally works, but there are still several potential problems:
I don't really know how to choose the steps, or how many sub intervals do I need to approximate the integrals. I've taken numerical analysis when I was an undergraduate, I think maybe I need to check my book about the expression of the error term, to decide the step length.
I compared my results with those from R. the integrate() function in R can take care of the integral over the interval [0,1]. That helps me because my function is undefined at 0 or 1, which takes infinite value. In my C++ code, I can only make my interval from [1e-4, 1-1e-4]. I tried different values like 1e-7, 1e-10, however, 1e-4 was the one most close to R's results....What should I do with it?
I've been working through this exercise, and my output is not what I expect.
(Check substrings) You can check whether a string is a substring of another string
by using the indexOf method in the String class. Write your own method for
this function. Write a program that prompts the user to enter two strings, and
checks whether the first string is a substring of the second.
** My code compromises with the problem's specifications in two ways: it can only display matching substrings to 3 letters, and it cannot work on string literals with less than 4 letters. I mistakenly began writing the program without using the suggested method, indexOf. My program's objective (although it shouldn't entirely deviate from the assignment's objective) is to design a program that determines whether two strings share at least three consecutive letters.
The program's primary error is that it generates numbers instead of char characters. I've run through several, unsuccessful ideas to discover what the logical error is. I first tried to idenfity whether the char characters (which, from my understanding, are underwritten in unicode) were converted to integers, considering that the outputted numbers are also three letters long. Without consulting a reference, I know this isn't true. A comparison between java and javac outputted permutation of 312, and a comparison between abab and ababbab ouputted combinations of 219. j should be > b. My next thought was that the ouputs were indexes of the arrays I used. Once again, this isn't true. A comparison between java and javac would ouput 0, if my reasoning were true.
public class Substring {
public static char [] array;
public static char [] array2;
public static void main (String[]args){
java.util.Scanner input = new java.util.Scanner (System.in);
System.out.println("Enter your two strings here, the longer one preceding the shorter one");
String container1 = input.next();
String container2 = input.next();
char [] placeholder = container1.toCharArray();
char [] placeholder2 = container2.toCharArray();
array = placeholder;
array2 = placeholder2;
for (int i = 0; i < placeholder2.length; i++){
for (int j = 0; j < placeholder.length; j ++){
if (array[j] == array2[i]) matcher(j,i);
}
}
}
public static void matcher(int higher, int lower){
if ((higher < array.length - 2) && (lower < array2.length - 2))
if (( array[higher+1] == array2[lower+1]) && (array[higher+2] == array2[lower+2]))
System.out.println(array[higher] + array[higher+1] + array[higher+2] );
}
}
The + operator promotes shorts, chars, and bytes operands to ints, so
array[higher] + array[higher+1] + array[higher+2]
has type int, not type char which means that
System.out.println(...)
binds to
System.out.println(int)
which displays its argument as a decimal number, instead of binding to
System.out.println(char)
which outputs the given character using the PrintStream's encoding.
Thinking about this question on testing string rotation, I wondered: Is there was such thing as a circular/cyclic hash function? E.g.
h(abcdef) = h(bcdefa) = h(cdefab) etc
Uses for this include scalable algorithms which can check n strings against each other to see where some are rotations of others.
I suppose the essence of the hash is to extract information which is order-specific but not position-specific. Maybe something that finds a deterministic 'first position', rotates to it and hashes the result?
It all seems plausible, but slightly beyond my grasp at the moment; it must be out there already...
I'd go along with your deterministic "first position" - find the "least" character; if it appears twice, use the next character as the tie breaker (etc). You can then rotate to a "canonical" position, and hash that in a normal way. If the tie breakers run for the entire course of the string, then you've got a string which is a rotation of itself (if you see what I mean) and it doesn't matter which you pick to be "first".
So:
"abcdef" => hash("abcdef")
"defabc" => hash("abcdef")
"abaac" => hash("aacab") (tie-break between aa, ac and ab)
"cabcab" => hash("abcabc") (it doesn't matter which "a" comes first!)
Update: As Jon pointed out, the first approach doesn't handle strings with repetition very well. Problems arise as duplicate pairs of letters are encountered and the resulting XOR is 0. Here is a modification that I believe fixes the the original algorithm. It uses Euclid-Fermat sequences to generate pairwise coprime integers for each additional occurrence of a character in the string. The result is that the XOR for duplicate pairs is non-zero.
I've also cleaned up the algorithm slightly. Note that the array containing the EF sequences only supports characters in the range 0x00 to 0xFF. This was just a cheap way to demonstrate the algorithm. Also, the algorithm still has runtime O(n) where n is the length of the string.
static int Hash(string s)
{
int H = 0;
if (s.Length > 0)
{
//any arbitrary coprime numbers
int a = s.Length, b = s.Length + 1;
//an array of Euclid-Fermat sequences to generate additional coprimes for each duplicate character occurrence
int[] c = new int[0xFF];
for (int i = 1; i < c.Length; i++)
{
c[i] = i + 1;
}
Func<char, int> NextCoprime = (x) => c[x] = (c[x] - x) * c[x] + x;
Func<char, char, int> NextPair = (x, y) => a * NextCoprime(x) * x.GetHashCode() + b * y.GetHashCode();
//for i=0 we need to wrap around to the last character
H = NextPair(s[s.Length - 1], s[0]);
//for i=1...n we use the previous character
for (int i = 1; i < s.Length; i++)
{
H ^= NextPair(s[i - 1], s[i]);
}
}
return H;
}
static void Main(string[] args)
{
Console.WriteLine("{0:X8}", Hash("abcdef"));
Console.WriteLine("{0:X8}", Hash("bcdefa"));
Console.WriteLine("{0:X8}", Hash("cdefab"));
Console.WriteLine("{0:X8}", Hash("cdfeab"));
Console.WriteLine("{0:X8}", Hash("a0a0"));
Console.WriteLine("{0:X8}", Hash("1010"));
Console.WriteLine("{0:X8}", Hash("0abc0def0ghi"));
Console.WriteLine("{0:X8}", Hash("0def0abc0ghi"));
}
The output is now:
7F7D7F7F
7F7D7F7F
7F7D7F7F
7F417F4F
C796C7F0
E090E0F0
A909BB71
A959BB71
First Version (which isn't complete): Use XOR which is commutative (order doesn't matter) and another little trick involving coprimes to combine ordered hashes of pairs of letters in the string. Here is an example in C#:
static int Hash(char[] s)
{
//any arbitrary coprime numbers
const int a = 7, b = 13;
int H = 0;
if (s.Length > 0)
{
//for i=0 we need to wrap around to the last character
H ^= (a * s[s.Length - 1].GetHashCode()) + (b * s[0].GetHashCode());
//for i=1...n we use the previous character
for (int i = 1; i < s.Length; i++)
{
H ^= (a * s[i - 1].GetHashCode()) + (b * s[i].GetHashCode());
}
}
return H;
}
static void Main(string[] args)
{
Console.WriteLine(Hash("abcdef".ToCharArray()));
Console.WriteLine(Hash("bcdefa".ToCharArray()));
Console.WriteLine(Hash("cdefab".ToCharArray()));
Console.WriteLine(Hash("cdfeab".ToCharArray()));
}
The output is:
4587590
4587590
4587590
7077996
You could find a deterministic first position by always starting at the position with the "lowest" (in terms of alphabetical ordering) substring. So in your case, you'd always start at "a". If there were multiple "a"s, you'd have to take two characters into account etc.
I am sure that you could find a function that can generate the same hash regardless of character position in the input, however, how will you ensure that h(abc) != h(efg) for every conceivable input? (Collisions will occur for all hash algorithms, so I mean, how do you minimize this risk.)
You'd need some additional checks even after generating the hash to ensure that the strings contain the same characters.
Here's an implementation using Linq
public string ToCanonicalOrder(string input)
{
char first = input.OrderBy(x => x).First();
string doubledForRotation = input + input;
string canonicalOrder
= (-1)
.GenerateFrom(x => doubledForRotation.IndexOf(first, x + 1))
.Skip(1) // the -1
.TakeWhile(x => x < input.Length)
.Select(x => doubledForRotation.Substring(x, input.Length))
.OrderBy(x => x)
.First();
return canonicalOrder;
}
assuming generic generator extension method:
public static class TExtensions
{
public static IEnumerable<T> GenerateFrom<T>(this T initial, Func<T, T> next)
{
var current = initial;
while (true)
{
yield return current;
current = next(current);
}
}
}
sample usage:
var sequences = new[]
{
"abcdef", "bcdefa", "cdefab",
"defabc", "efabcd", "fabcde",
"abaac", "cabcab"
};
foreach (string sequence in sequences)
{
Console.WriteLine(ToCanonicalOrder(sequence));
}
output:
abcdef
abcdef
abcdef
abcdef
abcdef
abcdef
aacab
abcabc
then call .GetHashCode() on the result if necessary.
sample usage if ToCanonicalOrder() is converted to an extension method:
sequence.ToCanonicalOrder().GetHashCode();
One possibility is to combine the hash functions of all circular shifts of your input into one meta-hash which does not depend on the order of the inputs.
More formally, consider
for(int i=0; i<string.length; i++) {
result^=string.rotatedBy(i).hashCode();
}
Where you could replace the ^= with any other commutative operation.
More examply, consider the input
"abcd"
to get the hash we take
hash("abcd") ^ hash("dabc") ^ hash("cdab") ^ hash("bcda").
As we can see, taking the hash of any of these permutations will only change the order that you are evaluating the XOR, which won't change its value.
I did something like this for a project in college. There were 2 approaches I used to try to optimize a Travelling-Salesman problem. I think if the elements are NOT guaranteed to be unique, the second solution would take a bit more checking, but the first one should work.
If you can represent the string as a matrix of associations so abcdef would look like
a b c d e f
a x
b x
c x
d x
e x
f x
But so would any combination of those associations. It would be trivial to compare those matrices.
Another quicker trick would be to rotate the string so that the "first" letter is first. Then if you have the same starting point, the same strings will be identical.
Here is some Ruby code:
def normalize_string(string)
myarray = string.split(//) # split into an array
index = myarray.index(myarray.min) # find the index of the minimum element
index.times do
myarray.push(myarray.shift) # move stuff from the front to the back
end
return myarray.join
end
p normalize_string('abcdef').eql?normalize_string('defabc') # should return true
Maybe use a rolling hash for each offset (RabinKarp like) and return the minimum hash value? There could be collisions though.