Develop Reference

Reducing a BigInteger value in C#

I'm somewhat new to working with BigIntegers and have tried some stuff to get this system working, but feel a little stuck at the moment and would really appreciate a nudge in the right direction or a solution.
I'm currently working on a system which reduces BigInteger values down to a more readable form, and this is working fine with my current implementation, but I would like to further expand on it to get decimals implemented.
To better give a picture of what I'm attempting, I'll break it down.
In this context, we have a method which is taking a BigInteger, and returning it as a string:
public static string ShortenBigInt (BigInteger moneyValue)
With this in mind, when a number such as 10,000 is passed to this method, 10k will be returned. Same for 1,000,000 which will return 1M.
This is done by doing:
for(int i = 0; i < prefixes.Length; i++)
{
if(!(moneyValue >= BigInteger.Pow(10, 3*i)))
{
moneyValue = moneyValue / BigInteger.Pow(10, 3*(i-1));
return moneyValue + prefixes[i-1];
}
}
This system is working by grabbing a string from an array of prefixes and reducing numbers down to their simplest forms and combining the two and returning it when inside that prefix range.
So with that context, the question I have is:
How might I go about returning this in the same way, where passing 100,000 would return 100k, but also doing something like 1,111,111 would return 1.11M?
Currently, passing 1,111,111M returns 1M, but I would like that additional .11 tagged on. No more than 2 decimals.
My original thought was to convert the big integer into a string, then chunk out the first few characters into a new string and parse a decimal in there, but since prefixes don't change until values reach their 1000th mark, it's harder to tell when to place the decimal place.
My next thought was using BigInteger.Log to reduce the value down into a decimal friendly number and do a simple division to get the value in its decimal form, but doing this didn't seem to work with my implementation.
This system should work for the following prefixes, dynamically:
k, M, B, T, qd, Qn, sx, Sp,
O, N, de, Ud, DD, tdD, qdD, QnD,
sxD, SpD, OcD, NvD, Vgn, UVg, DVg,
TVg, qtV, QnV, SeV, SPG, OVG, NVG,
TGN, UTG, DTG, tsTG, qtTG, QnTG, ssTG,
SpTG, OcTG, NoTG, QdDR, uQDR, dQDR, tQDR,
qdQDR, QnQDR, sxQDR, SpQDR, OQDDr, NQDDr,
qQGNT, uQGNT, dQGNT, tQGNT, qdQGNT, QnQGNT,
sxQGNT, SpQGNT, OQQGNT, NQQGNT, SXGNTL
Would anyone happen to know how to do something like this? Any language is fine, C# is preferable, but I'm all good with translating. Thank you in advance!

formatting it manually could work a bit like this:
(prefixes as a string which is an char[])
public static string ShortenBigInt(BigInteger moneyValue)
{
string prefixes = " kMGTP";
double m2 = (double)moneyValue;
for (int i = 1; i < prefixes.Length; i++)
{
var step = Math.Pow(10, 3 * i);
if (m2 / step < 1000)
{
return String.Format("{0:F2}", (m2/step)) + prefixes[i];
}
}
return "err";
}

Although Falco's answer does work, it doesn't work for what was requested. This was the solution I was looking for and received some help from a friend on it. This solution will go until there are no more prefixes left in your string array of prefixes. If you do run out of bounds, the exception will be thrown and handled by returning "Infinity".
This solution is better due to the fact there is no crunch down to doubles/decimals within this process. This solution does not have a number cap, only limit is the amount of prefixes you make/provide.
public static string ShortenBigInt(BigInteger moneyValue)
{
if (moneyValue < 1000)
return "" + moneyValue;
try
{
string moneyAsString = moneyValue.ToString();
string prefix = prefixes[(moneyAsString.Length - 1) / 3];
BigInteger chopAmmount = (moneyAsString.Length - 1) % 3 + 1;
int insertPoint = (int)chopAmmount;
chopAmmount += 2;
moneyAsString = moneyAsString.Remove(Math.Min(moneyAsString.Length - 1, (int)chopAmmount));
moneyAsString = moneyAsString.Insert(insertPoint, ".");
return moneyAsString + " " + prefix;
}
catch (Exception exceptionToBeThrown)
{
return "Infinity";
}
}

Dice Sorensen Distance error calculating Bigrams without using Intersect method

I have been programming an object to calculate the DiceSorensen Distance between two strings. The logic of the operation is not so difficult. You calculate how many two letter pairs exist in a string, compare it with a second string and then perform this equation
2(x intersect y)/ (|x| . |y|)
where |x| and |y| is the number of bigram elements in x & y. Reference can be found here for further clarity https://en.wikipedia.org/wiki/S%C3%B8rensen%E2%80%93Dice_coefficient
So I have tried looking up how to do the code online in various spots but every method I have come across uses the 'Intersect' method between two lists and as far as I am aware this won't work because if you have a string where the bigram already exists it won't add another one. For example if I had a string
'aaaa'
I would like there to be 3 'aa' bigrams but the Intersect method will only produce one, if i am incorrect on this assumption please tell me cause i wondered why so many people used the intersect method. My assumption is based on the MSDN website https://msdn.microsoft.com/en-us/library/bb460136(v=vs.90).aspx
So here is the code I have made
public static double SorensenDiceDistance(this string source, string target)
{
// formula 2|X intersection Y|
// --------------------
// |X| + |Y|
//create variables needed
List<string> bigrams_source = new List<string>();
List<string> bigrams_target = new List<string>();
int source_length;
int target_length;
double intersect_count = 0;
double result = 0;
Console.WriteLine("DEBUG: string length source is " + source.Length);
//base case
if (source.Length == 0 || target.Length == 0)
{
return 0;
}
//extract bigrams from string 1
bigrams_source = source.ListBiGrams();
//extract bigrams from string 2
bigrams_target = target.ListBiGrams();
source_length = bigrams_source.Count();
target_length = bigrams_target.Count();
Console.WriteLine("DEBUG: bigram counts are source: " + source_length + " . target length : " + target_length);
//now we have two sets of bigrams compare them in a non distinct loop
for (int i = 0; i < bigrams_source.Count(); i++)
{
for (int y = 0; y < bigrams_target.Count(); y++)
{
if (bigrams_source.ElementAt(i) == bigrams_target.ElementAt(y))
{
intersect_count++;
//Console.WriteLine("intersect count is :" + intersect_count);
}
}
}
Console.WriteLine("intersect line value : " + intersect_count);
result = (2 * intersect_count) / (source_length + target_length);
if (result < 0)
{
result = Math.Abs(result);
}
return result;
}
In the code somewhere you can see I call a method called listBiGrams and this is how it looks
public static List<string> ListBiGrams(this string source)
{
return ListNGrams(source, 2);
}
public static List<string> ListTriGrams(this string source)
{
return ListNGrams(source, 3);
}
public static List<string> ListNGrams(this string source, int n)
{
List<string> nGrams = new List<string>();
if (n > source.Length)
{
return null;
}
else if (n == source.Length)
{
nGrams.Add(source);
return nGrams;
}
else
{
for (int i = 0; i < source.Length - n; i++)
{
nGrams.Add(source.Substring(i, n));
}
return nGrams;
}
}
So my understanding of the code step by step is
1) pass in strings
2) 0 length check
3) create list and pass up bigrams into them
4) get the lengths of each bigram list
5) nested loop to check in source position[i] against every bigram in target string and then increment i until no more source list to check against
6) perform equation mentioned above taken from wikipedia
7) if result is negative Math.Abs it to return a positive result (however i know the result should be between 0 and 1 already this is what keyed me into knowing i was doing something wrong)
the source string i used is source = "this is not a correct string" and the target string was, target = "this is a correct string"
the result I got was -0.090909090908
I'm SURE (99%) that what I'm missing is something small like a mis-calculated length somewhere or a count mis-count. If anyone could point out what i'm doing wrong I'd be really grateful. Thank you for your time!

This looks like homework, yet this similarity metric on strings is new to me so I took a look.
Algorith implementation in various languages
As you may notice the C# version uses HashSet and takes advantage of the IntersectWith method.
A set is a collection that contains no duplicate elements, and whose
elements are in no particular order.
This solves your string 'aaaa' puzzle. Only one bigram there.
My naive implementation on Rextester
If you prefer Linq then I'd suggest Enumerable.Distinct, Enumerable.Union and Enumerable.Intersect. These should mimic very well the duplicate removal capabilities of the HashSet.
Also found this nice StringMetric framework written in Scala.

What wrong with this implement of this arcsine approximate in C#

This is a formula to approximate arcsine(x) using Taylor series from this blog
This is my implementation in C#, I don't know where is the wrong place, the code give wrong result when running:
When i = 0, the division will be 1/x. So I assign temp = 1/x at startup. For each iteration, I change "temp" after "i".
I use a continual loop until the two next value is very "near" together. When the delta of two next number is very small, I will return the value.
My test case:
Input is x =1, so excected arcsin(X) will be arcsin (1) = PI/2 = 1.57079633 rad.
class Arc{
static double abs(double x)
{
return x >= 0 ? x : -x;
}
static double pow(double mu, long n)
{
double kq = mu;
for(long i = 2; i<= n; i++)
{
kq *= mu;
}
return kq;
}
static long fact(long n)
{
long gt = 1;
for (long i = 2; i <= n; i++) {
gt *= i;
}
return gt;
}
#region arcsin
static double arcsinX(double x) {
int i = 0;
double temp = 0;
while (true)
{
//i++;
var iFactSquare = fact(i) * fact(i);
var tempNew = (double)fact(2 * i) / (pow(4, i) * iFactSquare * (2*i+1)) * pow(x, 2 * i + 1) ;
if (abs(tempNew - temp) < 0.00000001)
{
return tempNew;
}
temp = tempNew;
i++;
}
}
public static void Main(){
Console.WriteLine(arcsin());
Console.ReadLine();
}
}

In many series evaluations, it is often convenient to use the quotient between terms to update the term. The quotient here is
(2n)!*x^(2n+1) 4^(n-1)*((n-1)!)^2*(2n-1)
a[n]/a[n-1] = ------------------- * --------------------- -------
(4^n*(n!)^2*(2n+1)) (2n-2)!*x^(2n-1)
=(2n(2n-1)²x²)/(4n²(2n+1))
= ((2n-1)²x²)/(2n(2n+1))
Thus a loop to compute the series value is
sum = 1;
term = 1;
n=1;
while(1 != 1+term) {
term *= (n-0.5)*(n-0.5)*x*x/(n*(n+0.5));
sum += term;
n += 1;
}
return x*sum;
The convergence is only guaranteed for abs(x)<1, for the evaluation at x=1 you have to employ angle halving, which in general is a good idea to speed up convergence.

You are saving two different temp values (temp and tempNew) to check whether or not continuing computation is irrelevant. This is good, except that you are not saving the sum of these two values.
This is a summation. You need to add every new calculated value to the total. You are only keeping track of the most recently calculated value. You can only ever return the last calculated value of the series. So you will always get an extremely small number as your result. Turn this into a summation and the problem should go away.

NOTE: I've made this a community wiki answer because I was hardly the first person to think of this (just the first to put it down in a comment). If you feel that more needs to be added to make the answer complete, just edit it in!
The general suspicion is that this is down to Integer Overflow, namely one of your values (probably the return of fact() or iFactSquare()) is getting too big for the type you have chosen. It's going to negative because you are using signed types — when it gets to too large a positive number, it loops back into the negative.
Try tracking how large n gets during your calculation, and figure out how big a number it would give you if you ran that number through your fact, pow and iFactSquare functions. If it's bigger than the Maximum long value in 64-bit like we think (assuming you're using 64-bit, it'll be a lot smaller for 32-bit), then try using a double instead.

Cut and take new line String with maxchar

I tried to create a function for print all the articles of a billing with some max length vars, but when this max length is exceeded Index out of range errors appears or in another cases total and quantity Doesn't appear in line:
Max Length variables:
private Int32 MaxCharPage = 36;
private Int32 MaxCharArticleName = 15;
private Int32 MaxCharArticleQuantity = 4;
private Int32 MaxCharArticleSellPrice = 6;
private Int32 MaxCharArticleTotal = 8;
private Int32 MaxCharArticleLineSpace = 1;
This is my current function:
private IEnumerable<String> ArticleLine(Double Quantity, String Name, Double SellPrice, Double Total)
{
String QuantityChunk = (String)(Quantity).ToString("#,##0.00");
String PriceChunk = (String)(SellPrice).ToString("#,##0.00");
String TotalChunk = (String)(Total).ToString("#,##0.00");
// full chunks with "size" length
for (int i = 0; i < Name.Length / this.MaxCharArticleName; ++i)
{
String Chunk = String.Empty;
if (i == 0)
{
Chunk = QuantityChunk + new String((Char)32, (MaxCharArticleQuantity + MaxCharArticleLineSpace - QuantityChunk.Length)) +
Name.Substring(i * this.MaxCharArticleName, this.MaxCharArticleName) +
new String((Char)32, (MaxCharArticleLineSpace)) +
new String((Char)32, (MaxCharArticleSellPrice - PriceChunk.Length)) +
PriceChunk +
new String((Char)32, (MaxCharArticleLineSpace)) +
new String((Char)32, (MaxCharArticleTotal - TotalChunk.Length)) +
TotalChunk;
}
else
{
Chunk = new String((Char)32, (MaxCharArticleQuantity + MaxCharArticleLineSpace)) +
Name.Substring(i * this.MaxCharArticleName, this.MaxCharArticleName);
}
yield return Chunk;
}
if (Name.Length % this.MaxCharArticleName > 0)
{
String chunk = Name.Substring(Name.Length / this.MaxCharArticleName * this.MaxCharArticleName);
yield return new String((Char)32, (MaxCharArticleQuantity + MaxCharArticleLineSpace)) + chunk;
}
}
private void AddArticle(Double Quantity, String Name, Double SellPrice, Double Total)
{
Lines.AddRange(ArticleLine(Quantity, Name, SellPrice, Total).ToList());
}
For example:
private List<String> Lines = new List<String>();
private void Form1_Load(object sender, EventArgs e)
{
AddArticle(2.50, "EGGS", 0.50, 1.25); // Problem: Dont show the numbers like (Quantity, Sellprice, Total)
//AddArticle(100.52, "HAND SOAP /w EP", 5.00, 502.60); //OutOfRangeException
AddArticle(105.6, "LONG NAME ARTICLE DESCRIPTION", 500.03, 100.00);
//AddArticle(100, "LONG NAME ARTICLE DESCRIPTION2", 1500.03, 150003.00); // OutOfRangeException
foreach (String line in Lines)
{
Console.WriteLine(line);
}
}
Console Output:
LINE1: EGGS
LINE2:105.6LONG NAME ARTIC 500.03 100.00
LINE3: LE DESCRIPTION
Desired output:
LINE:2.50 EGGS 0.50 1.25
LINE:100. HAND SOAP /w EP 5.00 502.60
LINE: 52
LINE:105. LONG NAME ARTIC 500.03 100.00
LINE: 60 LE DESCRIPTION
LINE:100. LONG NAME ARTIC 1,500. 150,003.
LINE: 00 LE DESCRIPTION2 03 00

You are attempting to take values (string values, ultimately) and extract specified lengths from them (chunks), where the each individual chunk of a given group goes on one line, and the next chunk(s) go on the next line(s). There are several challenges in your posted code. One of the biggest is that you may not understand what the / operator does. It is, of course, used for division, but it is integer division, meaning you get a whole number as the result. E.g. 3 / 15 gives you 0, whereas 17 / 15 would give you 1. This means your loop never runs unless the length of the value is greater than the specified chunk limit.
Another possible issue is that you only perform this check against Name, not the other items (though you may have omitted the code for them for brevity reasons).
Your current code is also creating a lot of unnecessary strings, which will lead to performance degradation. Remember that in C# strings are immutable - meaning they cannot be changed. When you "change" the value of a string, you are actually creating another copy of the string.
The crux of your requirement is how to "chunk" the values in such a way that the correct output is achieved. One way to do this is to create an extension method that will take a string value and "chunkify" it for you. One such example is found here: Split String Into Array of Chunks. I've modified it slightly to use a List<T>, but an array would work just as well.
public static List<string> SplitIntoChunks(this string toSplit, int chunkSize)
{
int stringLength = toSplit.Length;
int chunksRequired = (int)Math.Ceiling(decimal)stringLength / (decimal)chunkSize);
List<string> chunks = new List<string>();
int lengthRemaining = stringLength;
for (int i = 0; i < chunksRequired; i++)
{
int lengthToUse = Math.Min(lengthRemaining, chunkSize);
int startIndex = chunkSize * i;
chunks.Add(toSplit.Substring(startIndex, lengthToUse));
lengthRemaining = lenghtRemaining - lengthToUse;
}
return chunks;
}
Say you have a string named myString. You would use the above method like this: string[] chunks = myString.SplitIntoChunks(15);, and you would receive an array of 15 character strings (depending on the size of the string).
A quick walk-through of the code (as there is not much explanation on the page). The size of the chunk is passed into the extension method. The length of the string is recorded, and the number of chunks for that string is determined using the Math.Ceiling function.
Then a for loop is constructed with the number of chunks required as the limit. Inside the loop, the length of the chunk is determined (using the lower of either the chunk size or the remaining length of the string), the starting index is calculated based on the chunk size and the loop index, and then the chunk is extracted via Substring. Finally remaining length is calculated, and once the loop ends the chunks are returned.
One way to use this extension method in your code would look like this. The extension method will need to be in a separate, static class (I suggest building a library that has a class dedicated solely to extension methods, as they come in quite handy). Note that I haven't had time to test this, and it's a bit kludgy for my tastes, but it should at least get you going in the right direction.
private IEnumerable<string> ArticleLine(double quantity, string name, double sellPrice, double total)
{
List<string> quantityChunks = quantity.ToString("#,##0.00").SplitIntoChunks(maxCharArticleQuantity);
List<string> nameChunks = name.SplitIntoChunks(maxCharArticleName);
List<string> sellPriceChunks = sellPrice.ToString("#,##0.00").SplitIntoChunks(maxCharArticleSellPrice);
List<string> totalChunks = total.ToString("#,##0.00").SplitIntoChunks(maxCharArticleTotal);
int maxLines = (new List<int>() { quantityChunks.Count,
nameChunks.Count,
sellPriceChunks.Count,
totalChunks.Count }).Max();
for (int i = 0; i < maxLines; i++)
{
lines.Add(String.Format("{0}{1}{2}{3}",
quantityChunks.Count > i ?
quantityChunks[i].PadLeft(maxCharArticleQuantity) :
String.Empty.PadLeft(maxCharArticleQuantity),
nameChunks.Count > i ?
nameChunks[i].PadLeft(maxCharArticleName) :
String.Empty.PadLeft(maxCharArticleName, ' '),
sellPriceChunks.Count > i ?
sellPriceChunks[i].PadLeft(maxCharArticleSellPrice) :
String.Empty.PadeLeft(maxCharArticleSellPrice),
totalChunks.Count > i ?
totalChunks[i].PadLeft(maxCharArticleTotal) :
String.Empty.PadLeft(maxCharArticleTotal));
}
return lines;
}
The above code does a couple of things. First, it calls SplitIntoChunks on each of the four variables.
Next, it uses the Max() extension method (you'll need to add a reference to System.Linq if you don't already have one, plus a using directive). to determine the maximum number of lines needed (based on the highest count of the four lists).
Finally, it uses a 4for loop to build the lines. Note that I use the ternary operator (?:) to build each line. The reason I went this route is so that the lines would be properly formatted, even if one or more of the 4 values didn't have something for that line. In other words:
quantityChunks.Count > i
If the count of items in quantityChunks is greater than i, then there is an entry for that item for that line.
quanityChunks[i].PadLeft(maxCharArticleQuantity, ' ')
If the condition evaluates to true, we use the corresponding entry (and pad it with spaces to keep alignment).
String.Empty.PadLeft(maxCharArticleQuantity, ' ')
If the condition is false, we simply put in spaces for the maximum number of characters for that position in the line.
Then you can print the output like this:
foreach(string line in lines)
{
Console.WriteLine(line);
}
The portions of the code where I check for the maximum number of lines and the use of a ternary operator in the String.Format feel very kludgy to me, but I don't have time to finesse it into something more respectable. I hope this at least points you in the right direction.
EDIT
Fixed the PadLeft syntax and removed the character specified, as space is used by default.

Cartesian product subset returning set of mostly 0

I'm trying to calculate
If we calculated every possible combination of numbers from 0 to (c-1)
with a length of x
what set would occur at point i
For example:
c = 4
x = 4
i = 3
Would yield:
[0000]
[0001]
[0002]
[0003] <- i
[0010]
....
[3333]
This is very nearly the same problem as in the related question Logic to select a specific set from Cartesian set. However, because x and i are large enough to require the use of BigInteger objects, the code has to be changed to return a List, and take an int, instead of a string array:
int PossibleNumbers;
public List<int> Get(BigInteger Address)
{
List<int> values = new List<int>();
BigInteger sizes = new BigInteger(1);
for (int j = 0; j < PixelArrayLength; j++)
{
BigInteger index = BigInteger.Divide(Address, sizes);
index = (index % PossibleNumbers);
values.Add((int)index);
sizes *= PossibleNumbers;
}
return values;
}
This seems to behave as I'd expect, however, when I start using values like this:
c = 66000
x = 950000
i = (66000^950000)/2
So here, I'm looking for the ith value in the cartesian set of 0 to (c-1) of length 950000, or put another way, the halfway point.
At this point, I just get a list of zeroes returned. How can I solve this problem?
Notes: It's quite a specific problem, and I apologise for the wall-of-text, I do hope it's not too much, I was just hoping to properly explain what I meant. Thanks to you all!
Edit: Here are some more examples: http://pastebin.com/zmSDQEGC

Here is a generic base converter... it takes a decimal for the base10 value to convert into your newBase and returns an array of int's. If you need a BigInteger this method works perfectly well with just changing the base10Value to BigInteger.
EDIT: Converted method to BigInteger since that's what you need.
EDIT 2: Thanks phoog for pointing out BigInteger is base2 so changing the method signature.
public static int[] ConvertToBase(BigInteger value, int newBase, int length)
{
var result = new Stack<int>();
while (value > 0)
{
result.Push((int)(value % newBase));
if (value < newBase)
value = 0;
else
value = value / newBase;
}
for (var i = result.Count; i < length; i++)
result.Push(0);
return result.ToArray();
}
usage...
int[] a = ConvertToBase(13, 4, 4) = [0,0,3,1]
int[] b = ConvertToBase(0, 4, 4) = [0,0,3,1]
int[] c = ConvertToBase(1234, 12, 4) = [0,8,6,10]
However the probelm you specifically state is a bit large to test it on. :)
Just calculating 66000 ^ 950000 / 2 is a good bit of work as Phoog mentioned. Unless of course you meant ^ to be the XOR operator. In which case it's quite fast.
EDIT: From the comments... The largest base10 number that can be represented given a particular newBase and length is...
var largestBase10 = BigInteger.Pow(newBase, length)-1;

The first expression of the problem boils down to "write 3 as a 4-digit base-4 number". So, if the problem is "write i as an x-digit base-c number", or, in this case, "write (66000^950000)/2 as a 950000-digit base 66000 number", then does that make it easier?
If you're specifically looking for the halfway point of the cartesian product, it's not so hard. If you assume that c is even, then the most significant digit is c / 2, and the rest of the digits are zero. If your return value is all zeros, then you may have an off-by-one error, or the like, since actually only one digit is incorrect.