Quick combination count

The recursive formula is simple:

C (n, k + 1) = C (n, k) * (n-k)/(k + 1)

Method Brute Force

After the test, C (0.2) can be found, C () to C () takes only s

 

#include <iostream>   #include <cstdio>   #include <cstring>   #include <algorithm>   #include <limits>   #include <cstdlib>     using namespace std;    const int MAXD = 100, DIG = 9, BASE = 1000000000;    const unsigned long long BOUND = numeric_limits <unsigned long long> :: max () - (unsigned long long) BASE * BASE;        class bignum  {  private:      int digits[MAXD];      int D;  public:        friend ostream &operator<<(ostream &out,bignum &c);        inline void trim()      {          while(D > 1 && digits[D-1] == 0 )              D--;      }        inline void dealint(long long x)      {          memset(digits,0,sizeof(digits));          D = 0;          do          {              digits[D++] = x % BASE;              x /= BASE;          }          while(x > 0);      }        inline void dealstr(char *s)      {          memset(digits,0,sizeof(digits));          int len = strlen(s),first = (len + DIG -1)%DIG + 1;            D = (len+DIG-1)/DIG;            for(int i = 0; i < first; i++)              digits[D-1] = digits[D-1]*10 + s[i] - '0';            for(int i = first, d = D-2; i < len; i+=DIG,d--)              for(int j = i; j < i+DIG; j++)                  digits[d] = digits[d]*10 + s[j]-'0';            trim();      }        inline char *print()      {          trim();            char *cdigits = new char[DIG * D + 1];            int pos = 0,d = digits[D-1];            do          {              cdigits[pos++] = d % 10 + '0';              d/=10;          }          while(d > 0);            reverse(cdigits,cdigits+pos);            for(int i = D - 2; i >= 0; i--,pos += DIG)              for(int j = DIG-1,t = digits[i]; j >= 0; j--)              {                  cdigits[pos+j] = t%10 + '0';                  t /= 10;              }            cdigits[pos] = '\0';            return cdigits;      }          bignum()      {          dealint(0);      }        bignum(long long x)      {          dealint(x);      }        bignum(int x)      {          dealint(x);      }        bignum(char *s)      {          dealstr(s);      }            inline bool operator < (const bignum &o) const      {          if(D != o.D)              return D < o.D;            for(int i = D-1; i>=0; i--)              if(digits[i] != o.digits[i])                  return digits[i] < o.digits[i];          return false; //equal         }        bool operator >  (const bignum & o)const      {          return o < *this;      }      bool operator <= (const bignum & o)const      {          return !(o < *this);      }      bool operator >= (const bignum & o)const      {          return !(*this < o);      }      bool operator != (const bignum & o)const      {          return o < *this || *this < o;      }      bool operator == (const bignum & o)const      {          return !(o < *this) && !(*this < o);      }          bignum &operator++()      {          *this = *this  + 1;          return *this;      }          bignum operator ++(int)      {          bignum old = *this;          ++(*this);          return old;      }        inline bignum operator << (int p) const      {          bignum temp;          temp.D = D + p;            for (int i = 0; i < D; i++)              temp.digits [i + p] = digits [i];            for (int i = 0; i < p; i++)              temp.digits [i] = 0;            return temp;      }        inline bignum operator >> (int p) const      {          bignum temp;          temp.D = D - p;            for (int i = 0; i < D - p; i++)              temp.digits [i] = digits [i + p];            for (int i = D - p; i < D; i++)              temp.digits [i] = 0;            return temp;      }          bignum &operator += (const bignum &b)      {          *this = *this + b;          return *this;      }        bignum &operator -= (const bignum &b)      {          *this = *this - b;          return *this;      }        bignum &operator *= (const bignum &b)      {          *this = *this * b;          return *this;      }        bignum &operator /= (const bignum &b)      {          *this = *this / b;          return *this;      }        bignum &operator %= (const bignum &b)      {          *this = *this % b;          return *this;      }        inline bignum operator + (const bignum &o) const      {          bignum sum = o;          int carry = 0;            for (sum.D = 0; sum.D < D || carry > 0; sum.D++)          {              sum.digits [sum.D] += (sum.D < D ? digits [sum.D] : 0) + carry;                if (sum.digits [sum.D] >= BASE)              {                  sum.digits [sum.D] -= BASE;                  carry = 1;              }              else                  carry = 0;          }            sum.D = max (sum.D, o.D);          sum.trim ();          return sum;      }      inline bignum operator - (const bignum &o) const      {          bignum diff = *this;            for (int i = 0, carry = 0; i < o.D || carry > 0; i++)          {              diff.digits [i] -= (i < o.D ? o.digits [i] : 0) + carry;                if (diff.digits [i] < 0)              {                  diff.digits [i] += BASE;                  carry = 1;              }              else                  carry = 0;          }            diff.trim ();          return diff;      }      inline bignum operator * (const bignum &o) const      {          bignum prod = 0;          unsigned long long sum = 0, carry = 0;            for (prod.D = 0; prod.D < D + o.D - 1 || carry > 0; prod.D++)          {              sum = carry % BASE;              carry /= BASE;                for (int j = max (prod.D - o.D + 1, 0); j <= min (D - 1, prod.D); j++)              {                  sum += (unsigned long long) digits [j] * o.digits [prod.D - j];                    if (sum >= BOUND)                  {                      carry += sum / BASE;                      sum %= BASE;                  }              }                carry += sum / BASE;              prod.digits [prod.D] = sum % BASE;          }            prod.trim ();          return prod;      }      inline bignum range (int a, int b) const      {          bignum temp = 0;          temp.D = b - a;            for (int i = 0; i < temp.D; i++)              temp.digits [i] = digits [i + a];            return temp;      }          inline double double_div (const bignum &o) const      {          double val = 0, oval = 0;          int num = 0, onum = 0;            for (int i = D - 1; i >= max (D - 3, 0); i--, num++)              val = val * BASE + digits [i];            for (int i = o.D - 1; i >= max (o.D - 3, 0); i--, onum++)              oval = oval * BASE + o.digits [i];            return val / oval * (D - num > o.D - onum ? BASE : 1);      }        inline pair <bignum, bignum> divmod (const bignum &o) const      {          bignum quot = 0, rem = *this, temp;            for (int i = D - o.D; i >= 0; i--)          {              temp = rem.range (i, rem.D);              int div = (int) temp.double_div (o);              bignum mult = o * div;                while (div > 0 && temp < mult)              {                  mult = mult - o;                  div--;              }                while (div + 1 < BASE && !(temp < mult + o))              {                  mult = mult + o;                  div++;              }                rem = rem - (o * div << i);                if (div > 0)              {                  quot.digits [i] = div;                  quot.D = max (quot.D, i + 1);              }          }            quot.trim ();          rem.trim ();          return make_pair (quot, rem);      }        inline bignum operator / (const bignum &o) const      {          return divmod (o).first;      }        inline bignum operator % (const bignum &o) const      {          return divmod (o).second;      }          inline bignum power (int exp) const      {          bignum p = 1, temp = *this;            while (exp > 0)          {              if (exp & 1) p = p * temp;              if (exp > 1) temp = temp * temp;              exp >>= 1;          }            return p;      }        inline bignum factorial() const      {          bignum ans = 1, num = *this;            if (num == 0 || num == 1)              return ans;          while (!(num < 0 || num == 0))          {              ans = ans * num;              num = num - 1;          }          return ans;      }  };    ostream &operator<<(ostream &out, bignum &c)  {      out<<c.print();      return out;  }    istream &operator >> (istream &in,bignum &c)  {      char s[10000];      in>>s;      c = s;      return in;  }  bignum gcd(bignum a,bignum b)  {      return b==0?a:gcd(b,a%b);  }        int main()  {        bignum c[3020];      freopen("D:\\a.txt","w",stdout);      int m, n;      n = 2000, m = 1;      {          c[0] = 1;          for (int k = 0; k <= 2000; k++)          {              c[k + 1] = c[k] * (n - k) / (k + 1);          }          for (int i = 0; i <= 2000; i++)          {              cout << "C" << "(" << n << "," << i << ") is " <<c[i] << endl;          }      }  }  #include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <limits>#include <cstdlib>using namespace std;const int MAXD = 100, DIG = 9, BASE = 1000000000;const unsigned long long BOUND = numeric_limits <unsigned long long> :: max () - (unsigned long long) BASE * BASE;class bignum{private:    int digits[MAXD];    int D;public:    friend ostream &operator<<(ostream &out,bignum &c);    inline void trim()    {        while(D > 1 && digits[D-1] == 0 )            D--;    }    inline void dealint(long long x)    {        memset(digits,0,sizeof(digits));        D = 0;        do        {            digits[D++] = x % BASE;            x /= BASE;        }        while(x > 0);    }    inline void dealstr(char *s)    {        memset(digits,0,sizeof(digits));        int len = strlen(s),first = (len + DIG -1)%DIG + 1;        D = (len+DIG-1)/DIG;        for(int i = 0; i < first; i++)            digits[D-1] = digits[D-1]*10 + s[i] - '0';        for(int i = first, d = D-2; i < len; i+=DIG,d--)            for(int j = i; j < i+DIG; j++)                digits[d] = digits[d]*10 + s[j]-'0';        trim();    }    inline char *print()    {        trim();        char *cdigits = new char[DIG * D + 1];        int pos = 0,d = digits[D-1];        do        {            cdigits[pos++] = d % 10 + '0';            d/=10;        }        while(d > 0);        reverse(cdigits,cdigits+pos);        for(int i = D - 2; i >= 0; i--,pos += DIG)            for(int j = DIG-1,t = digits[i]; j >= 0; j--)            {                cdigits[pos+j] = t%10 + '0';                t /= 10;            }        cdigits[pos] = '\0';        return cdigits;    }    bignum()    {        dealint(0);    }    bignum(long long x)    {        dealint(x);    }    bignum(int x)    {        dealint(x);    }    bignum(char *s)    {        dealstr(s);    }    inline bool operator < (const bignum &o) const    {        if(D != o.D)            return D < o.D;        for(int i = D-1; i>=0; i--)            if(digits[i] != o.digits[i])                return digits[i] < o.digits[i];        return false; //equal    }    bool operator >  (const bignum & o)const    {        return o < *this;    }    bool operator <= (const bignum & o)const    {        return !(o < *this);    }    bool operator >= (const bignum & o)const    {        return !(*this < o);    }    bool operator != (const bignum & o)const    {        return o < *this || *this < o;    }    bool operator == (const bignum & o)const    {        return !(o < *this) && !(*this < o);    }    bignum &operator++()    {        *this = *this  + 1;        return *this;    }    bignum operator ++(int)    {        bignum old = *this;        ++(*this);        return old;    }    inline bignum operator << (int p) const    {        bignum temp;        temp.D = D + p;        for (int i = 0; i < D; i++)            temp.digits [i + p] = digits [i];        for (int i = 0; i < p; i++)            temp.digits [i] = 0;        return temp;    }    inline bignum operator >> (int p) const    {        bignum temp;        temp.D = D - p;        for (int i = 0; i < D - p; i++)            temp.digits [i] = digits [i + p];        for (int i = D - p; i < D; i++)            temp.digits [i] = 0;        return temp;    }    bignum &operator += (const bignum &b)    {        *this = *this + b;        return *this;    }    bignum &operator -= (const bignum &b)    {        *this = *this - b;        return *this;    }    bignum &operator *= (const bignum &b)    {        *this = *this * b;        return *this;    }    bignum &operator /= (const bignum &b)    {        *this = *this / b;        return *this;    }    bignum &operator %= (const bignum &b)    {        *this = *this % b;        return *this;    }    inline bignum operator + (const bignum &o) const    {        bignum sum = o;        int carry = 0;        for (sum.D = 0; sum.D < D || carry > 0; sum.D++)        {            sum.digits [sum.D] += (sum.D < D ? digits [sum.D] : 0) + carry;            if (sum.digits [sum.D] >= BASE)            {                sum.digits [sum.D] -= BASE;                carry = 1;            }            else                carry = 0;        }        sum.D = max (sum.D, o.D);        sum.trim ();        return sum;    }    inline bignum operator - (const bignum &o) const    {        bignum diff = *this;        for (int i = 0, carry = 0; i < o.D || carry > 0; i++)        {            diff.digits [i] -= (i < o.D ? o.digits [i] : 0) + carry;            if (diff.digits [i] < 0)            {                diff.digits [i] += BASE;                carry = 1;            }            else                carry = 0;        }        diff.trim ();        return diff;    }    inline bignum operator * (const bignum &o) const    {        bignum prod = 0;        unsigned long long sum = 0, carry = 0;        for (prod.D = 0; prod.D < D + o.D - 1 || carry > 0; prod.D++)        {            sum = carry % BASE;            carry /= BASE;            for (int j = max (prod.D - o.D + 1, 0); j <= min (D - 1, prod.D); j++)            {                sum += (unsigned long long) digits [j] * o.digits [prod.D - j];                if (sum >= BOUND)                {                    carry += sum / BASE;                    sum %= BASE;                }            }            carry += sum / BASE;            prod.digits [prod.D] = sum % BASE;        }        prod.trim ();        return prod;    }    inline bignum range (int a, int b) const    {        bignum temp = 0;        temp.D = b - a;        for (int i = 0; i < temp.D; i++)            temp.digits [i] = digits [i + a];        return temp;    }    inline double double_div (const bignum &o) const    {        double val = 0, oval = 0;        int num = 0, onum = 0;        for (int i = D - 1; i >= max (D - 3, 0); i--, num++)            val = val * BASE + digits [i];        for (int i = o.D - 1; i >= max (o.D - 3, 0); i--, onum++)            oval = oval * BASE + o.digits [i];        return val / oval * (D - num > o.D - onum ? BASE : 1);    }    inline pair <bignum, bignum> divmod (const bignum &o) const    {        bignum quot = 0, rem = *this, temp;        for (int i = D - o.D; i >= 0; i--)        {            temp = rem.range (i, rem.D);            int div = (int) temp.double_div (o);            bignum mult = o * div;            while (div > 0 && temp < mult)            {                mult = mult - o;                div--;            }            while (div + 1 < BASE && !(temp < mult + o))            {                mult = mult + o;                div++;            }            rem = rem - (o * div << i);            if (div > 0)            {                quot.digits [i] = div;                quot.D = max (quot.D, i + 1);            }        }        quot.trim ();        rem.trim ();        return make_pair (quot, rem);    }    inline bignum operator / (const bignum &o) const    {        return divmod (o).first;    }    inline bignum operator % (const bignum &o) const    {        return divmod (o).second;    }    inline bignum power (int exp) const    {        bignum p = 1, temp = *this;        while (exp > 0)        {            if (exp & 1) p = p * temp;            if (exp > 1) temp = temp * temp;            exp >>= 1;        }        return p;    }    inline bignum factorial() const    {        bignum ans = 1, num = *this;        if (num == 0 || num == 1)            return ans;        while (!(num < 0 || num == 0))        {            ans = ans * num;            num = num - 1;        }        return ans;    }};ostream &operator<<(ostream &out, bignum &c){    out<<c.print();    return out;}istream &operator >> (istream &in,bignum &c){    char s[10000];    in>>s;    c = s;    return in;}bignum gcd(bignum a,bignum b){    return b==0?a:gcd(b,a%b);}int main(){bignum c[3020];    freopen("D:\\a.txt","w",stdout);int m, n;n = 2000, m = 1;{c[0] = 1;for (int k = 0; k <= 2000; k++){c[k + 1] = c[k] * (n - k) / (k + 1);}for (int i = 0; i <= 2000; i++){cout << "C" << "(" << n << "," << i << ") is " <<c[i] << endl;}}}