大数类

#define MAXN 9999  #define MAXSIZE 10  #define DLEN 4  class BigNum{private:int a[500];    //可以控制大数的位数   int len;       //大数长度  public:BigNum(){ len = 1; memset(a, 0, sizeof(a)); }   //构造函数  BigNum(const int);       //将一个int类型的变量转化为大数  BigNum(const char*);     //将一个字符串类型的变量转化为大数  BigNum(const BigNum &);  //拷贝构造函数  BigNum &operator=(const BigNum &);   //重载赋值运算符，大数之间进行赋值运算  friend istream& operator>>(istream&, BigNum&);   //重载输入运算符  friend ostream& operator<<(ostream&, BigNum&);   //重载输出运算符  BigNum operator+(const BigNum &) const;   //重载加法运算符，两个大数之间的相加运算   BigNum operator-(const BigNum &) const;   //重载减法运算符，两个大数之间的相减运算   BigNum operator*(const BigNum &) const;   //重载乘法运算符，两个大数之间的相乘运算   BigNum operator/(const int   &) const;    //重载除法运算符，大数对一个整数进行相除运算  BigNum operator^(const int  &) const;    //大数的n次方运算  int    operator%(const int  &) const;    //大数对一个int类型的变量进行取模运算      bool   operator>(const BigNum & T)const;   //大数和另一个大数的大小比较  bool   operator>(const int & t)const;      //大数和一个int类型的变量的大小比较  void print();       //输出大数  };BigNum::BigNum(const int b)     //将一个int类型的变量转化为大数  {int c, d = b;len = 0;memset(a, 0, sizeof(a));while (d > MAXN){c = d - (d / (MAXN + 1)) * (MAXN + 1);d = d / (MAXN + 1);a[len++] = c;}a[len++] = d;}BigNum::BigNum(const char*s)     //将一个字符串类型的变量转化为大数  {int t, k, index, l, i;memset(a, 0, sizeof(a));l = strlen(s);len = l / DLEN;if (l%DLEN)len++;index = 0;for (i = l - 1; i >= 0; i -= DLEN){t = 0;k = i - DLEN + 1;if (k<0)k = 0;for (int j = k; j <= i; j++)t = t * 10 + s[j] - '0';a[index++] = t;}}BigNum::BigNum(const BigNum & T) : len(T.len)  //拷贝构造函数  {int i;memset(a, 0, sizeof(a));for (i = 0; i < len; i++)a[i] = T.a[i];}BigNum & BigNum::operator=(const BigNum & n)   //重载赋值运算符，大数之间进行赋值运算  {int i;len = n.len;memset(a, 0, sizeof(a));for (i = 0; i < len; i++)a[i] = n.a[i];return *this;}istream& operator>>(istream & in, BigNum & b)   //重载输入运算符  {char ch[MAXSIZE * 4];int i = -1;in >> ch;int l = strlen(ch);int count = 0, sum = 0;for (i = l - 1; i >= 0;){sum = 0;int t = 1;for (int j = 0; j<4 && i >= 0; j++, i--, t *= 10){sum += (ch[i] - '0')*t;}b.a[count] = sum;count++;}b.len = count++;return in;}ostream& operator<<(ostream& out, BigNum& b)   //重载输出运算符  {int i;cout << b.a[b.len - 1];for (i = b.len - 2; i >= 0; i--){cout.width(DLEN);cout.fill('0');cout << b.a[i];}return out;}BigNum BigNum::operator+(const BigNum & T) const   //两个大数之间的相加运算  {BigNum t(*this);int i, big;      //位数     big = T.len > len ? T.len : len;for (i = 0; i < big; i++){t.a[i] += T.a[i];if (t.a[i] > MAXN){t.a[i + 1]++;t.a[i] -= MAXN + 1;}}if (t.a[big] != 0)t.len = big + 1;elset.len = big;return t;}BigNum BigNum::operator-(const BigNum & T) const   //两个大数之间的相减运算   {int i, j, big;bool flag;BigNum t1, t2;if (*this>T){t1 = *this;t2 = T;flag = 0;}else{t1 = T;t2 = *this;flag = 1;}big = t1.len;for (i = 0; i < big; i++){if (t1.a[i] < t2.a[i]){j = i + 1;while (t1.a[j] == 0)j++;t1.a[j--]--;while (j > i)t1.a[j--] += MAXN;t1.a[i] += MAXN + 1 - t2.a[i];}elset1.a[i] -= t2.a[i];}t1.len = big;while (t1.a[t1.len - 1] == 0 && t1.len > 1){t1.len--;big--;}if (flag)t1.a[big - 1] = 0 - t1.a[big - 1];return t1;}BigNum BigNum::operator*(const BigNum & T) const   //两个大数之间的相乘运算   {BigNum ret;int i, j, up;int temp, temp1;for (i = 0; i < len; i++){up = 0;for (j = 0; j < T.len; j++){temp = a[i] * T.a[j] + ret.a[i + j] + up;if (temp > MAXN){temp1 = temp - temp / (MAXN + 1) * (MAXN + 1);up = temp / (MAXN + 1);ret.a[i + j] = temp1;}else{up = 0;ret.a[i + j] = temp;}}if (up != 0)ret.a[i + j] = up;}ret.len = i + j;while (ret.a[ret.len - 1] == 0 && ret.len > 1)ret.len--;return ret;}BigNum BigNum::operator/(const int & b) const   //大数对一个整数进行相除运算  {BigNum ret;int i, down = 0;for (i = len - 1; i >= 0; i--){ret.a[i] = (a[i] + down * (MAXN + 1)) / b;down = a[i] + down * (MAXN + 1) - ret.a[i] * b;}ret.len = len;while (ret.a[ret.len - 1] == 0 && ret.len > 1)ret.len--;return ret;}int BigNum::operator %(const int & b) const    //大数对一个int类型的变量进行取模运算      {int i, d = 0;for (i = len - 1; i >= 0; i--){d = ((d * (MAXN + 1)) % b + a[i]) % b;}return d;}BigNum BigNum::operator^(const int & n) const    //大数的n次方运算  {BigNum t, ret(1);int i;if (n<0)exit(-1);if (n == 0)return 1;if (n == 1)return *this;int m = n;while (m>1){t = *this;for (i = 1; i << 1 <= m; i <<= 1){t = t*t;}m -= i;ret = ret*t;if (m == 1)ret = ret*(*this);}return ret;}bool BigNum::operator>(const BigNum & T) const   //大数和另一个大数的大小比较  {int ln;if (len > T.len)return true;else if (len == T.len){ln = len - 1;while (a[ln] == T.a[ln] && ln >= 0)ln--;if (ln >= 0 && a[ln] > T.a[ln])return true;elsereturn false;}elsereturn false;}bool BigNum::operator >(const int & t) const    //大数和一个int类型的变量的大小比较  {BigNum b(t);return *this>b;}void BigNum::print()    //输出大数  {int i;cout << a[len - 1];for (i = len - 2; i >= 0; i--){cout.width(DLEN);cout.fill('0');cout << a[i];}cout << endl;}