将基数为 10 的数字转换为 .NET 中任何基数的最快方法?

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【中文标题】将基数为 10 的数字转换为 .NET 中任何基数的最快方法?【英文标题】:Quickest way to convert a base 10 number to any base in .NET? 【发布时间】:2010-10-29 18:07:20 【问题描述】:

我有一个我写的旧的(ish)C#方法,它接受一个数字并将其转换为任何基数:

string ConvertToBase(int number, char[] baseChars);

这并不是超级快速和整洁。在 .NET 中是否有一种已知的好方法可以实现这一目标?

我正在寻找允许我使用 any 基数和任意字符串的东西。

这仅允许碱基 16、10、8 和 2:

Convert.ToString(1, x);

我想利用数字、全部小写和全部大写字母来利用它来实现非常高的基数。就像在 this thread 中一样,但对于 C# 而不是 javascript

有人知道在 C# 中执行此操作的好方法吗?

【问题讨论】:

【参考方案1】:

Convert.ToString 可用于将数字转换为其在指定基数中的等效字符串表示形式。

例子:

string binary = Convert.ToString(5, 2); // convert 5 to its binary representation
Console.WriteLine(binary);              // prints 101

但是,正如 cmets 所指出的,Convert.ToString 仅支持以下有限但通常足够的基数集:2、8、10 或 16。

更新(以满足转换为任何基的要求):

我不知道 BCL 中有任何方法能够将数字转换为任何基数,因此您必须编写自己的小型实用程序函数。一个简单的示例看起来像这样(请注意,这肯定可以通过替换字符串连接来更快):

class Program

    static void Main(string[] args)
    
        // convert to binary
        string binary = IntToString(42, new char[]  '0', '1' );

        // convert to hexadecimal
        string hex = IntToString(42, 
            new char[]  '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
                         'A', 'B', 'C', 'D', 'E', 'F');

        // convert to hexavigesimal (base 26, A-Z)
        string hexavigesimal = IntToString(42, 
            Enumerable.Range('A', 26).Select(x => (char)x).ToArray());

        // convert to sexagesimal
        string xx = IntToString(42, 
            new char[]  '0','1','2','3','4','5','6','7','8','9',
            'A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z',
            'a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x');
    

    public static string IntToString(int value, char[] baseChars)
    
        string result = string.Empty;
        int targetBase = baseChars.Length;

        do
        
            result = baseChars[value % targetBase] + result;
            value = value / targetBase;
         
        while (value > 0);

        return result;
    

    /// <summary>
    /// An optimized method using an array as buffer instead of 
    /// string concatenation. This is faster for return values having 
    /// a length > 1.
    /// </summary>
    public static string IntToStringFast(int value, char[] baseChars)
    
        // 32 is the worst cast buffer size for base 2 and int.MaxValue
        int i = 32;
        char[] buffer = new char[i];
        int targetBase= baseChars.Length;

        do
        
            buffer[--i] = baseChars[value % targetBase];
            value = value / targetBase;
        
        while (value > 0);

        char[] result = new char[32 - i];
        Array.Copy(buffer, i, result, 0, 32 - i);

        return new string(result);
    

更新 2(性能改进)

使用数组缓冲区而不是字符串连接来构建结果字符串可以提高性能,尤其是在大数字上(参见方法IntToStringFast)。在最好的情况下(即可能的最长输入),这种方法大约***倍。但是,对于 1 位数字(即目标基数中的 1 位数字),IntToString 会更快。

【讨论】:

应该注意的是,这只支持基数 2,8,10,16 - 而不是问题中的“任何”。因为你永远不知道什么时候需要六十进制;-p 六进制听起来很有趣。 太棒了。但是反函数在哪里呢? :// 我这里有一个首过反函数:***.com/questions/3579970/… 对于“十六进制”转换(对于类似列的 excel),我必须将这一行 result = baseChars[value % targetBase] + result; 替换为 result = baseChars[--value % targetBase] + result;。我没有针对其他情况进行测试,因为我只需要从列号转换为 excel 列名。【参考方案2】:

this forum post 的这门课能帮到你吗?

public class BaseConverter  

public static string ToBase(string number, int start_base, int target_base)  

  int base10 = this.ToBase10(number, start_base); 
  string rtn = this.FromBase10(base10, target_base); 
  return rtn; 

 

public static int ToBase10(string number, int start_base)  

  if (start_base < 2 || start_base > 36) return 0; 
  if (start_base == 10) return Convert.ToInt32(number); 

  char[] chrs = number.ToCharArray(); 
  int m = chrs.Length - 1; 
  int n = start_base; 
  int x; 
  int rtn = 0; 

  foreach(char c in chrs)  

    if (char.IsNumber(c)) 
      x = int.Parse(c.ToString()); 
    else 
      x = Convert.ToInt32(c) - 55; 

    rtn += x * (Convert.ToInt32(Math.Pow(n, m))); 

    m--; 

   

  return rtn; 

 

public static string FromBase10(int number, int target_base)  

  if (target_base < 2 || target_base > 36) return ""; 
  if (target_base == 10) return number.ToString(); 

  int n = target_base; 
  int q = number; 
  int r; 
  string rtn = ""; 

  while (q >= n)  

    r = q % n; 
    q = q / n; 

    if (r < 10) 
      rtn = r.ToString() + rtn; 
    else 
      rtn = Convert.ToChar(r + 55).ToString() + rtn; 

   

  if (q < 10) 
    rtn = q.ToString() + rtn; 
  else 
    rtn = Convert.ToChar(q + 55).ToString() + rtn; 

  return rtn; 

 


完全未经测试...让我知道它是否有效! (复制粘贴以防论坛帖子消失或其他情况......)

【讨论】:

关闭.. 稍后我会玩。需要一些工作才能获取任何字符,但这是朝着正确方向迈出的一步。我将速度与我自己的方法进行比较! 如果你改进它记得分享它。其他人可能也想要 ot =) @joshcomley 周末过得怎么样? ;) 这是一个长周末 :D【参考方案3】:

我使用它来将 Guid 存储为较短的字符串(但仅限于使用 106 个字符)。 如果有人对此感兴趣,是我将字符串解码回数值的代码(在这种情况下,我使用 2 ulongs 作为 Guid 值,而不是对 Int128 进行编码(因为我使用的是 3.5 而不是 4.0)。 为清楚起见,CODE 是一个具有 106 个唯一字符的字符串 const。 ConvertLongsToBytes 相当乏味。

private static Guid B106ToGuid(string pStr)
    
        try
        
            ulong tMutl = 1, tL1 = 0, tL2 = 0, targetBase = (ulong)CODE.Length;
            for (int i = 0; i < pStr.Length / 2; i++)
            
                tL1 += (ulong)CODE.IndexOf(pStr[i]) * tMutl;
                tL2 += (ulong)CODE.IndexOf(pStr[pStr.Length / 2 + i]) * tMutl;
                tMutl *= targetBase;
            
            return new Guid(ConvertLongsToBytes(tL1, tL2));
        
        catch (Exception ex)
        
            throw new Exception("B106ToGuid failed to convert string to Guid", ex);
        
    

【讨论】:

【参考方案4】:

我也在寻找一种将十进制数转换为 [2..36] 范围内的另一个基数的快速方法,因此我开发了以下代码。它易于遵循并使用 Stringbuilder 对象作为字符缓冲区的代理,我们可以逐个字符地索引该字符缓冲区。与替代方案相比,该代码似乎非常快,并且比初始化字符数组中的单个字符要快得多。

为了您自己的使用,您可能更喜欢: 1/ 返回一个空白字符串而不是抛出异常。 2/删除基数检查,使方法运行得更快 3/ 用 32 个 '0' 初始化 Stringbuilder 对象并删除行 result.Remove(0, i );。这将导致字符串返回前导零并进一步提高速度。 4/ 使 Stringbuilder 对象成为类中的静态字段,因此无论调用多少次 DecimalToBase 方法,Stringbuilder 对象都只会初始化一次。如果您执行此更改,上面的 3 将不再起作用。

我希望有人觉得这很有用:)

原子悖论

        static string DecimalToBase(int number, int radix)
    
        // Check that the radix is between 2 and 36 inclusive
        if ( radix < 2 || radix > 36 )
            throw new ArgumentException("ConvertToBase(int number, int radix) - Radix must be between 2 and 36.");

        // Create a buffer large enough to hold the largest int value represented in binary digits 
        StringBuilder result = new StringBuilder("                                ");  // 32 spaces

        // The base conversion calculates the digits in reverse order so use
        // an index to point to the last unused space in our buffer
        int i = 32; 

        // Convert the number to the new base
        do
        
            int remainder = number % radix;
            number = number / radix;
            if(remainder <= 9)
                result[--i] = (char)(remainder + '0');  // Converts [0..9] to ASCII ['0'..'9']
            else
                result[--i] = (char)(remainder + '7');  // Converts [10..36] to ASCII ['A'..'Z']
         while ( number > 0 );

        // Remove the unwanted padding from the front of our buffer and return the result
        // Note i points to the last unused character in our buffer
        result.Remove( 0, i );
        return (result.ToString());
    

【讨论】:

【参考方案5】:

我也有类似的需求,除了我还需要对“数字”进行数学运算。我在这里接受了一些建议,并创建了一个类来完成所有这些有趣的事情。它允许使用任何 unicode 字符来表示一个数字,并且它也适用于小数。

这个类很容易使用。只需创建一个类型为New BaseNumber 的数字,设置一些属性,然后关闭即可。例程会自动在基数 10 和基数 x 之间切换,并且您设置的值保留在您设置的基数中,因此不会丢失准确性(直到转换,但即使这样,精度损失也应该非常小,因为这例程尽可能使用DoubleLong

我无法控制这个例程的速度。它可能很慢,所以我不确定它是否适合提出问题的人的需求,但它肯定是灵活的,所以希望其他人可以使用它。

对于可能需要此代码来计算 Excel 中的下一列的其他任何人,我将包含我使用的利用此类的循环代码。

Public Class BaseNumber

    Private _CharacterArray As List(Of Char)

    Private _BaseXNumber As String
    Private _Base10Number As Double?

    Private NumberBaseLow As Integer
    Private NumberBaseHigh As Integer

    Private DecimalSeparator As Char = System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberDecimalSeparator
    Private GroupSeparator As Char = System.Globalization.CultureInfo.CurrentCulture.NumberFormat.NumberGroupSeparator

    Public Sub UseCapsLetters()
        'http://unicodelookup.com
        TrySetBaseSet(65, 90)
    End Sub

    Public Function GetCharacterArray() As List(Of Char)
        Return _CharacterArray
    End Function

    Public Sub SetCharacterArray(CharacterArray As String)
        _CharacterArray = New List(Of Char)
        _CharacterArray.AddRange(CharacterArray.ToList)

        TrySetBaseSet(_CharacterArray)
    End Sub

    Public Sub SetCharacterArray(CharacterArray As List(Of Char))
        _CharacterArray = CharacterArray
        TrySetBaseSet(_CharacterArray)
    End Sub

    Public Sub SetNumber(Value As String)
        _BaseXNumber = Value
        _Base10Number = Nothing
    End Sub

    Public Sub SetNumber(Value As Double)
        _Base10Number = Value
        _BaseXNumber = Nothing
    End Sub

    Public Function GetBaseXNumber() As String
        If _BaseXNumber IsNot Nothing Then
            Return _BaseXNumber
        Else
            Return ToBaseString()
        End If
    End Function

    Public Function GetBase10Number() As Double
        If _Base10Number IsNot Nothing Then
            Return _Base10Number
        Else
            Return ToBase10()
        End If
    End Function

    Private Sub TrySetBaseSet(Values As List(Of Char))
        For Each value As Char In _BaseXNumber
            If Not Values.Contains(value) Then
                Throw New ArgumentOutOfRangeException("The string has a value, " & value & ", not contained in the selected 'base' set.")
                _CharacterArray.Clear()
                DetermineNumberBase()
            End If
        Next

        _CharacterArray = Values

    End Sub

    Private Sub TrySetBaseSet(LowValue As Integer, HighValue As Integer)

        Dim HighLow As KeyValuePair(Of Integer, Integer) = GetHighLow()

        If HighLow.Key < LowValue OrElse HighLow.Value > HighValue Then
            Throw New ArgumentOutOfRangeException("The string has a value not contained in the selected 'base' set.")
            _CharacterArray.Clear()
            DetermineNumberBase()
        End If

        NumberBaseLow = LowValue
        NumberBaseHigh = HighValue

    End Sub

    Private Function GetHighLow(Optional Values As List(Of Char) = Nothing) As KeyValuePair(Of Integer, Integer)
        If Values Is Nothing Then
            Values = _BaseXNumber.ToList
        End If

        Dim lowestValue As Integer = Convert.ToInt32(Values(0))
        Dim highestValue As Integer = Convert.ToInt32(Values(0))

        Dim currentValue As Integer

        For Each value As Char In Values

            If value <> DecimalSeparator AndAlso value <> GroupSeparator Then
                currentValue = Convert.ToInt32(value)
                If currentValue > highestValue Then
                    highestValue = currentValue
                End If
                If currentValue < lowestValue Then
                    currentValue = lowestValue
                End If
            End If
        Next

        Return New KeyValuePair(Of Integer, Integer)(lowestValue, highestValue)

    End Function

    Public Sub New(BaseXNumber As String)
        _BaseXNumber = BaseXNumber
        DetermineNumberBase()
    End Sub

    Public Sub New(BaseXNumber As String, NumberBase As Integer)
        Me.New(BaseXNumber, Convert.ToInt32("0"c), NumberBase)
    End Sub

    Public Sub New(BaseXNumber As String, NumberBaseLow As Integer, NumberBaseHigh As Integer)
        _BaseXNumber = BaseXNumber
        Me.NumberBaseLow = NumberBaseLow
        Me.NumberBaseHigh = NumberBaseHigh
    End Sub

    Public Sub New(Base10Number As Double)
        _Base10Number = Base10Number
    End Sub

    Private Sub DetermineNumberBase()
        Dim highestValue As Integer

        Dim currentValue As Integer

        For Each value As Char In _BaseXNumber

            currentValue = Convert.ToInt32(value)
            If currentValue > highestValue Then
                highestValue = currentValue
            End If
        Next

        NumberBaseHigh = highestValue
        NumberBaseLow = Convert.ToInt32("0"c) 'assume 0 is the lowest

    End Sub

    Private Function ToBaseString() As String
        Dim Base10Number As Double = _Base10Number

        Dim intPart As Long = Math.Truncate(Base10Number)
        Dim fracPart As Long = (Base10Number - intPart).ToString.Replace(DecimalSeparator, "")

        Dim intPartString As String = ConvertIntToString(intPart)
        Dim fracPartString As String = If(fracPart <> 0, DecimalSeparator & ConvertIntToString(fracPart), "")

        Return intPartString & fracPartString

    End Function

    Private Function ToBase10() As Double
        Dim intPartString As String = _BaseXNumber.Split(DecimalSeparator)(0).Replace(GroupSeparator, "")
        Dim fracPartString As String = If(_BaseXNumber.Contains(DecimalSeparator), _BaseXNumber.Split(DecimalSeparator)(1), "")

        Dim intPart As Long = ConvertStringToInt(intPartString)
        Dim fracPartNumerator As Long = ConvertStringToInt(fracPartString)
        Dim fracPartDenominator As Long = ConvertStringToInt(GetEncodedChar(1) & String.Join("", Enumerable.Repeat(GetEncodedChar(0), fracPartString.ToString.Length)))

        Return Convert.ToDouble(intPart + fracPartNumerator / fracPartDenominator)

    End Function

    Private Function ConvertIntToString(ValueToConvert As Long) As String
        Dim result As String = String.Empty
        Dim targetBase As Long = GetEncodingCharsLength()

        Do
            result = GetEncodedChar(ValueToConvert Mod targetBase) & result
            ValueToConvert = ValueToConvert \ targetBase
        Loop While ValueToConvert > 0

        Return result
    End Function

    Private Function ConvertStringToInt(ValueToConvert As String) As Long
        Dim result As Long
        Dim targetBase As Integer = GetEncodingCharsLength()
        Dim startBase As Integer = GetEncodingCharsStartBase()

        Dim value As Char
        For x As Integer = 0 To ValueToConvert.Length - 1
            value = ValueToConvert(x)
            result += GetDecodedChar(value) * Convert.ToInt32(Math.Pow(GetEncodingCharsLength, ValueToConvert.Length - (x + 1)))
        Next

        Return result

    End Function

    Private Function GetEncodedChar(index As Integer) As Char
        If _CharacterArray IsNot Nothing AndAlso _CharacterArray.Count > 0 Then
            Return _CharacterArray(index)
        Else
            Return Convert.ToChar(index + NumberBaseLow)
        End If
    End Function

    Private Function GetDecodedChar(character As Char) As Integer
        If _CharacterArray IsNot Nothing AndAlso _CharacterArray.Count > 0 Then
            Return _CharacterArray.IndexOf(character)
        Else
            Return Convert.ToInt32(character) - NumberBaseLow
        End If
    End Function

    Private Function GetEncodingCharsLength() As Integer
        If _CharacterArray IsNot Nothing AndAlso _CharacterArray.Count > 0 Then
            Return _CharacterArray.Count
        Else
            Return NumberBaseHigh - NumberBaseLow + 1
        End If
    End Function

    Private Function GetEncodingCharsStartBase() As Integer
        If _CharacterArray IsNot Nothing AndAlso _CharacterArray.Count > 0 Then
            Return GetHighLow.Key
        Else
            Return NumberBaseLow
        End If
    End Function
End Class

现在让代码循环遍历 Excel 列:

    Public Function GetColumnList(DataSheetID As String) As List(Of String)
        Dim workingColumn As New BaseNumber("A")
        workingColumn.SetCharacterArray("@ABCDEFGHIJKLMNOPQRSTUVWXYZ")

        Dim listOfPopulatedColumns As New List(Of String)
        Dim countOfEmptyColumns As Integer

        Dim colHasData As Boolean
        Dim cellHasData As Boolean

        Do
            colHasData = True
            cellHasData = False
            For r As Integer = 1 To GetMaxRow(DataSheetID)
                cellHasData = cellHasData Or XLGetCellValue(DataSheetID, workingColumn.GetBaseXNumber & r) <> ""
            Next
            colHasData = colHasData And cellHasData

            'keep trying until we get 4 empty columns in a row
            If colHasData Then
                listOfPopulatedColumns.Add(workingColumn.GetBaseXNumber)
                countOfEmptyColumns = 0
            Else
                countOfEmptyColumns += 1
            End If

            'we are already starting with column A, so increment after we check column A
            Do
                workingColumn.SetNumber(workingColumn.GetBase10Number + 1)
            Loop Until Not workingColumn.GetBaseXNumber.Contains("@")

        Loop Until countOfEmptyColumns > 3

        Return listOfPopulatedColumns

    End Function

您会注意到 Excel 部分的重要部分是 0 由重新编号中的 @ 标识。所以我只是过滤掉所有带有@的数字,然后得到正确的序列(A、B、C、...、Z、AA、AB、AC、...)。

【讨论】:

【参考方案6】:

I recently blogged about this。我的实现在计算过程中不使用任何字符串操作,这使得它非常快。支持从 2 到 36 转换为任何数字系统:

/// <summary>
/// Converts the given decimal number to the numeral system with the
/// specified radix (in the range [2, 36]).
/// </summary>
/// <param name="decimalNumber">The number to convert.</param>
/// <param name="radix">The radix of the destination numeral system (in the range [2, 36]).</param>
/// <returns></returns>
public static string DecimalToArbitrarySystem(long decimalNumber, int radix)

    const int BitsInLong = 64;
    const string Digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";

    if (radix < 2 || radix > Digits.Length)
        throw new ArgumentException("The radix must be >= 2 and <= " + Digits.Length.ToString());

    if (decimalNumber == 0)
        return "0";

    int index = BitsInLong - 1;
    long currentNumber = Math.Abs(decimalNumber);
    char[] charArray = new char[BitsInLong];

    while (currentNumber != 0)
    
        int remainder = (int)(currentNumber % radix);
        charArray[index--] = Digits[remainder];
        currentNumber = currentNumber / radix;
    

    string result = new String(charArray, index + 1, BitsInLong - index - 1);
    if (decimalNumber < 0)
    
        result = "-" + result;
    

    return result;

我还实现了一个快速反函数,以防万一有人需要它: Arbitrary to Decimal Numeral System.

【讨论】:

我对这个页面上的所有解决方案都进行了性能测试,这是最快的,大约是最后短解决方案的两倍。 这是什么result = "-" + result?那是某种填充物吗?我如何修改代码以便只使用 A-Z 或 0-9 作为填充字符? result = "-" + result中的"-"代表负数的负号。这不是填充字符。 你可以取消字符串 concat 如果你把'-'放到index的charArray中,然后在你创建一个新字符串之前减少索引【参考方案7】:

参加这个聚会很晚,但我最近为工作中的一个项目编写了以下帮助程序类。它旨在将短字符串转换为数字并再次转换回来(一个简单的perfect hash 函数),但它也将在任意基数之间执行数字转换。 Base10ToString 方法实现回答了最初发布的问题。

需要传递给类构造函数的shouldSupportRoundTripping 标志,以防止在转换为base-10 并再次返回期间丢失数字字符串中的前导数字(鉴于我的要求,这很重要!)。大多数情况下,数字字符串中前导 0 的丢失可能不会成为问题。

不管怎样,代码如下:

using System;
using System.Collections.Generic;
using System.Linq;

namespace ***

    /// <summary>
    /// Contains methods used to convert numbers between base-10 and another numbering system.
    /// </summary>
    /// <remarks>
    /// <para>
    /// This conversion class makes use of a set of characters that represent the digits used by the target
    /// numbering system. For example, binary would use the digits 0 and 1, whereas hex would use the digits
    /// 0 through 9 plus A through F. The digits do not have to be numerals.
    /// </para>
    /// <para>
    /// The first digit in the sequence has special significance. If the number passed to the
    /// <see cref="StringToBase10"/> method has leading digits that match the first digit, then those leading
    /// digits will effectively be 'lost' during conversion. Much of the time this won't matter. For example,
    /// "0F" hex will be converted to 15 decimal, but when converted back to hex it will become simply "F",
    /// losing the leading "0". However, if the set of digits was A through Z, and the number "ABC" was
    /// converted to base-10 and back again, then the leading "A" would be lost. The <see cref="System.Boolean"/>
    /// flag passed to the constructor allows 'round-tripping' behaviour to be supported, which will prevent
    /// leading digits from being lost during conversion.
    /// </para>
    /// <para>
    /// Note that numeric overflow is probable when using longer strings and larger digit sets.
    /// </para>
    /// </remarks>
    public class Base10Converter
    
        const char NullDigit = '\0';

        public Base10Converter(string digits, bool shouldSupportRoundTripping = false)
            : this(digits.ToCharArray(), shouldSupportRoundTripping)
        
        

        public Base10Converter(IEnumerable<char> digits, bool shouldSupportRoundTripping = false)
        
            if (digits == null)
            
                throw new ArgumentNullException("digits");
            

            if (digits.Count() == 0)
            
                throw new ArgumentException(
                    message: "The sequence is empty.",
                    paramName: "digits"
                    );
            

            if (!digits.Distinct().SequenceEqual(digits))
            
                throw new ArgumentException(
                    message: "There are duplicate characters in the sequence.",
                    paramName: "digits"
                    );
            

            if (shouldSupportRoundTripping)
            
                digits = (new[]  NullDigit ).Concat(digits);
            

            _digitToIndexMap =
                digits
                .Select((digit, index) => new  digit, index )
                .ToDictionary(keySelector: x => x.digit, elementSelector: x => x.index);

            _radix = _digitToIndexMap.Count;

            _indexToDigitMap =
                _digitToIndexMap
                .ToDictionary(keySelector: x => x.Value, elementSelector: x => x.Key);
        

        readonly Dictionary<char, int> _digitToIndexMap;
        readonly Dictionary<int, char> _indexToDigitMap;
        readonly int _radix;

        public long StringToBase10(string number)
        
            Func<char, int, long> selector =
                (c, i) =>
                
                    int power = number.Length - i - 1;

                    int digitIndex;
                    if (!_digitToIndexMap.TryGetValue(c, out digitIndex))
                    
                        throw new ArgumentException(
                            message: String.Format("Number contains an invalid digit '0' at position 1.", c, i),
                            paramName: "number"
                            );
                    

                    return Convert.ToInt64(digitIndex * Math.Pow(_radix, power));
                ;

            return number.Select(selector).Sum();
        

        public string Base10ToString(long number)
        
            if (number < 0)
            
                throw new ArgumentOutOfRangeException(
                    message: "Value cannot be negative.",
                    paramName: "number"
                    );
            

            string text = string.Empty;

            long remainder;
            do
            
                number = Math.DivRem(number, _radix, out remainder);

                char digit;
                if (!_indexToDigitMap.TryGetValue((int) remainder, out digit) || digit == NullDigit)
                
                    throw new ArgumentException(
                        message: "Value cannot be converted given the set of digits used by this converter.",
                        paramName: "number"
                        );
                

                text = digit + text;
            
            while (number > 0);

            return text;
        
    

这也可以被子类化以派生自定义数字转换器:

namespace ***

    public sealed class BinaryNumberConverter : Base10Converter
    
        public BinaryNumberConverter()
            : base(digits: "01", shouldSupportRoundTripping: false)
        
        
    

    public sealed class HexNumberConverter : Base10Converter
    
        public HexNumberConverter()
            : base(digits: "0123456789ABCDEF", shouldSupportRoundTripping: false)
        
        
    

代码会这样使用:

using System.Diagnostics;

namespace ***

    class Program
    
        static void Main(string[] args)
        
            
                var converter = new Base10Converter(
                    digits: "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789abcdefghijklmnopqrstuvwxyz",
                    shouldSupportRoundTripping: true
                    );

                long number = converter.StringToBase10("Atoz");
                string text = converter.Base10ToString(number);
                Debug.Assert(text == "Atoz");
            

            
                var converter = new HexNumberConverter();

                string text = converter.Base10ToString(255);
                long number = converter.StringToBase10(text);
                Debug.Assert(number == 255);
            
        
    

【讨论】:

【参考方案8】:

也可以使用已接受版本的略微修改版本,并根据需要调整基本字符串:

public static string Int32ToString(int value, int toBase)

    string result = string.Empty;
    do
    
        result = "0123456789ABCDEF"[value % toBase] + result;
        value /= toBase;
    
    while (value > 0);

    return result;

【讨论】:

【参考方案9】:

快速“FROM”和“TO”方法

我迟到了,但我将之前的答案复合并改进了它们。我认为这两种方法比迄今为止发布的任何其他方法都快。我能够在单核机器上在不到 400 毫秒的时间内将 1,000,000 个数字从 36 进制转换为 36 进制。

以下示例适用于 base 62。更改 BaseChars 数组以在任何其他基础之间进行转换。

private static readonly char[] BaseChars = 
         "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz".ToCharArray();
private static readonly Dictionary<char, int> CharValues = BaseChars
           .Select((c,i)=>new Char=c, Index=i)
           .ToDictionary(c=>c.Char,c=>c.Index);

public static string LongToBase(long value)

   long targetBase = BaseChars.Length;
   // Determine exact number of characters to use.
   char[] buffer = new char[Math.Max( 
              (int) Math.Ceiling(Math.Log(value + 1, targetBase)), 1)];

   var i = buffer.Length;
   do
   
       buffer[--i] = BaseChars[value % targetBase];
       value = value / targetBase;
   
   while (value > 0);

   return new string(buffer, i, buffer.Length - i);


public static long BaseToLong(string number) 
 
    char[] chrs = number.ToCharArray(); 
    int m = chrs.Length - 1; 
    int n = BaseChars.Length, x;
    long result = 0; 
    for (int i = 0; i < chrs.Length; i++)
    
        x = CharValues[ chrs[i] ];
        result += x * (long)Math.Pow(n, m--);
    
    return result;  
 

编辑 (2018-07-12)

修复了@AdrianBotor(参见 cmets)发现的将 46655 转换为基数 36 的极端情况。这是由计算 Math.Log(46656, 36) 的小浮点错误引起的,该错误恰好是 3,但 .NET 返回 3 + 4.44e-16,这会导致输出缓冲区中出现额外字符。

【讨论】:

@AdrianBotor 无法重现您的问题:BaseToLong(LongToBase(46655)) == 46655 @Diego,抱歉回复晚了。让我们用0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ 初始化数组并转换值46655。结果应该是ZZZ,但在调试器中我得到\0ZZZ。只有这个值才能获得额外的\0。例如值46654 正确转换为ZZY @AdrianBotor 很好。通过将 LongToBase 中的 return 语句调整为 return new string(buffer, (int) i, buffer.Length - (int)i); 来解决【参考方案10】:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConvertToAnyBase

   class Program
    
        static void Main(string[] args)
        
            var baseNumber = int.Parse(Console.ReadLine());
            var number = int.Parse(Console.ReadLine());
            string conversion = "";


            while(number!=0)
            

                conversion += Convert.ToString(number % baseNumber);
                number = number / baseNumber;
            
            var conversion2 = conversion.ToArray().Reverse();
            Console.WriteLine(string.Join("", conversion2));


       
    

【讨论】:

这是从 1 到 10 的基数。【参考方案11】:

这是基于 Pavel 的回答,但取消了他不必要的负数字符串连接。基数也是由传入的字符定义的,所以如果你想使用字符 ABC 将数字转换为基数 3,请传递“ABC” - 3 的字符串长度是基数:

C#

public static string ToBase(long base10, string baseChars = "0123456789ABCDEFGHIJKLMNOPQRTSUVWXYZ")

    if (baseChars.Length < 2)
        throw new ArgumentException("baseChars must be at least 2 chars long");
    if (base10 == 0L)
        return baseChars[0].ToString();
    bool isNegative = base10 < 0L;
    int radix = baseChars.Length;
    int index = 64; // because it's how long a string will be if the basechars are 2 long (binary)
    var chars = new char[index + 1]; // 65 chars, 64 from above plus one for sign if it's negative
    base10 = Math.Abs(base10);
    while (base10 > 0L)
    
        chars[index] = baseChars[(int)(base10 % radix)];
        base10 /= radix;
        index--;
    

    if (isNegative)
    
        chars[index] = '-';
        index--;
    

    return new string(chars, index + 1, chars.Length - index - 1);

VB.NET

Public Shared Function ToBase(base10 As Long, Optional baseChars As String = "0123456789ABCDEFGHIJKLMNOPQRTSUVWXYZ") As String

    If baseChars.Length < 2 Then Throw New ArgumentException("baseChars must be at least 2 chars long")

    If base10 = 0 Then Return baseChars(0)

    Dim isNegative = base10 < 0
    Dim radix = baseChars.Length
    Dim index As Integer = 64 'because it's how long a string will be if the basechars are 2 long (binary)
    Dim chars(index) As Char '65 chars, 64 from above plus one for sign if it's negative

    base10 = Math.Abs(base10)


    While base10 > 0
        chars(index) = baseChars(base10 Mod radix)
        base10 \= radix

        index -= 1
    End While

    If isNegative Then
        chars(index) = "-"c
        index -= 1
    End If

    Return New String(chars, index + 1, UBound(chars) - index)

End Function

【讨论】:

【参考方案12】:

这是一种相当简单的方法,但它可能不是最快的。它非常强大,因为它是可组合的。

public static IEnumerable<int> ToBase(this int x, int b)

    IEnumerable<int> ToBaseReverse()
    
        if (x == 0)
        
            yield return 0;
            yield break;
        
        int z = x;
        while (z > 0)
        
            yield return z % b;
            z = z / b;
        
    

    return ToBaseReverse().Reverse();

将它与这个简单的扩展方法结合起来,现在可以得到任何基础:

public static string ToBase(this int number, string digits) =>
    String.Concat(number.ToBase(digits.Length).Select(x => digits[x]));

可以这样使用:

var result = 23.ToBase("01");
var result2 = 23.ToBase("012X");

Console.WriteLine(result);
Console.WriteLine(result2);

输出是:

10111 11X

【讨论】:

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