51nod求助

2018/03/06 17:04
阅读数 27

求助dalao们,51nod1170实在是不会了,有没有大佬讲一下,有兴趣的可以告诉我,我提供AC代码。

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Numerics;

namespace Problem51Nod
{
    class Program
    {
        public static void Main(String[] args)
        {
            //BigInteger m = BigInteger.Pow(5, 143) - 1;
            //BigInteger n = BigInteger.Pow(2, 331) + 1;
            //int k = 100;
            BigInteger m = BigInteger.Parse(Console.ReadLine());
            BigInteger n = BigInteger.Parse(Console.ReadLine());
            int k = Convert.ToInt32(Console.ReadLine());

            //Stopwatch timer = new Stopwatch();
            //timer.Start();
            Console.WriteLine(Cmn(m, n, k));
            //timer.Stop();
            //Console.WriteLine(timer.Elapsed);
        }

        static BigInteger[][] PowerTable = new BigInteger[6][];
        static List<BigInteger[][]>[] PreTable = new List<BigInteger[][]>[6];
        static BigInteger[,] CMatrix;

        static void InitCMatrix(int l)
        {
            CMatrix = new BigInteger[l + 1, l + 1];
            for (int i = 0; i <= l; i++)
                CMatrix[i, 0] = CMatrix[i, i] = 1;

            for (int i = 2; i <= l; i++)
                for (int j = 1; j * 2 <= i; j++)
                    CMatrix[i, j] = CMatrix[i, i - j] = CMatrix[i - 1, j - 1] + CMatrix[i - 1, j];
        }

        static void InitPowerTab(int l, int p)
        {
            PowerTable[p] = new BigInteger[l + 1];
            PowerTable[p][0] = 1;

            for (int j = 1; j < PowerTable[p].Length; j++)
                PowerTable[p][j] = PowerTable[p][j - 1] * p;
        }

        static void InitData(int l, BigInteger max, int p)
        {
            PreTable[p] = new List<BigInteger[][]>();
            BigInteger[] pre = MulTo(l, p);
            BigInteger[,] cMatrix = new BigInteger[l + 1, l + 1];

            for (int i = 0; i <= l; i++)
                for (int j = 0; j <= i; j++)
                    cMatrix[i, j] = CMatrix[i, j];

            int power = 1;
            for (BigInteger i = p; i <= max; i *= p)
            {
                BigInteger[][] cTable = new BigInteger[p - 1][];
                cTable[0] = pre;
                for (int j = 1; j < p; j++)
                {
                    BigInteger[] next = ReplaceWith(cTable[0], i * j % PowerTable[p][l], l, p, cMatrix);

                    if (j < p - 1)
                        cTable[j] = MulMod(cTable[j - 1], next, l, p);
                    else
                        pre = MulMod(cTable[j - 1], next, l, p);
                }

                PreTable[p].Add(cTable);
                power++;
            }
        }

        static BigInteger Cmn(BigInteger m, BigInteger n, int l)
        {
            InitCMatrix(l);
            InitPowerTab(l, 5);
            InitPowerTab(l, 2);
            BigInteger up5 = CalP(m, n, 5, l);
            BigInteger up2 = CalP(m, n, 2, l);
            BigInteger mod = ((up5 - up2) + PowerTable[5][l]) % PowerTable[5][l];
            mod = IMod(PowerTable[2][l], mod, PowerTable[5][l]) * PowerTable[2][l] + up2;
            return mod;
        }

        static BigInteger CalP(BigInteger m, BigInteger n, int p, int l)
        {
            BigInteger count = Count(m, p) - Count(n, p) - Count(m - n, p);
            if (count > l) return 0;
            InitData(l, m, p);
            BigInteger up = Cal(m, p, l) * PowerTable[p][(int)count];
            BigInteger down = Cal(n, p, l);
            down *= Cal(m - n, p, l);
            down %= PowerTable[p][l];
            up = IMod(down, up, PowerTable[p][l]);
            return up;
        }

        static BigInteger Count(BigInteger v, BigInteger mod)
        {
            BigInteger count = 0;

            while (v > 0)
            {
                v /= mod;
                count += v;
            }

            return count;
        }

        static List<BigInteger> Values = new List<BigInteger>();
        static List<int> Mods = new List<int>();

        static BigInteger Cal(BigInteger nums, int p, int l)
        {
            BigInteger numsBak = nums;
            Values.Clear();
            Mods.Clear();

            while (numsBak > 0)
            {
                Values.Add(numsBak);
                Mods.Add((int)(numsBak % p));
                numsBak /= p;
            }

            BigInteger result = 1;

            for (int i = 0; i < Values.Count; i++)
            {
                result *= CalSingle(i, p, l);
                result %= PowerTable[p][l];
            }

            return result;
        }

        static BigInteger CalSingle(int cIndex, int p, int l)
        {
            int len = Mods[cIndex];
            BigInteger sum = 0, last = (Values[cIndex] - len) % PowerTable[p][l];
            BigInteger[] pre = new BigInteger[] { 1 };
            BigInteger result = 1;
            cIndex++;

            for (int i = Mods.Count - 1; i >= cIndex; i--)
            {
                int index = Mods[i];

                if (index > 0)
                {
                    BigInteger modValue = 1, current = 0;
                    foreach (var item in PreTable[p][i - cIndex][index - 1])
                    {
                        if (item != 0)
                            current = (current + modValue * item) % PowerTable[p][l];

                        if (sum == 0 || modValue == 0)
                            break;

                        modValue = modValue * sum % PowerTable[p][l];
                    }

                    if (i - cIndex + 1 <= l)
                        sum = (sum + index * PowerTable[p][i - cIndex + 1]) % PowerTable[p][l];

                    result = (result * current) % PowerTable[p][l];
                }
            }

            for (int i = 1; i <= len; i++)
            {
                if (i % p == 0)
                    continue;

                result *= last + i;
                result %= PowerTable[p][l];
            }

            return result;
        }

        static BigInteger[] MulTo(int l, int p)
        {
            BigInteger[] result = new BigInteger[] { 1 };

            for (BigInteger i = 1; i < p; i++)
            {
                if (i % p == 0)
                    continue;

                BigInteger[] b = new BigInteger[] { i, 1 };
                result = MulMod(result, b, l, p);
            }

            return result;
        }

        static BigInteger[] MulMod(BigInteger[] a, BigInteger[] b, int l, int p)
        {
            int len = Math.Min(l + 1, a.Length + b.Length - 1);
            BigInteger[] result = new BigInteger[len];

            for (int i = 0; i < Math.Min(a.Length, l + 1); i++)
            {
                if (a[i] == 0)
                    continue;

                int upper = Math.Min(b.Length, l - i + 1);
                for (int j = 0; j < upper; j++)
                    result[i + j] += a[i] * b[j];
            }

            int last = 0;

            for (int i = 0; i < result.Length; i++)
            {
                result[i] %= PowerTable[p][l - i];
                if (result[i] > 0)
                    last = i + 1;
            }

            if (last < result.Length)
                Array.Resize(ref result, last);

            return result;
        }

        //2次方算法,考虑大数是3次方 除以大进制的常数
        static BigInteger[] ReplaceWith(BigInteger[] source, BigInteger into, int l, int p, BigInteger[,] cMatrix)
        {
            int len = source.Length;
            len = Math.Min(len, l + 1);
            BigInteger[] result = new BigInteger[len];
            BigInteger[] power = new BigInteger[len];
            power[0] = 1;

            for (int i = 1; i < len; i++)
                power[i] = power[i - 1] * into % PowerTable[p][l];

            for (int i = 0; i < len; i++)
            {
                if (source[i] == 0)
                    continue;

                for (int j = 0; j <= i; j++)
                {
                    if (power[i] == 0) continue;
                    var tmp = power[i - j] * source[i] % PowerTable[p][l - j];
                    if (tmp == 0) continue;
                    result[j] += tmp * cMatrix[i, j];
                }
            }

            for (int i = 0; i < result.Length; i++)
                result[i] %= PowerTable[p][l - i];

            return result;
        }

        public static BigInteger EuclidExtend(BigInteger X, BigInteger Y, out BigInteger A, out BigInteger B)
        {
            if (Y == 0) { A = 1; B = 0; return X; }
            BigInteger quotient = X / Y;
            BigInteger gcd = EuclidExtend(Y, X - Y * quotient, out A, out B);
            BigInteger Temp = A; A = B; B = Temp - quotient * A;
            return gcd;
        }

        public static bool Linear(BigInteger X, BigInteger Y, BigInteger N, out BigInteger xResult, out BigInteger yResult)
        {
            BigInteger gcd = EuclidExtend(X, Y, out xResult, out yResult);
            if (N % gcd != 0) { return false; }
            xResult = xResult * N / gcd % Y;
            xResult = xResult >= 0 ? xResult : xResult + Y;
            yResult = yResult * N / gcd % X;
            yResult = yResult <= 0 ? yResult : yResult - X;
            return true;
        }

        public static BigInteger IMod(BigInteger A, BigInteger B, BigInteger P)
        {
            BigInteger x, y;
            Linear(A, P, B, out x, out y);
            return x;
        }
    }
}
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