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| TestResults/ |
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| <?xml version="1.0" encoding="UTF-8"?> | ||
| <TestLists xmlns="http://microsoft.com/schemas/VisualStudio/TeamTest/2010"> | ||
| <TestList name="Lists of Tests" id="8c43106b-9dc1-4907-a29f-aa66a61bf5b6"> | ||
| <RunConfiguration id="ee51332a-2095-4e7d-83c4-431590abb05b" name="Local" storage="local.testsettings" type="Microsoft.VisualStudio.TestTools.Common.TestRunConfiguration, Microsoft.VisualStudio.QualityTools.Common, Version=10.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a" /> | ||
| </TestList> | ||
| </TestLists> |
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| using System; | ||
| using System.Collections.Generic; | ||
| using System.Linq; | ||
| using System.Text; | ||
| using System.Numerics; | ||
|
|
||
| namespace Ckknight.ProjectEuler.Collections | ||
| { | ||
| public class BigContinuedFraction | ||
| { | ||
| private BigContinuedFraction(BigInteger floor, IEnumerable<BigInteger> nonPeriodicQuotients, IEnumerable<BigInteger> periodicQuotients) | ||
| { | ||
| _floor = floor; | ||
| _nonPeriodicQuotients = nonPeriodicQuotients ?? Enumerable.Empty<BigInteger>(); | ||
| _periodicQuotients = periodicQuotients ?? Enumerable.Empty<BigInteger>(); | ||
| } | ||
|
|
||
| public BigContinuedFraction(BigInteger floor) | ||
| : this(floor, default(IEnumerable<BigInteger>), default(IEnumerable<BigInteger>)) { } | ||
|
|
||
| public BigContinuedFraction(BigInteger floor, IEnumerable<BigInteger> nonPeriodicQuotients) | ||
| : this(floor, nonPeriodicQuotients, default(IEnumerable<BigInteger>)) | ||
| { | ||
| if (nonPeriodicQuotients == null) | ||
| { | ||
| throw new ArgumentNullException("nonPeriodicQuotients"); | ||
| } | ||
| } | ||
|
|
||
| public BigContinuedFraction(BigInteger floor, IEnumerable<BigInteger> nonPeriodicQuotients, BigInteger[] periodicQuotients) | ||
| : this(floor, nonPeriodicQuotients, (IEnumerable<BigInteger>)periodicQuotients) | ||
| { | ||
| if (nonPeriodicQuotients == null) | ||
| { | ||
| throw new ArgumentNullException("nonPeriodicQuotients"); | ||
| } | ||
| else if (periodicQuotients == null) | ||
| { | ||
| throw new ArgumentNullException("periodicQuotients"); | ||
| } | ||
| } | ||
|
|
||
| public static readonly BigContinuedFraction Zero = new BigContinuedFraction(0); | ||
| public static readonly BigContinuedFraction One = new BigContinuedFraction(1); | ||
|
|
||
| private readonly BigInteger _floor; | ||
| public BigInteger Floor | ||
| { | ||
| get | ||
| { | ||
| return _floor; | ||
| } | ||
| } | ||
|
|
||
| private readonly IEnumerable<BigInteger> _nonPeriodicQuotients; | ||
| public IEnumerable<BigInteger> NonPeriodicQuotients | ||
| { | ||
| get | ||
| { | ||
| return _nonPeriodicQuotients; | ||
| } | ||
| } | ||
|
|
||
| private readonly IEnumerable<BigInteger> _periodicQuotients; | ||
| public IEnumerable<BigInteger> PeriodicQuotients | ||
| { | ||
| get | ||
| { | ||
| return _periodicQuotients; | ||
| } | ||
| } | ||
|
|
||
| public IEnumerable<BigInteger> Quotients | ||
| { | ||
| get | ||
| { | ||
| foreach (BigInteger quotient in _nonPeriodicQuotients) | ||
| { | ||
| yield return quotient; | ||
| } | ||
|
|
||
| while (true) | ||
| { | ||
| bool found = false; | ||
| foreach (BigInteger quotient in _periodicQuotients) | ||
| { | ||
| if (!found) | ||
| { | ||
| found = true; | ||
| } | ||
| yield return quotient; | ||
| } | ||
| if (!found) | ||
| { | ||
| break; | ||
| } | ||
| } | ||
| } | ||
| } | ||
|
|
||
| private const int MaxNonPeriodicLengthShown = 10; | ||
| public override string ToString() | ||
| { | ||
| StringBuilder sb = new StringBuilder(); | ||
| sb.Append('['); | ||
| sb.Append(_floor); | ||
|
|
||
| BigInteger[] partialNonPeriodicQuotients = _nonPeriodicQuotients as BigInteger[]; | ||
| if (partialNonPeriodicQuotients == null) | ||
| { | ||
| partialNonPeriodicQuotients = _nonPeriodicQuotients.Take(MaxNonPeriodicLengthShown + 1).ToArray(); | ||
| } | ||
| int length = partialNonPeriodicQuotients.Length; | ||
| if (length > MaxNonPeriodicLengthShown) | ||
| { | ||
| length = MaxNonPeriodicLengthShown; | ||
| } | ||
| for (int i = 0; i < length; i++) | ||
| { | ||
| if (i == 0) | ||
| { | ||
| sb.Append("; "); | ||
| } | ||
| else | ||
| { | ||
| sb.Append(", "); | ||
| } | ||
| sb.Append(partialNonPeriodicQuotients[i]); | ||
| } | ||
| if (partialNonPeriodicQuotients.Length > MaxNonPeriodicLengthShown) | ||
| { | ||
| sb.Append(", ..."); | ||
| } | ||
|
|
||
| BigInteger[] periodicQuotients = _periodicQuotients as BigInteger[] ?? _periodicQuotients.ToArray(); | ||
| if (periodicQuotients.Length > 0) | ||
| { | ||
| if (length == 0) | ||
| { | ||
| sb.Append("; "); | ||
| } | ||
| else | ||
| { | ||
| sb.Append(", "); | ||
| } | ||
| sb.Append('('); | ||
| for (int i = 0; i < periodicQuotients.Length; i++) | ||
| { | ||
| if (i > 0) | ||
| { | ||
| sb.Append(", "); | ||
| } | ||
| sb.Append(periodicQuotients[i]); | ||
| } | ||
| sb.Append(')'); | ||
| } | ||
|
|
||
| sb.Append(']'); | ||
| return sb.ToString(); | ||
| } | ||
|
|
||
| public static BigContinuedFraction Sqrt(BigInteger value) | ||
| { | ||
| BigInteger sqrt = MathUtilities.BigSqrt(value); | ||
|
|
||
| if (sqrt * sqrt == value) | ||
| { | ||
| return new BigContinuedFraction(sqrt); | ||
| } | ||
| else | ||
| { | ||
| var period = CollectionUtilities.Repeat(default(object)) | ||
| .SelectWithAggregate(new { m = BigInteger.Zero, d = BigInteger.One, a = sqrt }, (x, i) => | ||
| { | ||
| BigInteger m = x.d * x.a - x.m; | ||
| BigInteger d = (value - m * m) / x.d; | ||
| BigInteger a = (sqrt + m) / d; | ||
| return new { m, d, a }; | ||
| }) | ||
| .TakeWhileDistinct() | ||
| .Select(x => x.a) | ||
| .ToArray(); | ||
|
|
||
| return new BigContinuedFraction(sqrt, Enumerable.Empty<BigInteger>(), period); | ||
| } | ||
| } | ||
|
|
||
| public static BigContinuedFraction FromBigFraction(BigFraction fraction) | ||
| { | ||
| if (fraction.Denominator.IsZero) | ||
| { | ||
| throw new ArithmeticException("Cannot generate continued fraction from NaN, Infinity, or -Infinity"); | ||
| } | ||
|
|
||
| bool first = true; | ||
| BigInteger initial = BigInteger.Zero; | ||
| List<BigInteger> quotients = new List<BigInteger>(); | ||
| while (true) | ||
| { | ||
| BigFraction remainder; | ||
| BigInteger floor = BigFraction.DivRem(fraction, BigFraction.One, out remainder).Numerator; | ||
|
|
||
| if (first) | ||
| { | ||
| first = false; | ||
| initial = floor; | ||
| } | ||
| else | ||
| { | ||
| quotients.Add(floor); | ||
| } | ||
|
|
||
| if (remainder.IsZero) | ||
| { | ||
| return new BigContinuedFraction(initial, quotients.ToArray()); | ||
| } | ||
|
|
||
| fraction = BigFraction.Reciprocal(remainder); | ||
| } | ||
| } | ||
|
|
||
| public IEnumerable<BigFraction> GetBigFractions() | ||
| { | ||
| return this.Quotients | ||
| .PrependItem(this.Floor) | ||
| .SelectWithAggregate(new { Alpha = BigFraction.Zero, Bravo = BigFraction.PositiveInfinity }, (x, v) => | ||
| new | ||
| { | ||
| Alpha = x.Bravo, | ||
| Bravo = new BigFraction( | ||
| v * x.Bravo.Numerator + x.Alpha.Numerator, | ||
| v * x.Bravo.Denominator + x.Alpha.Denominator) | ||
| }) | ||
| .Select(x => x.Bravo); | ||
| } | ||
| } | ||
| } |
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