.cpp
#include"BigData.h"
BigData::BigData(INT64 value)
:_value(value)
{
INT64ToString(); //构造函数时将数字转换为字符串
}
BigData::BigData(const char* pData)//对大数进行处理.
{
//几种情况:" ","+123456","00001234","12345xyz","123456789";
if (NULL == pData) //如果是空
{
assert(false ); //断言false,返回
return;
}
char* pStr = (char *)pData;
char cSymbol = pData [0];//第一位
if ('+' == cSymbol || '-' == cSymbol)
{
pStr++; //后移
}
else if (cSymbol >= '0' && cSymbol <= '9')
{
cSymbol = '+'; //将符号位置为+
}
else
return;
//处理"000000000000001234" 情况
while ('0' == *pStr)
{
pStr++;
}
//处理 带字母的情况
_strData.resize(strlen( pData) + 1);//string中resize()函数改变本字符串的大小
_strData[0] = cSymbol; //第一位存放符号位
_value = 0;
int icount = 1;
while (*pStr >= '0' && *pStr <= '9') //字母不处理,丢弃
{
_value = 10 * _value + *pStr - '0';
_strData[icount++] = *pStr;
pStr++;
}
_strData.resize(icount); //将本字符串的大小调到icount
if ('-' == cSymbol) //负数
{
_value = 0 - _value; //负值
}
}
bool BigData ::IsINT64OverFlow()const//溢出判断
{//64位中数字范围为:[-Ox8FFFFFFF FFFFFFFF,Ox7FFFFFFF FFFFFFFF]
std:: string temp = "+9223372036854775807" ;
if ('-' == _strData[0])
{
temp = "-9223372036854775808";
}
//1.比较该大数与边界的size。2.相等时进行字符串直接比较
if (_strData.size() < temp.size() || _strData.size() == temp.size() && _strData <= temp)
return true ;
else
return false ;
}
void BigData ::INT64ToString()//将value转换为字符串
{//append()在字符串的末尾添加num个字符ch-----basic_string &(append(size_t num,char ch))
char cSymbol = '+' ; //正号
if (_value < 0)
{
cSymbol = '-';
}
//12345->"54321"
INT64 temp = _value;
_strData.append(1, cSymbol); //先添加符号位
if (cSymbol == '-' )//负数转变成正数再模除
{
temp = 0 - temp;
}
while (temp)
{
_strData.append(1, temp % 10 + '0');
temp /= 10;
}
//"54321"->"12345"
char* pLeft = (char *)_strData.c_str() + 1;
char* pRight = pLeft + _strData.size() - 2;//包含符号位,故减2
while (pLeft < pRight) //倒序交换
{
char tmp = *pLeft;
*pLeft = *pRight;
*pRight = tmp;
pLeft++;
pRight--;
}
}
//operator<<
std::ostream& (operator<<(std:: ostream& _cout , const BigData& bigdata))//输出大数
{//判断是否溢出,'+'不需要输出
if (bigdata .IsINT64OverFlow())//没有溢出
{
_cout << bigdata ._value << std::endl;
}
else
{ //c_str()函数返回一个指向正规C字符串的指针, 内容与本字符串相同
char* pData = (char *)bigdata._strData.c_str();
if ('+' == pData[0])
pData++;
_cout << pData << std::endl;
}
return _cout ;
}
//operator+
BigData BigData ::operator+(const BigData& bigdata )
{
//两个数都没溢出,结果也没溢出,直接进行相加
if (IsINT64OverFlow() && bigdata .IsINT64OverFlow())
{
//异号
if (_strData[0] != bigdata ._strData[0])
{
return _value + bigdata ._value;
}
else //同号
{ //两个数同号,没溢出的情况:如果边界是10,则10-3=7>=6 8,-10-(-3)=-7=<-6 -8
//正数时,最大值-value>=结果,才不会溢出
//负数时,最大负数-value<=结果,才不会溢出
if ((_value >= 0 && (MAX_INT64 - _value >= bigdata._value)) ||
(_value < 0 && (MIN_INT64 - _value <= bigdata._value)))
{
return _value + bigdata ._value;
}
else //溢出->调用溢出加法
{
return BigData (Add(_strData, bigdata._strData).c_str());
}
}
}
//两个数至少一个溢出,结果溢出
if (_strData[0] == bigdata ._strData[0]) //同号
{
return BigData (Add(_strData, bigdata._strData).c_str());
}
//异号
else
{ //两个数异号a,b;b为正数需要换负号,b为负数需要换正号
//将b的符号进行转换,在调用大数减法
string _StrData = bigdata ._strData;//注意定义字符串
if (_StrData[0] == '+' )
{
_StrData[0] = '-';
}
else
{
_StrData[0] = '+';
}
return BigData (Sub(_strData, _StrData).c_str());
}
}
//溢出加法
std::string BigData::Add(std::string left, std:: string right )
{
int iLsize = left .size(); //size
int iRsize = right .size();
if (iLsize < iRsize)//选出大的长度给iLsize
{
std::swap( left, right );
std::swap(iLsize, iRsize);
}
std:: string sRet;
sRet.resize(iLsize + 1); //相加不会超过较大数的size+1
sRet[0] = left[0];
char Step = 0;//进位标识符
//
//模除得到每位的数字及进位Step
for (int iIdx = 1; iIdx < iLsize; iIdx++)
{
int cRet = left [iLsize - iIdx] + Step - '0';
if (iIdx < iRsize)
{
cRet += right[iRsize - iIdx] - '0' ;//cRet转为数字:-‘0’
}
sRet[iLsize - iIdx + 1] = cRet % 10 + '0';//sRet比iLsize多一位,存放字符,故+‘0’
Step = cRet / 10;
}
sRet[1] = Step + '0'; //???
return sRet;
}
BigData BigData ::operator-(const BigData& bigdata )
{
//两个数都没溢出,结果也没溢出,相减
if (IsINT64OverFlow() && bigdata .IsINT64OverFlow())
{
if (_strData[0] == bigdata ._strData[0])
{
return _value - bigdata ._value; //
}
else
{
//两个数异号,相减没溢出
//-10 + 3 = -7 <= -6(减式:3-(-6));10+(-3)= 7 >= 6(减式:-3-(6))
if (_value >= 0 && (MIN_INT64 + _value <= bigdata._value) ||
_value < 0 && (MAX_INT64 + _value >= bigdata._value))
{
return _value + bigdata ._value;
}
else
{ //调用溢出加法
BigData(Add(_strData, bigdata._strData).c_str());
}
}
}
//两个数至少一个溢出,
//同号调用减法
if (_strData[0] == bigdata ._strData[0])
{
return BigData (Sub(_strData, bigdata._strData).c_str());
}
else //异号调用加法
{
return BigData (Add(_strData, bigdata._strData).c_str());
}
}
std::string BigData::Sub(std::string left, std:: string right )
{
int iLsize = left .size();
int iRsize = right .size();
char cSymbol = left [0];//符号位
if (iLsize < iRsize || (iLsize == iRsize && left < right))//左边小于右边都进行交换
{ //-12-(-21)=9,21-34=-13发现两数的差与减数的相反
std::swap( left, right );
std::swap(iLsize, iRsize);
if (cSymbol == '-' )
{
cSymbol = '+';
}
else
{
cSymbol = '-';
}
}
std:: string sRet;
sRet.resize(iLsize); //用大的长度进行开辟空间
sRet[0] = cSymbol; //保存符号位
for (int iIdx = 1; iIdx < iLsize; iIdx++)//结束标志为iLsize-1,不是iLsize
{
//从低到高,取left每一位;
char cRet = left [iLsize - iIdx] - '0';
//在right范围内从低到高,取right每一位,然后相减;
if (iIdx < iRsize)
{
cRet -= right[iRsize - iIdx] - '0' ;
}
//判断是否借位
if (cRet < 0)
{
left[iLsize - iIdx - 1] -= 1; //上一位减一
cRet += 10; //
}
sRet[iLsize - iIdx] = cRet + '0';
}
return sRet;
}
BigData BigData ::operator*(const BigData& bigdata )
{//无溢出
if (IsINT64OverFlow() && bigdata .IsINT64OverFlow())
{
if (_strData[0] == bigdata ._strData[0])//同号
{
//例如:边界是10,10 / 2 = 5 > 4; 10 / -2 = -5 < -4;
//结果不会溢出
if (_value > 0 && MAX_INT64 / _value >= bigdata._value ||
_value < 0 && MAX_INT64 / _value <= bigdata._value)
{
return _value*bigdata ._value;
}
}
else //异号
{
//例如:边界是-10,-10 / 2 = -5 < -4; -10 / -2 = 5 > 4;
//不会溢出
if (_value>0 && MIN_INT64 / _value <= bigdata._value ||
_value < 0 && MIN_INT64 / _value >= bigdata._value)
{
return _value*bigdata ._value;
}
}
}
//两数至少有一个溢出
if (_value != 0 && bigdata ._value != 0)
{
return BigData (Mul(_strData, bigdata._strData).c_str());
}
}
//溢出乘法
std::string BigData::Mul(std::string left, std:: string right )
{
int iLsize = left .size();
int iRsize = right .size();
char cSymbol = '+' ;//确认符号位
if (left [0] != right[0])
{
cSymbol = '-';
}
if (iLsize > iRsize)//使较小的数为left,提高效率。eg:99*12345678
{
swap( left, right );
swap(iLsize, iRsize);
}
std:: string sRet;
//两个数相乘最大位数为两个数位数的和,left和right中有符号位故减1
sRet.assign(iLsize + iRsize - 1, '0');//assign()为字符串赋新值'0'
sRet[0] = cSymbol;
int iDataLen = iLsize + iRsize - 1;
int ioffset = 0;//pian移位
//先取左边一位和右边相乘;再考虑移位可得到左边每位与右边相乘的结果
for (int iLdx = 1; iLdx < iLsize; iLdx++)
{
char cLeft = left [iLsize - iLdx] - '0';
if (cLeft == 0)//如果left中含有0,偏移量加1
{
ioffset++;
continue;
}
char Step = 0;
//99*999=89910+8991;
for (int iRdx = 1; iRdx < iRsize; iRdx++)
{
char cRet = cLeft * (right [iRsize - iRdx] - '0') + Step;
cRet += sRet[iDataLen - iRdx - ioffset] - '0';//cRet存放当前最终乘加的结果
sRet[iDataLen - iRdx - ioffset] = cRet % 10 + '0';//存放字符+'0'
Step = cRet / 10;
}
sRet[iDataLen - iRsize - ioffset] += Step;
ioffset++;
}
return sRet;
}
BigData BigData ::operator/(const BigData& bigdata )
{
//1、除数为0
if (bigdata ._strData[1] == '0')
{
assert(false );
}
//2、两个数没溢出
if (IsINT64OverFlow() && bigdata .IsINT64OverFlow())
{
return _value / bigdata ._value;
}
//3、除数为1或-1
if (bigdata ._value == 1 || bigdata._value == -1)
{
return _value;
}
//4、除数和被除数相等
//data()返回内容的字符数组形式
if (strcmp(_strData.c_str() + 1, bigdata ._strData.c_str() + 1) == 0)
{
if (_strData[0] != bigdata ._strData[0])
{
return BigData (INT64(-1));
}
return BigData (INT64(1));
}
//除数大于被除数,返回0
if (_strData.size() < bigdata ._strData.size() ||
_strData.size() == bigdata._strData.size() &&
strcmp(_strData.c_str() + 1, bigdata._strData.c_str() + 1) < 0)
{
return BigData (INT64(0));
}
//调用溢出除法
return BigData (Div(_strData, bigdata._strData).c_str());
}
std::string BigData::Div(std::string left, std:: string right )
{//此处用append()对字符串依次赋值
std:: string sRet;
sRet.append(1, '+');
if (left [0] != right[0])
{
sRet[0] = '-';
}
char* pLeft = (char *)left.c_str() + 1;
char* pRight = (char *)right.c_str() + 1;
int DataLen = right .size() - 1;//标记相除的除数位数
int Lsize = left .size() - 1;
int Rsize = right .size() - 1;
//eg:222222/33首先取到22和33比较大小,如果大就直接相除,否则DataLen++;
for (int iIdx = 0; iIdx < Lsize;)
{
if (!(IsLeftstrBig(pLeft, DataLen, pRight, Rsize)))//如果取到的数小于除数时,结果商0,向后再取一位
{
sRet.append(1, '0');
DataLen++;
}
else
{
sRet.append(1, SubLoop(pLeft, DataLen, pRight, Rsize));//循环相减得到该位的商
//判断pLeft中进行循环相减后依次去掉0,
while (*pLeft == '0' && DataLen > 0)
{
pLeft++;
DataLen--;
iIdx++;
}
DataLen++;
}
if (DataLen > Rsize + 1)//pLeft比pRight大一位结果为0,则pLeft中含有0
{
pLeft++;
DataLen--;
iIdx++;
}
if (DataLen + iIdx > Lsize)//判断是否除法结束
break;
}
return sRet;
}
//循环相减
char BigData ::SubLoop(char* pLeft, int Lsize, const char * pRight, int Rsize)
{
assert(pLeft && pRight);
char cRet = 0;
while (IsLeftstrBig(pLeft , Lsize, pRight, Rsize ))//直到被减数小于减数停止运算
{
for (int iIdx = 0; iIdx < Rsize; iIdx++) //进行减运算
{
char ret = pLeft [Lsize - iIdx - 1] - '0';
ret -= pRight[Rsize - iIdx - 1] - '0';
if (ret < 0)
{
pLeft[Lsize - iIdx - 2] -= 1;
ret += 10;
}
pLeft[Lsize - iIdx - 1] = ret + '0';
}
while (*pLeft == '0'&& Lsize>0)
{
pLeft++;
Lsize--;
}
cRet++;
}
return cRet + '0' ;
}
//判断是否left大于right
bool BigData ::IsLeftstrBig(const char* pLeft , int Lsize, const char * pRight, int Rsize)
{
assert(pLeft && pRight);
char* pleft = (char *)pLeft;
char* pright = (char *)pRight;
if (Lsize > Rsize && *pleft > '0')//eg:112和33
{
return true ;
}
else if (Lsize == Rsize)//eg:57和33
{
while (pright)
{
if (*pleft > *pright)
{
return true ;
}
else if (*pleft == *pright)
{
pleft++;
pright++;
}
else
return false ;
}
}
return false ;
}
.h
#ifndef BIG_DATA_H
#define BIG_DATA_H
#include<iostream>
using namespace std;
#include<assert.h>
#include<string>
#define UN_INTT 0xCCCCCCCCCCCCCCCC
#define MAX_INT64 0x7FFFFFFFFFFFFFFF
#define MIN_INT64 0x8000000000000000
typedef long long INT64;
//内置类型
class BigData
{
public:
BigData( INT64 value);
BigData( const char * pData);//对大数进行处理,优化
friend std::ostream & (operator<<(std::ostream& _cout, const BigData& bigdata));//输出大数
public:
//大数的四则运算
BigData operator+(const BigData& bigdata); //返回值不能传引用
BigData operator-(const BigData& bigdata);
BigData operator*(const BigData& bigdata);
BigData operator/(const BigData& bigdata);
std:: string Add(std::string left, std::string right);
std:: string Sub(std::string left, std::string right);
std:: string Mul(std::string left, std::string right);
std:: string Div(std::string left, std::string right);
private:
bool IsINT64OverFlow()const ;//判断大数是否溢出
void INT64ToString();//由于值在_value中,需将_value转化成string类型
char SubLoop(char * pLeft, int Lsize, const char * pRight, int Rsize);//循环相减
bool IsLeftstrBig(const char* pLeft, int Lsize, const char* pRight, int Rsize);//判断是否left大于right
private:
std:: string _strData;
INT64 _value;
};
#endif
test.cpp
#define _CRT_SECURE_NO_WARNINGS 1
#include<iostream>
using namespace std;
#include"BigData.h"
void Test1()
{
//BigData b1(1234);
//BigData b2("123456");
//BigData b3("+1234567");
//BigData b4("+1234567aaaa");
//BigData b5("+");
//BigData b6(" ");
//BigData b7("-12345678");
//BigData b8("-0000000012345aaa");
//cout << b1 << endl;
//cout << b2 << endl;
//cout << b3 << endl;
//cout << b4 << endl;
//cout << b5 << endl;
//cout << b6 << endl;
//cout << b7 << endl;
//cout << b8 << endl;
//b3 = b2 + b1;
}
//test Add
void Test2()
{
/*BigData left1(1234);
BigData right1(4321);
BigData ret = (left1 + right1);
cout << ret << endl;*/
/*BigData left2(9223372036854775807);
BigData right2(2);
BigData ret = (left2 + right2);
cout << ret << endl;*/
/*BigData left3(-9223372036854775807);
cout << left3 << endl;
BigData right3(-6);
cout << right3 << endl;
BigData ret = (left3 + right3);
cout << ret << endl;*/
/*BigData left2("999999999999999999999999999999");
cout << left2 << endl;
BigData right2("111111111111111111111111111111");
cout << right2 << endl;
BigData ret = (left2 + right2);
cout << ret << endl;*/
}
void Test3()
{
/* BigData left2(1234);
cout << left2 << endl;
BigData right2(34);
cout << right2 << endl;
BigData ret = (left2 - right2);
cout << ret << endl;*/
/*BigData left2(9223372036854775807);
cout << left2 << endl;
BigData right2(-999);
cout << right2 << endl;
BigData ret = (left2 - right2);
cout << ret << endl;*/
/*BigData left2(9223372036854775807);
cout << left2 << endl;
BigData right2(999);
cout << right2 << endl;
BigData ret = (left2 - right2);
cout << ret << endl;*/
/*BigData left2(-9223372036854775807);
cout << left2 << endl;
BigData right2(-999);
cout << right2 << endl;
BigData ret = (left2 - right2);
cout << ret << endl;*/
BigData left2("1111111111111111111111111111111111111" );
cout << left2 << endl;
BigData right2("99" );
cout << right2 << endl;
BigData ret = (left2 - right2);
cout << ret << endl;
BigData left3(9223372036854775807);
cout << left3 << endl;
BigData right3("-999" );
cout << right3 << endl;
BigData ret3 = (left3 - right3);
cout << ret3 << endl;
}
//test mul
void Test4()
{
/*BigData left2("999");
cout << left2 << endl;
BigData right2("9999999999999999999999999999999999999999");
cout << right2 << endl;
BigData ret = (left2 * right2);
cout << ret << endl;
*/
/*BigData left2("-999");
cout << left2 << endl;
BigData right2("99999999999999");
cout << right2 << endl;
BigData ret = (left2 * right2);
cout << ret << endl;*/
}
//Div
void Test5()
{
/*BigData left1(1234);
BigData right1(4321);
BigData ret = (left1 / right1);
cout << ret << endl;*/
/*BigData left1(123456789);
BigData right1(4321);
BigData ret = (left1 / right1);
cout << ret << endl;*/
BigData left2("999999999999999999999999999999" );
//cout << left2 << endl;
BigData right2("111111111111111111111111111111" );
//cout << right2 << endl;
BigData ret = (left2 / right2);
cout << ret << endl;
}
int main()
{
//Test1();
//Test2();
//Test3();
//Test4();
Test5();
system( "pause");
return 0;
}
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