我目前正在编写一个可以表示无限大数(理论上)的类。此类的构造函数从字符串值创建对象，这就是为什么数字可能非常大但大小未知的原因。
我开始编写此类的原因是因为我希望能够编写一个程序，该程序能够对任意大的数字进行数学计算。因此，我开始编写一个类，该类可以很好地处理整数、 float 、 double 、(希望如此)小数等标准范围内的值。
以下是该类的声明和主要构造函数:
/// <summary>
/// Creates a new instance of the LargeDecimal class, which represents either a whole or decimal number.
/// </summary>
/// <param name="number">The string representation of the number.</param>
public LargeDecimal(string value)
{
string number = value.Replace(" ", "");
if (number.Contains("-") && (number.IndexOf('-') == 0)) {
number = number.Replace("-", "");
IsNegative = true;
}
// Determining whether the number is whole or contains a decimal.
if (number.IndexOf('.') == -1) {
// Does not contain a decimal.
for (int i = 0; i < number.Length; i++)
wholeDigits.Add(int.Parse(number[i].ToString()));
IsWhole = true;
}
else {
// Still check if number is whole. Add all decimal digits.
string[] numArray = number.Split('.');
int sumOfDecimalDigits = 0;
for (int i = 0; i < numArray[1].ToString().Length; i++)
sumOfDecimalDigits += int.Parse(numArray[1].ToString()[i].ToString());
if (sumOfDecimalDigits <= 0) {
// Is a whole number.
for (int i = 0; i < numArray[0].ToString().Length; i++)
wholeDigits.Add(int.Parse(numArray[0].ToString()[i].ToString()));
IsWhole = true;
}
else {
// Is not a whole number.
for (int i = 0; i < numArray[0].ToString().Length; i++)
wholeDigits.Add(int.Parse(numArray[0].ToString()[i].ToString()));
for (int i = 0; i < numArray[1].ToString().Length; i++)
decimalDigits.Add(int.Parse(numArray[1].ToString()[i].ToString()));
IsWhole = false;
}
}
}
该类基本上是通过两个 int 类型的列表来表示一个数字，其中一个列表表示构成数字的整个分区的数字，另一个列表表示构成数字的小数部分的数字编号(如果适用)。
我编写了一个 Add 方法，它接受两个 LargeDecimal 对象，将它们的值相加，然后返回一个新的 LargeDecimal 对象，其总和作为其值。虽然不完整，但它确实适用于仅为整数且均为正数或均为负数的 LargeDecimal 对象(图片!)。
我意识到添加比较两个值(大于/小于/等于)的方法在计算中非常有用。但是，我不确定如何检查 LargeDecimal 对象的值是大于还是小于另一个 LargeDecimal 的值。
在某些情况下，我可以只比较 wholeDigits 列表中的项目数量，但只有当两个值的项目数量不同时才会这样。 我不确定如何比较两个数字，例如:15498765423654973246 和 15499111137583924246。
而且我认为如果我尝试比较两个小数会变得更加困难:8573819351.86931 和 8573809999.85999
我不希望将整数计算与位值结合使用(例如，在数字 831 中，数字 8 的值将是 8 * 100，3 的值将是 3 * 10，而 1 的值将是 1 * 1)，因为我希望此类能够表示任何给定大小、长度和范围的值(而 int 不能处理最大 2147483647 的值)。
如有任何帮助，我们将不胜感激!谢谢大家!
最佳答案
我将从实现 IComparable 开始:
public class LargeDecimal : IComparable<LargeDecimal>
实现看起来像:
public int CompareTo(LargeDecimal other)
{
if (other == null) return 1;
if (ReferenceEquals(this, other)) return 0;
if (IsNegative != other.IsNegative)
{
if (other.IsNegative) return 1;
return -1;
}
int multiplier = (IsNegative) ? -1 : 1;
if (wholeDigits.Count > other.wholeDigits.Count) return 1 * multiplier;
if (wholeDigits.Count < other.wholeDigits.Count) return -1 * multiplier;
for (int i = 0; i < wholeDigits.Count; i++)
{
if (wholeDigits[i] > other.wholeDigits[i]) return 1 * multiplier;
if (wholeDigits[i] < other.wholeDigits[i]) return -1 * multiplier;
}
for (int i = 0; i < Math.Min(decimalDigits.Count, other.decimalDigits.Count); i++)
{
if (decimalDigits[i] > other.decimalDigits[i]) return 1 * multiplier;
if (decimalDigits[i] < other.decimalDigits[i]) return -1 * multiplier;
}
if (decimalDigits.Count > other.decimalDigits.Count) return 1 * multiplier;
if (decimalDigits.Count < other.decimalDigits.Count) return -1 * multiplier;
return 0;
}
更新
今晚吃晚饭时我一直在想这个项目，所以为了好玩我又做了一些。不确定这是否有帮助，但我想我会分享我的想法。
首先，我添加了一些字段来使这个类真正起作用:
public bool IsNegative { get; private set; }
public bool IsWhole { get; private set; }
private List<int> wholeDigits;
private List<int> decimalDigits;
其次，我覆盖了 ToString 方法，因此数字可以很好地显示:
public override string ToString()
{
return string.Format("{0}{1}{2}{3}",
(IsNegative) ? "-" : "",
string.Join("", wholeDigits),
(IsWhole) ? "" : ".",
(IsWhole) ? "" : string.Join("", decimalDigits));
}
然后我实现了 Equals 方法，因此它们可以按预期用于数字类型:
public static bool Equals(LargeDecimal first, LargeDecimal second)
{
return ReferenceEquals(first, null)
? ReferenceEquals(second, null)
: first.Equals(second);
}
public override bool Equals(object obj)
{
return Equals(obj as LargeDecimal);
}
protected bool Equals(LargeDecimal other)
{
return CompareTo(other) == 0;
}
public override int GetHashCode()
{
unchecked
{
var hashCode = (wholeDigits != null)
? wholeDigits.GetHashCode()
: 0;
hashCode = (hashCode * 397) ^
(decimalDigits != null ? decimalDigits.GetHashCode() : 0);
hashCode = (hashCode * 397) ^ IsNegative.GetHashCode();
hashCode = (hashCode * 397) ^ IsWhole.GetHashCode();
return hashCode;
}
}
接下来，我添加了一些实用方法来帮助完成一些即将到来的任务:
private void ResetToZero()
{
wholeDigits = new List<int> { 0 };
decimalDigits = new List<int> { 0 };
IsWhole = true;
IsNegative = false;
}
private void NormalizeLists()
{
RemoveLeadingZeroes(wholeDigits);
RemoveTrailingZeroes(decimalDigits);
IsWhole = (decimalDigits.Count == 0
|| (decimalDigits.Count == 1 && decimalDigits[0] == 0));
}
private void AddLeadingZeroes(List<int> list, int numberOfZeroes)
{
if (list == null) return;
for (int i = 0; i < numberOfZeroes; i++)
{
list.Insert(0, 0);
}
}
private void AddTrailingZeroes(List<int> list, int numberOfZeroes)
{
if (list == null) return;
for (int i = 0; i < numberOfZeroes; i++)
{
list.Add(0);
}
}
private void RemoveLeadingZeroes(List<int> list, bool leaveOneIfEmpty = true)
{
if (list == null) return;
var temp = list;
for (int i = 0; i < temp.Count; i++)
{
if (temp[i] == 0)
{
list.RemoveAt(i);
}
else
{
break;
}
}
if (leaveOneIfEmpty && !list.Any()) list.Add(0);
}
private void RemoveTrailingZeroes(List<int> list, bool leaveOneIfEmpty = true)
{
if (list == null) return;
var temp = list;
for (int i = temp.Count -1; i >= 0; i--)
{
if (temp[i] == 0)
{
list.RemoveAt(i);
}
else
{
break;
}
}
if (leaveOneIfEmpty && !list.Any()) list.Add(0);
}
接下来，我添加了一些构造函数。将数字设置为“0”的默认设置，一个解析字符串，另一个从另一个 LargeDecimal 复制值:
public LargeDecimal() : this("0") { }
public LargeDecimal(string value)
{
if (value == null) throw new ArgumentNullException("value");
string number = value.Replace(" ", ""); // remove spaces
number = number.TrimStart('0'); // remove leading zeroes
IsNegative = (number.IndexOf('-') == 0); // check for negative
number = number.Replace("-", ""); // remove dashes
// add a zero if there were no numbers before a decimal point
if (number.IndexOf('.') == 0) number = "0" + number;
// Initialize lists
wholeDigits = new List<int>();
decimalDigits = new List<int>();
// Get whole and decimal parts of the number
var numberParts = number.Split(new[] {'.'},
StringSplitOptions.RemoveEmptyEntries);
IsWhole = numberParts.Length == 1;
// Add whole digits to the list
wholeDigits.AddRange(numberParts[0].Select(n => int.Parse(n.ToString())));
// Add decimal digits to the list (if there are any)
if (numberParts.Length > 1 &&
numberParts[1].Sum(n => int.Parse(n.ToString())) > 0)
{
numberParts[1] = numberParts[1].TrimEnd('0');
decimalDigits.AddRange(numberParts[1].Select(n => int.Parse(n.ToString())));
}
NormalizeLists();
}
public LargeDecimal(LargeDecimal initializeFrom)
{
wholeDigits = initializeFrom.wholeDigits
.GetRange(0, initializeFrom.wholeDigits.Count);
decimalDigits = initializeFrom.decimalDigits
.GetRange(0, initializeFrom.decimalDigits.Count);
IsWhole = initializeFrom.IsWhole;
IsNegative = initializeFrom.IsNegative;
NormalizeLists();
}
然后我实现了 Add 和 Subtract 方法
public void Add(LargeDecimal other)
{
if (other == null) return;
if (IsNegative != other.IsNegative)
{
// Get the absolue values of the two operands
var absThis = new LargeDecimal(this) {IsNegative = false};
var absOther = new LargeDecimal(other) {IsNegative = false};
// If the signs are different and the values are the same, reset to 0.
if (absThis == absOther)
{
ResetToZero();
return;
}
// Since the signs are different, we will retain the sign of the larger number
IsNegative = absThis < absOther ? other.IsNegative : IsNegative;
// Assign the difference of the two absolute values
absThis.Subtract(absOther);
wholeDigits = absThis.wholeDigits.GetRange(0, absThis.wholeDigits.Count);
decimalDigits = absThis.decimalDigits.GetRange(0, absThis.decimalDigits.Count);
NormalizeLists();
return;
}
// start with the larger decimal digits list
var newDecimalDigits = new List<int>();
newDecimalDigits = decimalDigits.Count > other.decimalDigits.Count
? decimalDigits.GetRange(0, decimalDigits.Count)
: other.decimalDigits.GetRange(0, other.decimalDigits.Count);
// and add the smaller one to it
int carry = 0; // Represents the value of the 'tens' digit to carry over
for (int i = Math.Min(decimalDigits.Count, other.decimalDigits.Count) - 1; i >= 0; i--)
{
var result = decimalDigits[i] + other.decimalDigits[i] + carry;
carry = Convert.ToInt32(Math.Floor((decimal) result / 10));
result = result % 10;
newDecimalDigits[i] = result;
}
var newWholeDigits = new List<int>();
newWholeDigits = wholeDigits.Count > other.wholeDigits.Count
? wholeDigits.GetRange(0, wholeDigits.Count)
: other.wholeDigits.GetRange(0, other.wholeDigits.Count);
for (int i = Math.Min(wholeDigits.Count, other.wholeDigits.Count) - 1; i >= 0; i--)
{
var result = wholeDigits[i] + other.wholeDigits[i] + carry;
carry = Convert.ToInt32(Math.Floor((decimal)result / 10));
result = result % 10;
newWholeDigits[i] = result;
}
if (carry > 0) newWholeDigits.Insert(0, carry);
wholeDigits = newWholeDigits.GetRange(0, newWholeDigits.Count);
decimalDigits = newDecimalDigits.GetRange(0, newDecimalDigits.Count);
NormalizeLists();
}
public void Subtract(LargeDecimal other)
{
if (other == null) return;
// If the other value is the same as this one, then the difference is zero
if (Equals(other))
{
ResetToZero();
return;
}
// Absolute values will be used to determine how we subtract
var absThis = new LargeDecimal(this) {IsNegative = false};
var absOther = new LargeDecimal(other) {IsNegative = false};
// If the signs are different, then the difference will be the sum
if (IsNegative != other.IsNegative)
{
absThis.Add(absOther);
wholeDigits = absThis.wholeDigits.GetRange(0, absThis.wholeDigits.Count);
decimalDigits = absThis.decimalDigits.GetRange(0, absThis.decimalDigits.Count);
NormalizeLists();
return;
}
// Subtract smallNumber from bigNumber to get the difference
LargeDecimal bigNumber;
LargeDecimal smallNumber;
if (absThis < absOther)
{
bigNumber = new LargeDecimal(absOther);
smallNumber = new LargeDecimal(absThis);
}
else
{
bigNumber = new LargeDecimal(absThis);
smallNumber = new LargeDecimal(absOther);
}
// Pad the whole number and decimal number lists where necessary so that both
// LargeDecimal objects have the same count of whole and decimal numbers.
AddTrailingZeroes(
bigNumber.decimalDigits.Count < smallNumber.decimalDigits.Count
? bigNumber.decimalDigits
: smallNumber.decimalDigits,
Math.Abs(bigNumber.decimalDigits.Count - smallNumber.decimalDigits.Count));
AddLeadingZeroes(smallNumber.wholeDigits,
Math.Abs(bigNumber.wholeDigits.Count - smallNumber.wholeDigits.Count));
var newWholeDigits = new List<int>();
var newDecimalDigits = new List<int>();
bool borrowed = false; // True if we borrowed 1 from next number
for (int i = bigNumber.decimalDigits.Count - 1; i >= 0; i--)
{
if (borrowed)
{
bigNumber.decimalDigits[i] -= 1; // We borrowed one from this number last time
borrowed = false;
}
if (bigNumber.decimalDigits[i] < smallNumber.decimalDigits[i])
{
bigNumber.decimalDigits[i] += 10; // Borrow from next number and add to this one
borrowed = true;
}
// Since we're working from the back of the list, always add to the front
newDecimalDigits.Insert(0, bigNumber.decimalDigits[i] - smallNumber.decimalDigits[i]);
}
for (int i = bigNumber.wholeDigits.Count - 1; i >= 0; i--)
{
if (borrowed)
{
bigNumber.wholeDigits[i] -= 1;
borrowed = false;
}
if (bigNumber.wholeDigits[i] < smallNumber.wholeDigits[i])
{
bigNumber.wholeDigits[i] += 10;
borrowed = true;
}
newWholeDigits.Insert(0, bigNumber.wholeDigits[i] - smallNumber.wholeDigits[i]);
}
if (absThis < absOther) IsNegative = !IsNegative;
wholeDigits = newWholeDigits.GetRange(0, newWholeDigits.Count);
decimalDigits = newDecimalDigits.GetRange(0, newDecimalDigits.Count);
NormalizeLists();
}
最后覆盖数字运算符:
public static LargeDecimal operator +(LargeDecimal first, LargeDecimal second)
{
if (first == null) return second;
if (second == null) return first;
var result = new LargeDecimal(first);
result.Add(second);
return result;
}
public static LargeDecimal operator -(LargeDecimal first, LargeDecimal second)
{
if (first == null) return second;
if (second == null) return first;
var result = new LargeDecimal(first);
result.Subtract(second);
return result;
}
public static bool operator >(LargeDecimal first, LargeDecimal second)
{
if (first == null) return false;
return first.CompareTo(second) > 0;
}
public static bool operator <(LargeDecimal first, LargeDecimal second)
{
if (second == null) return false;
return second.CompareTo(first) > 0;
}
public static bool operator >=(LargeDecimal first, LargeDecimal second)
{
if (first == null) return false;
return first.CompareTo(second) >= 0;
}
public static bool operator <=(LargeDecimal first, LargeDecimal second)
{
if (second == null) return false;
return second.CompareTo(first) >= 0;
}
public static bool operator ==(LargeDecimal first, LargeDecimal second)
{
return Equals(first, second);
}
public static bool operator !=(LargeDecimal first, LargeDecimal second)
{
return !Equals(first, second);
}
感谢有趣的挑战!!
关于c# - 如何检查表示数字的对象是否大于另一个？，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/27748276/