/// <summary>生成随机的银行卡卡号
/// </summary>
/// <param name="prefix"> </param>
/// <param name="length"></param>
/// <returns></returns>
public static string GetFixNumberString(int prefix = 0, int length = 16)
{
if (length < 1)
{
throw new ArgumentException("卡号长度不能小于1");
}
var prefixLength = UtilityMath.GetLength(prefix);
var sb = new StringBuilder(length);
if (prefix > 0)
{
if (prefixLength > length)
{
sb.Append(prefix.ToString().Substring(0, length));
}
else
{
sb.Append(prefix);
}
}
for (int i = 0; i < length - prefixLength; i++)
{
sb.Append(Random.Next(0, 9));
}
return(sb.ToString());
}
public static Result LargeSum(Problem arguments)
{
string m;
string sequence = arguments.Sequence;
int digits = Convert.ToInt32(arguments.LongNumber);
string[] numbers = sequence.Split(',').ToArray <string>();
int height = numbers.Length;
int width = numbers[0].Length;
int[,] matrix = UtilityMath.LoadMatrix(numbers, height, width);
string sum = UtilityMath.AddMatrix(matrix);
if (digits < sum.Length)
{
m = string.Format("The first {0} digits of the large sum are {1}.", digits, sum.Substring(0, digits));
}
else
{
m = "Error: not enough digits specified.";
}
var r = new Result(arguments.Id, m);
return(r);
}
public PrimeSet(int c)
{
Count = c;
Primes = UtilityMath.ErathostenesSieve(3, 20000);
Minimums = Enumerable.Repeat(int.MaxValue, 5).ToArray();
Pairs = new HashSet <int> [Primes.Length];
Set = new int[Count];
var IsPrime = UtilityMath.IsPrimeUsingSquares.Memoize();
for (int a = 0; a < Primes.Length; a++)
{
Pairs[a] = new HashSet <int>();
int x = Primes[a];
for (int b = 0; b < Primes.Length; b++)
{
if (a == b)
{
continue;
}
int y = Primes[b];
if (IsPrime(UtilityMath.NumericConcat(x, y)) &&
IsPrime(UtilityMath.NumericConcat(y, x)))
{
Pairs[a].Add(y);
}
}
}
}
public static Result LargestProductInGrid(Problem arguments)
{
string sequence = arguments.Sequence;
int adjacent = Convert.ToInt32(arguments.LongNumber);
int maxProduct = int.MinValue, product = 0;
CellList VisitedCellBlocks = new CellList(); //so we don't calculate on repeated blocks of adjcent cells
//initialize grid from string sequence
string[][] grid = sequence.Split(':').Select(row => row.Split(',')).ToArray();
int size = grid.Length;
//get highest adajacent product of adjacents to every grid cell
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
product = UtilityMath.GetAdjacentMaxproduct(i, j, adjacent, size, grid, VisitedCellBlocks);
if (product > maxProduct)
{
maxProduct = product;
}
}
}
var m = string.Format("The greatest product of {0} adjacent numbers in the same direction (up, down, left, right, or diagonally) in the {1}×{1} grid is {2}.", adjacent, size, maxProduct);
var r = new Result(arguments.Id, m);
return(r);
}
/// <summary>
/// https://projecteuler.net/problem=53
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result CombinatoricSelections(Problem arguments)
{
var limit = arguments.IntNumber;
var count = 0;
//todo: use factaorial in loop and cache it in array
for (int n = 1; n <= 100; n++)
{
for (int r = 1; r < n; r++)
{
if (UtilityMath.BinomialCoefficients(n, r) >= limit)
{
count++;
}
}
}
var answer = count.ToString();
var message = string.Format("{0} not necessarily distinct, values of nCr, for 1 ≤ n ≤ 100, are greater than {1}.", answer, limit);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var result = new Result(arguments.Id, message)
{
Answer = answer
};
return(result);
}
public static Result LargestProductInSeries(Problem arguments)
{
string sequence = arguments.Sequence;
int digits = Convert.ToInt32(arguments.LongNumber);
string segment = string.Empty, digit = string.Empty;
int start = 0;
long product = long.MinValue;
while (start + digits < sequence.Length)
{
segment = sequence.Substring(start, digits);
start++;
long p = UtilityMath.GetProduct(segment);
if (p > product)
{
product = p;
digit = segment;
}
}
var m = string.Format("the adjacent digits [{0}] in the 1000-digit number that have the greatest product which is {1}.", string.Join("x", digit.ToArray()), product);
var r = new Result(arguments.Id, m);
return(r);
}
/// <summary>
/// https://projecteuler.net/problem=56
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result PowerfulDigitSum(Problem arguments)
{
var limit = arguments.IntNumber;
long max = 100; // include all 100 * 1^b to begin with
for (int a = 2; a < limit; a++)
{
for (int b = 1; b < limit; b++)
{
var ab = BigInteger.Pow(a, b);
var sum = UtilityMath.DigitsSum(ab.ToString());
if (sum > max)
{
max = sum;
}
}
}
var answer = max.ToString();
var message = string.Format("The maximum digital sum of natural numbers of the form, a^b, where a, b < {0}, is {1}.", limit, answer);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var r = new Result(arguments.Id, message)
{
Answer = answer
};
return(r);
}
static Result LargestPrimeFactor(Problem arguments)
{
//n=600851475143;143;8462696833;
long number = arguments.LongNumber;
Tree <long> factors = new Tree <long>();
string m;
UtilityMath.GetPrimeFactors(number, factors);
bool isPrime = factors.Size == 0;
long max = (long)factors.Max();
if (isPrime)
{
m = string.Format("The prime factors of {0} are [{1}], maximum is {2}", number, factors.ToString(), max);
}
else
{
m = string.Format("{0} is not a prime, but its prime factors are [{1}] with maximum {2}", number, factors.ToString(), max);
}
var r = new Result(arguments.Id, m);
return(r);
}
/// <summary>
/// https://projecteuler.net/problem=61
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result CyclicalFigurateNumbers(Problem arguments)
{
var numbers = UtilityMath.GetPolygonalNumbers <int>(1009, 9999).ToArray();
var count = numbers.Length;
var types = Enumerable.Range(0, count).ToArray <int>(); // array of polygonal number types used
var setNumberOrder = UtilityString.GeneratePermutations <int>(types); // permutation of the types indicat1ing all combinations of these in a sequence of numbers
var s = UtilityMath.GetNumericalCyclicalSet(setNumberOrder, numbers);
var answer = s.set.Sum().ToString();
var message = string.Format("The sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, is represented by a different number in the set is {0}.", answer);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var r = new Result(arguments.Id, message)
{
Answer = answer
};
return(r);
}
/// <summary>
/// https://projecteuler.net/problem=64
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result OddPeriodSquareRoots(Problem arguments)
{
var count = 0;
var upperBound = arguments.IntNumber;
for (int n = 2; n <= upperBound; n++)
{
if (UtilityMath.IsPerferctSquare(n))
{
continue;
}
var p = UtilityMath.GetContinuedFractionExpansionPeriodicLengthForNonPerfectSquare(n);
if (p % 2 == 1) //only if odd
{
count++;
}
}
var answer = count.ToString();
var message = string.Format("The number of continued fractions for N ≤ {0} have an odd period is {1}.", upperBound, answer);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var r = new Result(arguments.Id, message)
{
Answer = answer
};
return(r);
}
/// <summary>
/// https://projecteuler.net/problem=75
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result SingularIntegerRightTriangles(Problem arguments)
{
var perimeter = arguments.IntNumber;
var values = 0;
var a = UtilityMath.GetPythagoreanTriples_Pitagoras(120, false);
for (int L = 12; L < perimeter; L++)
{
if (GetSingularPythagoreanTriples(L) == 1)
{
values++;
}
}
var answer = values.ToString();
var message = string.Format("Given that L is the length of the wire, {0} values of L ≤ {1} can form exactly one integer sided right angle triangle.", answer, perimeter);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var r = new Result(arguments.Id, message)
{
Answer = answer
};
return(r);
}
static void Problem5(ProblemArguments arguments)
{
long maximum = arguments.Number;
int[] multiples = new int[maximum];
bool found = false;
long number = 0;
for (int i = 1; i <= maximum; i++)
{
multiples[i - 1] = i;
}
while (!found && number < long.MaxValue)
{
if (!found)
{
number += maximum;
}
found = UtilityMath.IsMultiple(multiples, number);
}
if (found)
{
Console.WriteLine("{0} is the smallest positive number that is evenly divisible by {1}", number, string.Join(",", multiples));
}
else
{
Console.WriteLine("No evenly positive multiple number found.");
}
}
static void Problem4_1(ProblemArguments arguments)
{
long number = 993 * 913;
if (UtilityMath.IsPalindrome(number))
{
Console.WriteLine("x. {0} is palipndrome", number);
}
}
//Override
public void updateAIPosition()
{ //get delta x and y for rotating coordinates
Point position = target.getAbsolutePositionOf(UtilityMath.dividePoint(this.targetPosition, zoomFactor));
MovingCamera.this.setDX((position.x - MovingCamera.this.getX()) / 30.0);
MovingCamera.this.setDY((position.y - MovingCamera.this.getY()) / 30.0);
getAngularComposite().setAngleInRadians(-target.getAngularComposite().getAngleInRadians());
//zoomFactor = zoom;
}
public static Result PowerDigitSum(Problem arguments)
{
var e = Convert.ToInt16(arguments.LongNumber);
var b = arguments.IntNumber;
var p = UtilityMath.PowOverflow(b, e);
var s = UtilityMath.DigitsSum(p);
var m = string.Format("Sum of digits of {0}^{1} is {2}.", b, e, s);
var r = new Result(arguments.Id, m);
return(r);
}
public static void Main(string[] args)
{
//UtilityHelper.Measure(() => SimpleForeach(), true, "Foreach loop:");
//UtilityHelper.Measure(() => ParallelForeach(2), true, "Parallel Foreach loop:");
UtilityHelper.Measure(() =>
{
var f = UtilityMath.GetFactors(12000).ToArray();
Array.Sort(f);
f[0] = 1;
}, true, "Factor:");
UtilityHelper.Measure(() => ProductSumNumbers(12000), true, "ProductSumNumbers answer:");
}
private HashSet <int> MakePairs(int a)
{
HashSet <int> pairs = new HashSet <int>();
for (int b = a + 1; b < Primes.Length; b++)
{
if (UtilityMath.IsPrimeUsingSquares(UtilityMath.NumericConcat(Primes[a], Primes[b])) &&
UtilityMath.IsPrimeUsingSquares(UtilityMath.NumericConcat(Primes[b], Primes[a])))
{
pairs.Add(Primes[b]);
}
}
return(pairs);
}
public static void Problem10(ProblemArguments arguments)
{
long sum = 0, limit = arguments.Number;
for (long i = 2; i <= limit; i++)
{
if (UtilityMath.IsPrime(i))
{
sum += i;
}
}
Console.WriteLine("The sum of all the primes below {0} is {1}.", limit, sum);
}
/// <summary>
/// https://projecteuler.net/problem=59
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result XorDecryption(Problem arguments)
{
const char FirstChar = 'a';
const char LastChar = 'z';
var sum = 0;
var key = string.Empty;
var text = string.Empty;
var cvsinfo = arguments.Sequence.Split('|');
var fileName = cvsinfo[0];
var delimiter = Convert.ToChar(cvsinfo[1]);
var qualifier = Convert.ToChar(cvsinfo[2]);
var cyphers = UtilityFile.ReadCsvToArray(fileName, delimiter, qualifier);
var ascii = cyphers.Select(X => Convert.ToInt32(X)).ToArray();
var allPossiblePasswords = (from a in FirstChar.To(LastChar)
from b in FirstChar.To(LastChar)
from c in FirstChar.To(LastChar)
select new[] { Convert.ToInt32(a), Convert.ToInt32(b), Convert.ToInt32(c) }).ToArray();
foreach (var password in allPossiblePasswords)
{
var decrypted = UtilityMath.Encrypt(ascii, password);
text = new string(decrypted.Select(x => Convert.ToChar(x)).ToArray());
if (text.Contains(" the ")) //perform simple check: if Text contains single word 'the' it is in english
{
key = new string(password.Select(x => Convert.ToChar(x)).ToArray());
break;
}
}
sum = text.Aggregate(0, (runningTotal, next) => runningTotal += next);
var answer = sum.ToString();
var message = string.Format("The sum of the ASCII values in the original English text is {0}.", answer);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var r = new Result(arguments.Id, message)
{
Answer = answer
};
return(r);
}
public static Result NumbersToLetters(Problem arguments)
{
long sum = 0;
long lower = arguments.Numbers[0];
long upper = arguments.Numbers[1];
for (long number = lower; number <= upper; number++)
{
sum += LengthWordRepresentation(UtilityMath.NumberToLetters(number));
}
var m = string.Format("The number of letters used if all the numbers from {0} to {1} inclusive were written out in words is {2}.", lower, upper, sum);
var r = new Result(arguments.Id, m);
return(r);
}
/// <summary>
/// For right triangles, using Euclid formula, modified function for problem75
/// </summary>
/// <param name="p">Triangle perimeter</param>
/// <returns></returns>
private static int GetSingularPythagoreanTriples(long p)
{
var count = 0;
var bound = (long)Math.Sqrt(p / 2);
long m;
for (m = 2; m <= bound; m++)
{
if ((p / 2) % m == 0)
{ // m found
long k;
if (m % 2 == 0)
{ // ensure that we find an odd number for k
k = m + 1;
}
else
{
k = m + 2;
}
while (k < 2 * m && k <= p / (2 * m))
{
if (p / (2 * m) % k == 0 && UtilityMath.EuclidianGCD(k, m) == 1)
{
long d = p / 2 / (k * m);
long n = k - m;
long a = d * (m * m - n * n);
long b = 2 * d * n * m;
long c = d * (m * m + n * n);
if (a + b + c == p)
{
count++;
}
// only consider those which only have one combination
if (count > 1)
{
return(0);
}
}
k += 2;
}
}
}
return(count);
}
public static void Problem12(ProblemArguments arguments)
{
long count = arguments.Number;
long number = (long)Math.Pow((double)count, 2);
long number_of_divisors = 0;
do
{
number++;
if (UtilityMath.IsTriangularNumber(number))
{
number_of_divisors = 0;// UtilityMath.NumberOfDivisor(number);
}
} while (number_of_divisors < count);
Console.WriteLine("The value of the first triangle number to have over {0} divisors is {1}.", count, number);
}
static Result LargestPalindromeProduct(Problem arguments)
{
long digits = arguments.LongNumber;
long limit = (long)Math.Pow(10, digits) - 1;
long number = 0;
long i, j, pi = 0, pj = 0;
bool found = false;
long palindrome = UtilityMath.GenericLimit <long> .MinValue;
string m;
i = limit;
j = limit;
while (i > Math.Pow(10, digits - 1))
{
j = limit;
while (!found && j > Math.Pow(10, digits - 1))
{
number = i * j;
found = UtilityMath.IsPalindrome(number);
j--;
}
i--;
if (found && number > palindrome)
{
pi = i + 1;
pj = j + 1;
palindrome = number;
found = false;
}
}
if (palindrome == UtilityMath.GenericLimit <long> .MinValue && i == Math.Pow(10, digits - 1) && j == Math.Pow(10, digits - 1))
{
m = string.Format("No palindrome found");
}
else
{
m = string.Format("The largest palindrome made from the product of two 3-digit numbers is {0} = {1} x {2}", palindrome, pi, pj);
}
var r = new Result(arguments.Id, m);
return(r);
}
public static Result SummationOfPrimes(Problem arguments)
{
long sum = 0, limit = arguments.LongNumber;
for (long i = 2; i <= limit; i++)
{
if (UtilityMath.IsPrime(i))
{
sum += i;
}
}
var m = string.Format("the sum of all the primes below {0} is {1}.", limit, sum);
var r = new Result(arguments.Id, m);
return(r);
}
/// <summary>
/// https://projecteuler.net/problem=68
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result Magic5GonRing(Problem arguments)
{
var n = arguments.ListOfNumbers;
var ringSize = arguments.IntNumber;
var sideLength = 3;
var ring = UtilityMath.GetPentagonalRing(n, sideLength, ringSize);
// traverse ring in circular index from smaller outer node
// if iendex go: n, 0, 1,..., n-2, n-1
var index = new int[ringSize];
var v = 0;
index[0] = ringSize - 1;
for (var i = 1; i < ringSize; i++)
{
index[i] = v;
v++;
}
var builder = new StringBuilder();
foreach (var i in index)
{
var side = ring[i];
foreach (var d in side)
{
builder.Append(d.ToString());
}
}
string answer = builder.ToString();
var message = string.Format("The maximum 16-digit string for a \"magic\" 5-gon ring is {0}.", answer);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var r = new Result(arguments.Id, message)
{
Answer = answer
};
return(r);
}
public static Result LatticePaths(Problem arguments)
{
ulong gridSize = arguments.BigNumber;
var x
= UtilityMath.FactorialOverFlow(gridSize);
var y = UtilityMath.FactorialOverFlow(2 * gridSize);
BigInteger a = BigInteger.Parse(x);
BigInteger b = BigInteger.Parse(y);
BigInteger n = BigInteger.Pow(a, 2);
BigInteger routes = BigInteger.Divide(b, n);
var m = string.Format("There are {0} route(s) in a {1}x{1} grid.", routes, gridSize);
var r = new Result(arguments.Id, m);
return(r);
}
/// <summary>
/// https://projecteuler.net/problem=58
/// </summary>
/// <param name="arguments"></param>
/// <returns></returns>
public static Result SpiralPrimes(Problem arguments)
{
bool IsPrime(int n)
{
return(n != 1 && (n != 3 || n % 3 == 0) && (n != 2 || n % 2 == 0) && UtilityMath.IsPrimeUsingSquares(n));
}
double ratio = 1;
var step = 0;
var length = 1;
var corner = 1;
var count = 0;
while (ratio > 0.10)
{
length += 2;
step += 2;
for (int i = 1; i < 4; i++)
// only check primality for three corners, so just skip the southwest corner numbers
{
corner += step;
if (IsPrime(corner))
{
count++;
}
}
corner += step;
ratio = (double)count / (2 * length - 1);
}
var answer = length.ToString();
var message = string.Format("The side length of the square spiral for which the ratio of primes along both diagonals first falls below {0}% is {1}.", ratio * 100, answer);
if (Answers[arguments.Id] != answer)
{
message += string.Format(" => INCORRECT ({0})", Answers[arguments.Id]);
}
var r = new Result(arguments.Id, message)
{
Answer = answer
};
return(r);
}
static void Problem4(ProblemArguments arguments)
{
long digits = arguments.Number;
long limit = (long)Math.Pow(10, digits) - 1;
long number = 0;
long i, j, pi = 0, pj = 0;
bool found = false;
long palindrome = UtilityMath.GenericLimit <long> .MinValue;
i = limit;
j = limit;
while (i > Math.Pow(10, digits - 1))
{
j = limit;
while (!found && j > Math.Pow(10, digits - 1))
{
number = i * j;
found = UtilityMath.IsPalindrome(number);
j--;
}
i--;
if (found && number > palindrome)
{
pi = i + 1;
pj = j + 1;
palindrome = number;
found = false;
}
}
if (palindrome == UtilityMath.GenericLimit <long> .MinValue && i == Math.Pow(10, digits - 1) && j == Math.Pow(10, digits - 1))
{
Console.WriteLine("No palindrome found");
}
else
{
Console.WriteLine("The largest palindrome made from the product of two 3-digit numbers is {0} = {1} x {2}", palindrome, pi, pj);
}
//int digit = sequence[1]-48; //convert character to it's integer representation
}
public Shape getGraphicRelativeRotationalBounds(double graphicsSizeFactorX, double graphicsSizeFactorY, double angleRadians, int areaExtender)
{
Rectangle box = new Rectangle();
int scaledWidth = (int)(this.getImage().getWidth(null) * graphicsSizeFactorX * this.getSizeFactor());
int sclaedHeight = (int)(this.getImage().getHeight(null) * graphicsSizeFactorY * this.getSizeFactor());
box.setSize(
scaledWidth + areaExtender,
sclaedHeight + areaExtender);
box.setLocation(
(int)((-areaExtender / 2 + this.getOffsetX()) * graphicsSizeFactorX * this.getSizeFactor()),
(int)((-areaExtender / 2 + this.getOffsetY()) * graphicsSizeFactorY * this.getSizeFactor())
);
Point[] cornersArray = new Point[] {
new Point((int)box.getMinX(), (int)box.getMinY()),
new Point((int)box.getMaxX(), (int)box.getMinY()),
new Point((int)box.getMaxX(), (int)box.getMaxY()),
new Point((int)box.getMinX(), (int)box.getMaxY())
};
int[] newCornersX = new int[cornersArray.length];
int[] newCornersY = new int[cornersArray.length];
for (int i = 0; i < cornersArray.length; ++i)
{
Point rotatedCorner = UtilityMath.getRotationalAbsolutePositionOf(cornersArray[i], angleRadians);
newCornersX[i] = rotatedCorner.x;
newCornersY[i] = rotatedCorner.y;
}
Shape rotatedRectangle = new Polygon(newCornersX, newCornersY, newCornersX.length);
box.setLocation(
(int)((-areaExtender / 2 + this.getOffsetX()) * graphicsSizeFactorX * this.getSizeFactor()),
(int)((-areaExtender / 2 + this.getOffsetY()) * graphicsSizeFactorY * this.getSizeFactor())
);
return(rotatedRectangle);
}
public static Result DivisibleTriangularNumber(Problem arguments)
{
long count = arguments.LongNumber;
long number = (long)Math.Pow((double)count, 2);
long number_of_divisors = 0;
do
{
number++;
if (UtilityMath.IsTriangularNumber(number))
{
number_of_divisors = 0;// UtilityMath.NumberOfDivisor(number);
}
} while (number_of_divisors < count);
var m = string.Format("The value of the first triangle number to have over {0} divisors is {1}.", count, number);
var r = new Result(arguments.Id, m);
return(r);
}