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C#，《小白学程序》第二十七课：大数四则运算之“运算符重载”的算法及源程序

article 2024/11/15 13:39:17

1 文本格式

using System;
using System.Text;
using System.Collections;
using System.Collections.Generic;

/// <summary>
/// 大数的四则（加减乘除）运算
/// 及其运算符重载（取余数）
/// </summary>
public class BigNumber
{
    private string Buffer { get; set; } = "";
    private string Sign { get; set; } = "";
    public BigNumber(int n) { Next(n); }
    public BigNumber(string b, string s = "")
    {
        Buffer = b;
        Sign = s;
    }
    public BigNumber Clone()
    {
        BigNumber r = new BigNumber(Buffer, Sign);
        return r;
    }
    public int Length { get { return Buffer.Length; } }

    /// <summary>
    /// 随机生成任意长度的大数（BigNumber）
    /// </summary>
    /// <param name="n">位数</param>
    /// <returns></returns>
    public void Next(int n)
    {
        Random rnd = new Random();
        StringBuilder sb = new StringBuilder();
        sb.Append((rnd.Next(9) + 1).ToString());
        for (int i = 1; i < n; i++)
        {
            sb.Append((rnd.Next(10)).ToString());
        }
        Buffer = sb.ToString();
    }

    /// <summary>
    /// 字符串型的数字转为数组(低位（右）在前)
    /// </summary>
    /// <param name="a"></param>
    /// <param name="n">最大位数，后面留0</param>
    /// <returns></returns>
    public static int[] string_to_digitals(string a, int n)
    {
        char[] c = a.ToCharArray();
        int[] d = new int[n];
        for (int i = a.Length - 1, j = 0; i >= 0; i--)
        {
            if (c[i] == '-') continue;
            d[j++] = c[i] - '0';
        }
        return d;
    }

    /// <summary>
    /// 数组型数字转为字符串型(低位（右）在前)
    /// </summary>
    /// <param name="d"></param>
    /// <returns></returns>
    public static string digitals_to_string(int[] d)
    {
        int n = d.Length;
        int k = n - 1;
        while ((k >= 0) && (d[k] == 0)) k--;
        if (k >= 0)
        {
            StringBuilder sb = new StringBuilder();
            for (; k >= 0; k--) sb.Append(d[k]);
            return sb.ToString();
        }
        else
        {
            return "0";
        }
    }

    /// <summary>
    /// 大数加法 c = a + b
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static string big_integer_plus(string a, string b)
    {
        int n = Math.Max(a.Length, b.Length) + 1;
        // 位数不长的数字直接计算
        if (n <= 18)
        {
            return (ulong.Parse(a) + ulong.Parse(b)).ToString();
        }

        int[] da = string_to_digitals(a, n);
        int[] db = string_to_digitals(b, n);

        int[] dc = new int[n];
        Array.Copy(da, dc, n);
        for (int i = 0; i < (n - 1); i++)
        {
            dc[i] = dc[i] + db[i];
            if (dc[i] > 9)
            {
                dc[i] -= 10;
                dc[i + 1] += 1;
            }
        }
        return digitals_to_string(dc);
    }

    /// <summary>
    /// 大数减法 c = a - b
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static string big_integer_subtract(string a, string b)
    {
        int na = a.Length;
        int nb = b.Length;
        int n = Math.Max(na, nb) + 1;
        if (n <= 18)
        {
            return (ulong.Parse(a) - ulong.Parse(b)).ToString();
        }
        int[] da = string_to_digitals(a, n);
        int[] db = string_to_digitals(b, n);

        for (int i = 0; i < na; i++)
        {
            da[i] -= db[i];
            if (da[i] < 0)
            {
                da[i] += 10;
                da[i + 1] -= 1;
            }
        }
        return digitals_to_string(da);
    }

    /// <summary>
    /// 大数乘法 c = a * b
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static string big_integer_multiply(string a, string b)
    {
        int na = a.Length;
        int nb = b.Length;
        int n = na + nb + 1;
        int[] da = string_to_digitals(a, n);
        int[] db = string_to_digitals(b, n);

        int[] dc = new int[n];
        for (int i = 0; i < na; i++)
        {
            for (int j = 0; j < nb; j++)
            {
                dc[i + j] += da[i] * db[j];
            }
        }
        for (int i = 0; i < n; i++)
        {
            if (dc[i] >= 10)
            {
                dc[i + 1] += (dc[i] / 10);
                dc[i] %= 10;
            }
        }

        return digitals_to_string(dc);
    }

    /// <summary>
    /// 比较a，b的大小，返回1，0，-1
    /// 数据从低位（右）往高位（左）存储;
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static int big_integer_compare(int[] a, int[] b)
    {
        for (int i = a.Length - 1; i >= 0; i--)
        {
            if (a[i] > b[i]) return 1;
            else if (a[i] < b[i]) return -1;
        }
        return 0;
    }

    public static int big_integer_compare(string a, string b)
    {
        int n = Math.Max(a.Length, b.Length);
        int[] da = string_to_digitals(a, n);
        int[] db = string_to_digitals(a, n);
        return big_integer_compare(da, db);
    }

    /// <summary>
    /// 大数除法 c = a / b % d
    /// c 为商，d 为余数。
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <param name="d">余数</param>
    /// <returns>商c</returns>
    public static string big_integer_divide(string a, string b, out string d)
    {
        int n = a.Length;
        int[] db = string_to_digitals(b, n);

        string q = a;
        List<string> p = new List<string>();
        int[] dq = string_to_digitals(q, n);
        while (big_integer_compare(dq, db) >= 0)
        {
            int len = q.Length - b.Length;
            string v2 = b + String.Join("", new int[len]);
            int[] dv = string_to_digitals(v2, n);
            if (big_integer_compare(dq, dv) < 0)
            {
                len--;
                v2 = b + String.Join("", new int[len]);
                dv = string_to_digitals(v2, n);
            }

            string v1 = "1" + String.Join("", new int[len]);
            while (big_integer_compare(dq, dv) >= 0)
            {
                p.Add(v1);
                q = big_integer_subtract(q, v2);
                dq = string_to_digitals(q, n);
            }
        }

        d = q;

        string r = p[0];
        for (int i = 1; i < p.Count; i++)
        {
            r = big_integer_plus(r, p[i]);
        }
        return r;
    }

    #region 四则运算符（含取余数）重载

    // 运算符重载是一种常用的编程技术。
    // 用于支持“非数值类型的数据（比如类）”以常用的运算符 +-*/% 等等进行运算，使得代码简约直观。
    // 没有运算符重载的语言（比如golang）一般都不适合数值计算。

    public static BigNumber operator +(BigNumber a, BigNumber b)
    {
        return new BigNumber(big_integer_plus(a.Buffer, b.Buffer));
    }
    public static BigNumber operator -(BigNumber a, BigNumber b)
    {
        if (a > b || a == b)
            return new BigNumber(big_integer_subtract(a.Buffer, b.Buffer));
        else
            return new BigNumber(big_integer_subtract(b.Buffer, a.Buffer), "-");
    }
    public static BigNumber operator *(BigNumber a, BigNumber b)
    {
        return new BigNumber(big_integer_multiply(a.Buffer, b.Buffer));
    }
    public static BigNumber operator /(BigNumber a, BigNumber b)
    {
        return new BigNumber(big_integer_divide(a.Buffer, b.Buffer, out string _));
    }
    public static BigNumber operator %(BigNumber a, BigNumber b)
    {
        string c = big_integer_divide(a.Buffer, b.Buffer, out string d);
        return new BigNumber(d);
    }
    public static bool operator >(BigNumber a, BigNumber b)
    {
        return big_integer_compare(a.Buffer, b.Buffer) > 0;
    }
    public static bool operator <(BigNumber a, BigNumber b)
    {
        return big_integer_compare(a.Buffer, b.Buffer) < 0;
    }
    public static bool operator ==(BigNumber a, BigNumber b)
    {
        return big_integer_compare(a.Buffer, b.Buffer) == 0;
    }
    public static bool operator !=(BigNumber a, BigNumber b)
    {
        return big_integer_compare(a.Buffer, b.Buffer) != 0;
    }
    public static bool Equals(BigNumber a, BigNumber b) { return (a == b); }

    public override string ToString()
    {
        return Sign + Buffer;
    }
    #endregion
}
 

2 代码格式

using System;
using System.Text;
using System.Collections;
using System.Collections.Generic;

/// <summary>
/// 大数的四则（加减乘除）运算
/// 及其运算符重载（取余数）
/// </summary>
public class BigNumber
{
    private string Buffer { get; set; } = "";
    private string Sign { get; set; } = "";
    public BigNumber(int n) { Next(n); }
    public BigNumber(string b, string s = "")
    {
        Buffer = b;
        Sign = s;
    }
    public BigNumber Clone()
    {
        BigNumber r = new BigNumber(Buffer, Sign);
        return r;
    }
    public int Length { get { return Buffer.Length; } }

    /// <summary>
    /// 随机生成任意长度的大数（BigNumber）
    /// </summary>
    /// <param name="n">位数</param>
    /// <returns></returns>
    public void Next(int n)
    {
        Random rnd = new Random();
        StringBuilder sb = new StringBuilder();
        sb.Append((rnd.Next(9) + 1).ToString());
        for (int i = 1; i < n; i++)
        {
            sb.Append((rnd.Next(10)).ToString());
        }
        Buffer = sb.ToString();
    }

    /// <summary>
    /// 字符串型的数字转为数组(低位（右）在前)
    /// </summary>
    /// <param name="a"></param>
    /// <param name="n">最大位数，后面留0</param>
    /// <returns></returns>
    public static int[] string_to_digitals(string a, int n)
    {
        char[] c = a.ToCharArray();
        int[] d = new int[n];
        for (int i = a.Length - 1, j = 0; i >= 0; i--)
        {
            if (c[i] == '-') continue;
            d[j++] = c[i] - '0';
        }
        return d;
    }

    /// <summary>
    /// 数组型数字转为字符串型(低位（右）在前)
    /// </summary>
    /// <param name="d"></param>
    /// <returns></returns>
    public static string digitals_to_string(int[] d)
    {
        int n = d.Length;
        int k = n - 1;
        while ((k >= 0) && (d[k] == 0)) k--;
        if (k >= 0)
        {
            StringBuilder sb = new StringBuilder();
            for (; k >= 0; k--) sb.Append(d[k]);
            return sb.ToString();
        }
        else
        {
            return "0";
        }
    }

    /// <summary>
    /// 大数加法 c = a + b
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static string big_integer_plus(string a, string b)
    {
        int n = Math.Max(a.Length, b.Length) + 1;
        // 位数不长的数字直接计算
        if (n <= 18)
        {
            return (ulong.Parse(a) + ulong.Parse(b)).ToString();
        }

        int[] da = string_to_digitals(a, n);
        int[] db = string_to_digitals(b, n);

        int[] dc = new int[n];
        Array.Copy(da, dc, n);
        for (int i = 0; i < (n - 1); i++)
        {
            dc[i] = dc[i] + db[i];
            if (dc[i] > 9)
            {
                dc[i] -= 10;
                dc[i + 1] += 1;
            }
        }
        return digitals_to_string(dc);
    }

    /// <summary>
    /// 大数减法 c = a - b
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static string big_integer_subtract(string a, string b)
    {
        int na = a.Length;
        int nb = b.Length;
        int n = Math.Max(na, nb) + 1;
        if (n <= 18)
        {
            return (ulong.Parse(a) - ulong.Parse(b)).ToString();
        }
        int[] da = string_to_digitals(a, n);
        int[] db = string_to_digitals(b, n);

        for (int i = 0; i < na; i++)
        {
            da[i] -= db[i];
            if (da[i] < 0)
            {
                da[i] += 10;
                da[i + 1] -= 1;
            }
        }
        return digitals_to_string(da);
    }

    /// <summary>
    /// 大数乘法 c = a * b
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static string big_integer_multiply(string a, string b)
    {
        int na = a.Length;
        int nb = b.Length;
        int n = na + nb + 1;
        int[] da = string_to_digitals(a, n);
        int[] db = string_to_digitals(b, n);

        int[] dc = new int[n];
        for (int i = 0; i < na; i++)
        {
            for (int j = 0; j < nb; j++)
            {
                dc[i + j] += da[i] * db[j];
            }
        }
        for (int i = 0; i < n; i++)
        {
            if (dc[i] >= 10)
            {
                dc[i + 1] += (dc[i] / 10);
                dc[i] %= 10;
            }
        }

        return digitals_to_string(dc);
    }

    /// <summary>
    /// 比较a，b的大小，返回1，0，-1
    /// 数据从低位（右）往高位（左）存储;
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static int big_integer_compare(int[] a, int[] b)
    {
        for (int i = a.Length - 1; i >= 0; i--)
        {
            if (a[i] > b[i]) return 1;
            else if (a[i] < b[i]) return -1;
        }
        return 0;
    }

    public static int big_integer_compare(string a, string b)
    {
        int n = Math.Max(a.Length, b.Length);
        int[] da = string_to_digitals(a, n);
        int[] db = string_to_digitals(a, n);
        return big_integer_compare(da, db);
    }

    /// <summary>
    /// 大数除法 c = a / b % d
    /// c 为商，d 为余数。
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <param name="d">余数</param>
    /// <returns>商c</returns>
    public static string big_integer_divide(string a, string b, out string d)
    {
        int n = a.Length;
        int[] db = string_to_digitals(b, n);

        string q = a;
        List<string> p = new List<string>();
        int[] dq = string_to_digitals(q, n);
        while (big_integer_compare(dq, db) >= 0)
        {
            int len = q.Length - b.Length;
            string v2 = b + String.Join("", new int[len]);
            int[] dv = string_to_digitals(v2, n);
            if (big_integer_compare(dq, dv) < 0)
            {
                len--;
                v2 = b + String.Join("", new int[len]);
                dv = string_to_digitals(v2, n);
            }

            string v1 = "1" + String.Join("", new int[len]);
            while (big_integer_compare(dq, dv) >= 0)
            {
                p.Add(v1);
                q = big_integer_subtract(q, v2);
                dq = string_to_digitals(q, n);
            }
        }

        d = q;

        string r = p[0];
        for (int i = 1; i < p.Count; i++)
        {
            r = big_integer_plus(r, p[i]);
        }
        return r;
    }

    #region 四则运算符（含取余数）重载

    // 运算符重载是一种常用的编程技术。
    // 用于支持“非数值类型的数据（比如类）”以常用的运算符 +-*/% 等等进行运算，使得代码简约直观。
    // 没有运算符重载的语言（比如golang）一般都不适合数值计算。

    public static BigNumber operator +(BigNumber a, BigNumber b)
    {
        return new BigNumber(big_integer_plus(a.Buffer, b.Buffer));
    }
    public static BigNumber operator -(BigNumber a, BigNumber b)
    {
        if (a > b || a == b)
            return new BigNumber(big_integer_subtract(a.Buffer, b.Buffer));
        else
            return new BigNumber(big_integer_subtract(b.Buffer, a.Buffer), "-");
    }
    public static BigNumber operator *(BigNumber a, BigNumber b)
    {
        return new BigNumber(big_integer_multiply(a.Buffer, b.Buffer));
    }
    public static BigNumber operator /(BigNumber a, BigNumber b)
    {
        return new BigNumber(big_integer_divide(a.Buffer, b.Buffer, out string _));
    }
    public static BigNumber operator %(BigNumber a, BigNumber b)
    {
        string c = big_integer_divide(a.Buffer, b.Buffer, out string d);
        return new BigNumber(d);
    }
    public static bool operator >(BigNumber a, BigNumber b)
    {
        return big_integer_compare(a.Buffer, b.Buffer) > 0;
    }
    public static bool operator <(BigNumber a, BigNumber b)
    {
        return big_integer_compare(a.Buffer, b.Buffer) < 0;
    }
    public static bool operator ==(BigNumber a, BigNumber b)
    {
        return big_integer_compare(a.Buffer, b.Buffer) == 0;
    }
    public static bool operator !=(BigNumber a, BigNumber b)
    {
        return big_integer_compare(a.Buffer, b.Buffer) != 0;
    }
    public static bool Equals(BigNumber a, BigNumber b) { return (a == b); }

    public override string ToString()
    {
        return Sign + Buffer;
    }
    #endregion
}


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