[源碼分享]基於加法的高效極大數乘法

數學乘法 從小學開始就一直是基於加法的，所以，我寫了一個基於加法的大數乘法。擴展方法省去了類型轉換的損耗，

原理如下：

         1 2 3

      *     5 6

------------------------

           7 3 8

+     6 1 5  0  這裏加個0

-------------------------

=     6  8 8 8

 

好，直接上代碼

 

 

using System.Text;

namespace LongNumber
{
    public static class LongNumberHelper
    {
        /// <summary>
        /// 大數相乘
        /// </summary>
        /// <param name="s1"></param>
        /// <param name="s2"></param>
        /// <returns></returns>
        public static string LongNumberMul(string s1, string s2)
        {
            string result = "";
            for (int i = s2.Length - 1; i >= 0; i--)
            {
                var s = StrMulChar(s1, s2[i], s2.Length - 1 - i);//計算s2每個數的乘積並給結果加足夠的0
                result = LongNumberAdd(result, s);//結果集累加
            }
            return result;
        }
        /// <summary>
        /// 分步計算並進位
        /// </summary>
        /// <param name="s1"></param>
        /// <param name="s2"></param>
        /// <param name="count"></param>
        /// <returns></returns>
        private static string StrMulChar(string s1, char s2, int count)
        {
            StringBuilder sb = new StringBuilder();
            int temp = 0;
            for (int i = s1.Length - 1; i >= 0; i--)
            {
                var s = s1[i].CharToInt() * s2.CharToInt() + temp;
                temp = 0;
                while (s >= 10)
                {
                    temp++;
                    s -= 10;
                }
                sb.Insert(0, s);
            }
            if (temp > 0)
            {
                sb.Insert(0, temp);
            }
            sb.Append('0', count);//給結果加0
            return sb.ToString();
        }
        /// <summary>
        /// 極大數加法
        /// </summary>
        /// <param name="s1"></param>
        /// <param name="s2"></param>
        /// <returns></returns>
        public static string LongNumberAdd(string s1, string s2)
        {
            string result = "";
            if (s1.Length > s2.Length)
            {
                result = AddToResult(s1, s2);
            }
            else
            {
                result = AddToResult(s2, s1);
            }
            return result;
        }
        /// <summary>
        /// 長的加短的
        /// </summary>
        /// <param name="s1">長的數</param>
        /// <param name="s2">短的數</param>
        /// <returns></returns>
        private static string AddToResult(string s1, string s2)
        {
            var len = s1.Length - s2.Length;
            int temp = 0;
            StringBuilder sb = new StringBuilder();
            for (int i = s1.Length - 1; i >= 0; i--)
            {
                int s;
                if (i - len >= 0)
                {
                    s = s1[i].CharToInt() + s2[i - len].CharToInt() + temp;
                }
                else
                {
                    s = s1[i].CharToInt() + temp;
                }
                temp = 0;
                while (s >= 10)
                {
                    temp++;
                    s -= 10;
                }
                sb.Insert(0, s);
            }
            if (temp > 0)
            {
                sb.Insert(0, temp);
            }
            return sb.ToString();
        }
        /// <summary>
        /// 字符轉換int
        /// </summary>
        /// <param name="s"></param>
        /// <returns></returns>
        static int CharToInt(this char s)
        {
            switch (s)
            {
                case '0': return 0;
                case '1': return 1;
                case '2': return 2;
                case '3': return 3;
                case '4': return 4;
                case '5': return 5;
                case '6': return 6;
                case '7': return 7;
                case '8': return 8;
                case '9': return 9;
                default:
                    return 0;
            }
        }
    }
}