题目描述：
应用中需要解决大数运算问题。请设计有符号大数类，能支持大数＋、－运算和输出。假定本题大数在200位以内。
输入描述：
输入两行分别为两个有符号大数
输出描述：
输出它们的和、差（每个占1行）
输入样例：
-1234567890987654321333888999666
147655765659657669789687967867
输出样例：
-1086912125327996651544201031799
-1382223656647311991123576967533
——————————————————————————————————————
代码：
#include
using namespace std;
class CBigNumber; //向前声明
ostream & operator << (ostream &os, const CBigNumber &rhs); //VC要求
class CUBigNumber; //向前声明
ostream & operator << (ostream &os, const CUBigNumber &rhs); //VC要求
//无符号大整数类，超过256位废弃
class CUBigNumber {
friend class CBigNumber;
private :
char m_digitsA [256];//各位数字，为便于运算，从低位开始存放，有效0~m_len-1
int m_len;//有效位数
public :
CUBigNumber () {} //无参构造,值不确定
CUBigNumber (unsigned int x); //用常规小整数构造
CUBigNumber (char *digitsA); //用字符串构造
CUBigNumber operator + (const CUBigNumber &rhs) const;//
CUBigNumber operator - (const CUBigNumber &rhs) const;//
CUBigNumber operator * (const CUBigNumber &rhs) const;//
CUBigNumber operator / (const CUBigNumber &rhs) const;//
CUBigNumber operator % (const CUBigNumber &rhs) const;//
operator unsigned int () const; //转换为常规小整数，高位废弃
bool operator > (const CUBigNumber &rhs) const; //
bool operator < (const CUBigNumber &rhs) const; //
bool operator == (const CUBigNumber &rhs) const; //
bool operator != (const CUBigNumber &rhs) const;
bool operator >= (const CUBigNumber &rhs) const; //
bool operator <= (const CUBigNumber &rhs) const; //
friend ostream & operator << (ostream &os, const CUBigNumber &rhs);//
private :
void _Multi10 ();//10倍
CUBigNumber _Divide (const CUBigNumber &rhs, CUBigNumber &remainder) const;//相除，结果分整数和余数部分
_Normalize (); //规整化表示, 去除多余0, 0用m_len为0表示(不用m_len为1,数据0表示, 有利于比较处理)
};
class CBigNumber; //向前声明
ostream & operator << (ostream &os, const CBigNumber &rhs); //VC要求
class CBigNumber {
private :
CUBigNumber m_bigValue; //绝对值部分
bool m_bPlus; //有效位数
public :
CBigNumber () {} //无参构造,值不确定
CBigNumber (int x); //用常规小整数构造
CBigNumber (char *digitsA); //用字符串构造
CBigNumber operator + (const CBigNumber &rhs) const;
CBigNumber operator - (const CBigNumber &rhs) const;
CBigNumber operator - () const;
CBigNumber operator * (const CBigNumber &rhs) const;
CBigNumber operator / (const CBigNumber &rhs) const;
CBigNumber operator % (const CBigNumber &rhs) const;
operator int () const;
bool operator > (const CBigNumber &rhs) const;
bool operator < (const CBigNumber &rhs) const;
bool operator == (const CBigNumber &rhs) const;
bool operator != (const CBigNumber &rhs) const;
bool operator >= (const CBigNumber &rhs) const;
bool operator <= (const CBigNumber &rhs) const;
friend ostream & operator << (ostream &os, const CBigNumber &rhs);
private :
_Normalize (); //规整化表示, 绝对值和符号规整化，0时m_bPlus为true表示(有利于比较处理)
};
//规整化表示, 去除多余0, 0用m_len为0表示(不用m_len为1,数据0表示, 有利于比较处理)
CUBigNumber::_Normalize ()
{
while (m_len > 0 && m_digitsA [m_len-1] == 0)
m_len--;
}
CUBigNumber::CUBigNumber (unsigned int x) : m_len (0)
{
while (x) {
m_digitsA [m_len ++] = x % 10;
x /= 10;
}
}
//转换为常规小整数，高位废弃
CUBigNumber::operator unsigned int () const
{
unsigned int x = 0;
unsigned mul = 1;
for (int i = 0; i < 9 && i < m_len; i++) {
x = x + this->m_digitsA [i] * mul;
mul = mul * 10;
}
return x;
}
CUBigNumber::CUBigNumber (char *digitsA)
{
m_len = strlen (digitsA);
for (int i = 0; i_Normalize ();
}
void CUBigNumber::_Multi10 ()
{
if (m_len == 0)
return;
for (int i = m_len; i> 0; i--) {
m_digitsA [i] = m_digitsA [i-1];
}
m_digitsA [0] = 0;
m_len ++;
}
CUBigNumber CUBigNumber::operator + (const CUBigNumber &rhs) const
{
CUBigNumber bigNumber;
int carry = 0;//进位
int i = 0;
while (i < m_len && i < rhs.m_len) {
bigNumber.m_digitsA [i] = this->m_digitsA [i] + rhs.m_digitsA [i] + carry;
carry = bigNumber.m_digitsA [i] / 10;
bigNumber.m_digitsA [i] = bigNumber.m_digitsA [i] % 10;
i++;
}
while (i < m_len) {
bigNumber.m_digitsA [i] = this->m_digitsA [i] + carry;
carry = bigNumber.m_digitsA [i] / 10;
bigNumber.m_digitsA [i] = bigNumber.m_digitsA [i] % 10;
i++;
}
while (i < rhs.m_len) {
bigNumber.m_digitsA [i] = rhs.m_digitsA [i] + carry;
carry = bigNumber.m_digitsA [i] / 10;
bigNumber.m_digitsA [i] = bigNumber.m_digitsA [i] % 10;
i++;
}
if (carry && i < 256) {
bigNumber.m_digitsA [i] = carry;
i++;
}
bigNumber.m_len = i;
bigNumber._Normalize ();
return bigNumber;
}
CUBigNumber CUBigNumber::operator - (const CUBigNumber &rhs) const
{
if (*this <= rhs)
return CUBigNumber ((unsigned int) 0);
CUBigNumber bigNumber;
int carry = 0;//借位
int i = 0;
while (i < rhs.m_len) {
bigNumber.m_digitsA [i] = this->m_digitsA [i] - rhs.m_digitsA [i] + carry;
if (bigNumber.m_digitsA [i] < 0) {
bigNumber.m_digitsA [i] += 10;
carry = -1;
} else
carry = 0;
i++;
}
while (i < m_len) {
bigNumber.m_digitsA [i] = this->m_digitsA [i] + carry;
if (bigNumber.m_digitsA [i] < 0)
carry = -1;
else
carry = 0;
i++;
}
bigNumber.m_len = i;
bigNumber._Normalize ();
return bigNumber;
}
CUBigNumber CUBigNumber::operator * (const CUBigNumber &rhs) const
{
CUBigNumber bigResult ((unsigned int) 0);//结果
CUBigNumber bigSecond (rhs);//被乘数
for (int digit = 0; digit < m_len; digit++) {
int x = m_digitsA [digit];
if (x == 0) {
bigSecond._Multi10 ();
continue;
}
CUBigNumber partResult;//部分结果
int carry = 0;
int i = 0;
while (i < bigSecond.m_len) {
partResult.m_digitsA [i] = x * bigSecond.m_digitsA [i] + carry;
carry = partResult.m_digitsA [i] / 10;
partResult.m_digitsA [i] = partResult.m_digitsA [i] % 10;
i++;
}
if (carry && i < 256) {
partResult.m_digitsA [i] = carry;
i++;
}
partResult.m_len = i;
bigResult = bigResult + partResult;
bigSecond._Multi10 ();
}
bigResult._Normalize ();
return bigResult;
}
//相除，结果分整数和余数部分
CUBigNumber CUBigNumber::_Divide (const CUBigNumber &rhs, CUBigNumber &remainder) const
{
if (*this < rhs) {
remainder = *this;
return CUBigNumber ((unsigned int) 0);
}
//取高rhs.m_len -1位
remainder.m_len = rhs.m_len -1;
int i;
for (i =0; i< remainder.m_len; i++) {
remainder.m_digitsA [remainder.m_len-1-i] = this->m_digitsA [this->m_len - 1 - i];
}
CUBigNumber bigResult ((unsigned int) 0);
for (i = remainder.m_len; i < m_len; i++) {
//再取1位
remainder._Multi10 ();
remainder.m_digitsA [0] = this->m_digitsA [this->m_len - 1 - i];
if (remainder.m_len == 0 && remainder.m_digitsA [0] != 0)
remainder.m_len = 1;
//计算得1位结果
int x = 0;
while (remainder >= rhs) {
remainder = remainder - rhs;
x ++;
}
//添加到低位
bigResult._Multi10 ();
bigResult.m_digitsA [0] = x;
if (bigResult.m_len == 0 && bigResult.m_digitsA [0] != 0)
bigResult.m_len = 1;
}
remainder._Normalize ();
bigResult._Normalize ();
return bigResult;
}
CUBigNumber CUBigNumber::operator / (const CUBigNumber &rhs) const
{
CUBigNumber remainder;
return this->_Divide (rhs, remainder);
}
CUBigNumber CUBigNumber::operator % (const CUBigNumber &rhs) const
{
CUBigNumber remainder;
this->_Divide (rhs, remainder);
return remainder;
}
bool CUBigNumber::operator < (const CUBigNumber &rhs) const
{
//比较位数
if (this->m_len > rhs.m_len) {
return false;
} else if (this->m_len < rhs.m_len) {
return true;
}
//从高位开始比较
for (int i = m_len-1; i >= 0; i--) {
if (m_digitsA [i] > rhs.m_digitsA [i])
return false;
else if (m_digitsA [i] < rhs.m_digitsA [i])
return true;
}
return false;//相等
}
bool CUBigNumber::operator > (const CUBigNumber &rhs) const
{
//比较位数
if (this->m_len > rhs.m_len) {
return true;
} else if (this->m_len < rhs.m_len) {
return false;
}
//从高位开始比较
for (int i = m_len-1; i >= 0; i--) {
if (m_digitsA [i] > rhs.m_digitsA [i])
return true;
else if (m_digitsA [i] < rhs.m_digitsA [i])
return false;
}
return false;//相等
}
bool CUBigNumber::operator == (const CUBigNumber &rhs) const
{
//比较位数
if (this->m_len != rhs.m_len ) {
return false;
}
for (int i = m_len-1; i >= 0; i--) {
if (m_digitsA [i] != rhs.m_digitsA [i])
return false;
}
return true;
}
bool CUBigNumber::operator != (const CUBigNumber &rhs) const
{
return !(*this == rhs);
}
bool CUBigNumber::operator >= (const CUBigNumber &rhs) const
{
return ! (*this < rhs);
}
bool CUBigNumber::operator <= (const CUBigNumber &rhs) const
{
return ! (*this > rhs);
}
ostream & operator << (ostream &os, const CUBigNumber &rhs)
{
if (rhs.m_len == 0)
cout << 0;
for (int i = 0; i< rhs.m_len; i++) {
cout << (char) (rhs.m_digitsA [rhs.m_len-1-i] + '0');
}
return os;
}
//规整化表示, 绝对值和符号规整化，0时m_bPlus为true表示(有利于比较处理)
CBigNumber::_Normalize ()
{
this->m_bigValue._Normalize ();
if (this->m_bigValue.m_len == 0)
m_bPlus = true;
}
CBigNumber::CBigNumber (int x)
{
if (x >= 0) {
m_bigValue = CUBigNumber (x);
m_bPlus = true;
} else {
m_bigValue = CUBigNumber (-x);
m_bPlus = false;
}
}
CBigNumber::CBigNumber (char *digitsA)
{
if (digitsA [0] == '+') {
m_bigValue = CUBigNumber (digitsA+1);
m_bPlus = true;
} else if (digitsA [0] == '-') {
m_bigValue = CUBigNumber (digitsA+1);
m_bPlus = false;
} else {
m_bigValue = CUBigNumber (digitsA);
m_bPlus = true;
}
this->_Normalize ();
}
CBigNumber CBigNumber::operator + (const CBigNumber &rhs) const
{
CBigNumber result;
if (this->m_bPlus && rhs.m_bPlus) {
result.m_bigValue = this->m_bigValue + rhs.m_bigValue;
result.m_bPlus = true;
} else if (!this->m_bPlus && !rhs.m_bPlus) {
result.m_bigValue = this->m_bigValue + rhs.m_bigValue;
result.m_bPlus = false;
} else {
if (this->m_bigValue >= rhs.m_bigValue) {
result.m_bigValue = this->m_bigValue - rhs.m_bigValue;
result.m_bPlus = this->m_bPlus;
} else {
result.m_bigValue = rhs.m_bigValue - this->m_bigValue;
result.m_bPlus = !this->m_bPlus;
}
}
result._Normalize ();
return result;
}
CBigNumber CBigNumber::operator - () const
{
CBigNumber result (*this);
result.m_bPlus = !result.m_bPlus;
result._Normalize ();
return result;
}
CBigNumber CBigNumber::operator - (const CBigNumber &rhs) const
{
return *this + (-rhs);
}
CBigNumber CBigNumber::operator * (const CBigNumber &rhs) const
{
CBigNumber result ;
result.m_bigValue = this->m_bigValue * rhs.m_bigValue;
result.m_bPlus = (this->m_bPlus && rhs.m_bPlus) || (!this->m_bPlus && !rhs.m_bPlus);
result._Normalize ();
return result;
}
CBigNumber CBigNumber::operator / (const CBigNumber &rhs) const
{
CBigNumber result ;
result.m_bigValue = this->m_bigValue / rhs.m_bigValue;
result.m_bPlus = (this->m_bPlus && rhs.m_bPlus) || (!this->m_bPlus && !rhs.m_bPlus);
result._Normalize ();
return result;
}
CBigNumber CBigNumber::operator % (const CBigNumber &rhs) const
{
CBigNumber result ;
result.m_bigValue = this->m_bigValue % rhs.m_bigValue;
result.m_bPlus = (this->m_bPlus && rhs.m_bPlus) || (!this->m_bPlus && !rhs.m_bPlus);
result._Normalize ();
return result;
}
//转换为常规小整数，高位废弃
CBigNumber::operator int () const
{
int result;
result = (unsigned int) (this->m_bigValue);
if (!this->m_bPlus)
result = -result;
return result;
}
bool CBigNumber::operator > (const CBigNumber &rhs) const
{
if (this->m_bPlus && rhs.m_bPlus) {
//均为正数
return m_bigValue > rhs.m_bigValue;
}
if (!this->m_bPlus && !rhs.m_bPlus) {
//均为负数
return m_bigValue < rhs.m_bigValue;
}
//符号不同
return this->m_bPlus;
}
bool CBigNumber::operator == (const CBigNumber &rhs) const
{
return this->m_bPlus == rhs.m_bPlus && m_bigValue == rhs.m_bigValue;
}
bool CBigNumber::operator != (const CBigNumber &rhs) const
{
return !(*this == rhs);
}
bool CBigNumber::operator < (const CBigNumber &rhs) const
{
return !(*this >= rhs);
}
bool CBigNumber::operator >= (const CBigNumber &rhs) const
{
return (*this > rhs) || (*this == rhs);
}
bool CBigNumber::operator <= (const CBigNumber &rhs) const
{
return !(*this > rhs);
}
ostream & operator << (ostream &os, const CBigNumber &rhs)
{
if (!rhs.m_bPlus)
os << '-';
os << rhs.m_bigValue;
return os;
}
//测试演示程序
int main ()
{
char str [257];
cin >> str;
CBigNumber bigNumber1 (str);
cin >> str;
CBigNumber bigNumber2 (str);
CBigNumber bigNumber3;
bigNumber3 = bigNumber1 + bigNumber2;
cout << bigNumber3 << endl;
bigNumber3 = bigNumber1 - bigNumber2;
cout << bigNumber3 << endl;
return 0;
}