之前就保留过简陋的几个用外部数组变量实现的简单大数模板，也没有怎么用过，今天就想着整合封装一下，封装成C++的类，以后需要调用的时候也方便得多。
实现了基本的加减乘除和取模运算的操作符重载，大数除以大数难度太大就没实现，另外还实现了比较运算符，方便实际使用贴近内置类型的体验。
话不多说，贴代码。
/*BigInt.h*/
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#define MAXBIT 1007
#define BITTYPE int
class BigInt {
private:
BITTYPE bit[MAXBIT];
bool negative;//负数标志
public:
BigInt(); //默认构造函数，值为0
BigInt(const int); //构造函数
BigInt(const char *); //构造函数
BigInt(const BigInt &); //复制构造函数
/*重载赋值运算符*/
BigInt& operator=(const BigInt&);
BigInt& operator=(const int );
/*重载算数运算符*/
BigInt operator+(const BigInt& )const;
BigInt operator+(const int )const;
BigInt operator-(const BigInt& )const;
BigInt operator-(const int )const;
BigInt operator*(const BigInt& )const;
BigInt operator*(const int )const;
BigInt operator/(const int )const;
int operator%(const int )const;
/*重载比较运算符*/
bool operator>(const BigInt& )const;
bool operator>(const int )const;
bool operator>=(const BigInt& )const;
bool operator>=(const int )const;
bool operator<(const BigInt& )const;
bool operator<(const int )const;
bool operator<=(const BigInt& )const;
bool operator<=(const int )const;
bool operator==(const BigInt& )const;
bool operator==(const int )const;
bool operator!=(const BigInt& )const;
bool operator!=(const int )const;
void print() const;//输出数值
bool isZero() const;//是否为0
bool isPositive() const;//是否为正数
bool isNegative() const;//是否为负数
bool nonNegative() const;//是否为非负数
private:
BigInt opposite()const;//取相反数
BigInt absoluteAdd(const BigInt&)const;//加上绝对值
BigInt absoluteMinus(const BigInt&)const;//减去绝对值小于自身的数的绝对值
bool absoluteEqual(const BigInt&)const;//绝对值等于
bool absoluteGreater(const BigInt&)const;//绝对值大于
bool absoluteEqualGreater(const BigInt&)const;//绝对值大于等于
};
BigInt::BigInt()
{
memset(bit,,sizeof(bit));
negative = false;
}
BigInt::BigInt(const int n)
{
memset(bit,,sizeof(bit));
int nn = n;
) negative = false;
else {
negative = true;
nn = -nn;
}
;
while (nn) {
bit[pos++] = nn % ;
nn /= ;
}
}
BigInt::BigInt(const char *s)
{
int len = strlen(s);
bool valid = true;//符合数字格式
) {
]!=]!=])) valid = false;
; i<len; ++i) {
if (!isdigit(s[i])) valid = false;
}
}
) {
])) valid = false;
}
|| !valid) {
memset(bit,,sizeof(bit));
negative = false;
return;
}
, end = len-;
] == '+') {
negative = false;
++beg;
}
] == '-') {
bool zeroFlag = true;
; i<len; ++i) {
') {
zeroFlag = false;
break;
}
}
if (zeroFlag) negative = false;
else negative = true;
++beg;
}
else negative = false;
memset(bit,,sizeof(bit));
for (int i=beg; i<=end; ++i) {
bit[len--i] = s[i] - ';
}
}
BigInt::BigInt(const BigInt& n)
{
memcpy(bit,n.bit,sizeof(bit));
negative = n.negative;
}
BigInt& BigInt::operator=(const BigInt& n)
{
memcpy(bit,n.bit,sizeof(bit));
negative = n.negative;
return *this;
}
BigInt& BigInt::operator=(const int n)
{
return *this = BigInt(n);
}
BigInt BigInt::operator+(const BigInt& n)const
{
if ((!negative && !n.negative) || (negative && n.negative)) {
return this->absoluteAdd(n);
}
else {
if (absoluteEqual(n)) return BigInt();
else if (absoluteEqualGreater(n)) return this->absoluteMinus(n);
else return n.absoluteMinus(*this);
}
}
BigInt BigInt::operator+(const int n)const
{
return *this + BigInt(n);
}
BigInt BigInt::operator-(const BigInt& n)const
{
return *this + n.opposite();
}
BigInt BigInt::operator-(const int n)const
{
return *this - BigInt(n);
}
BigInt BigInt::operator*(const BigInt& n)const
{
if (isZero() || n.isZero()) return BigInt();
BigInt bi = BigInt();
if ((!negative && !n.negative) || (negative && n.negative)) {
bi.negative = false;
}
else bi.negative = true;
; i<MAXBIT; ++i) ; j<MAXBIT-i; ++j) {
bi.bit[i+j] += bit[i] * n.bit[j];
}
; i<MAXBIT-; ++i) {//进位
bi.bit[i+] += bi.bit[i] / ;
bi.bit[i] %= ;
}
return bi;
}
BigInt BigInt::operator*(const int n)const
{
return *this * BigInt(n);
}
BigInt BigInt::operator/(const int n)const
{//除以0直接返回0
) return BigInt();
BigInt bi = BigInt();
) || (negative && n<)) {
bi.negative = false;
}
else bi.negative = true;
;//累计除数
; i>=; --i) {
div = div * + bit[i];
bi.bit[i] = div / n;
div %= n;
}
return bi;
}
int BigInt::operator%(const int n)const
{
;//累计余数
; i>=; --i) {
//mod = ((mod*(MAXBIT+1/*??*/)) + bit[i]) % n;
mod = ((mod*) + bit[i]) % n;
}
return mod;
}
bool BigInt::operator>(const BigInt& n)const
{
if (!negative && n.negative) return true;
else if (negative && !n.negative) return false;
else if (!negative && !n.negative) return absoluteGreater(n);
else return n.absoluteGreater(*this);
}
bool BigInt::operator>(const int n)const
{
return *this > BigInt(n);
}
bool BigInt::operator>=(const BigInt& n)const
{
if (!negative && n.negative) return true;
else if (negative && !n.negative) return false;
else if (!negative && !n.negative) return absoluteEqualGreater(n);
else return n.absoluteEqualGreater(*this);
}
bool BigInt::operator>=(const int n)const
{
return *this >= BigInt(n);
}
bool BigInt::operator<(const BigInt& n)const
{
return n > *this;
}
bool BigInt::operator<(const int n)const
{
return *this < BigInt(n);
}
bool BigInt::operator<=(const BigInt& n)const
{
return n >= *this;
}
bool BigInt::operator<=(const int n)const
{
return *this <= BigInt(n);
}
bool BigInt::operator==(const BigInt& n)const
{
if (negative != n.negative) return false;
; i<MAXBIT; ++i) {
if (bit[i] != n.bit[i]) return false;
}
return true;
}
bool BigInt::operator==(const int n)const
{
return *this == BigInt(n);
}
bool BigInt::operator!=(const BigInt& n)const
{
if (negative != n.negative) return true;
; i<MAXBIT; ++i) {
if (bit[i] != n.bit[i]) return true;
}
return false;
}
bool BigInt::operator!=(const int n)const
{
return *this != BigInt(n);
}
void BigInt::print()const
{
if (negative) printf("-");
;
; --pos) {
if (bit[pos]) break;
}
; --i) printf("%d",bit[i]);
}
bool BigInt::isZero()const
{
bool zeroFlag = true;
; i<MAXBIT; ++i) {
) {
zeroFlag = false;
break;
}
}
return zeroFlag;
}
bool BigInt::isPositive()const
{
return !negative && !isZero();
}
bool BigInt::isNegative()const
{
return negative;
}
bool BigInt::nonNegative()const
{
return !negative;
}
BigInt BigInt::opposite()const
{
BigInt n(*this);
if (!n.isZero()) n.negative = !n.negative;
return n;
}
BigInt BigInt::absoluteAdd(const BigInt& n)const
{
BigInt bi(*this);
;//进位
; i<MAXBIT; ++i) {
bi.bit[i] = (bit[i] + n.bit[i] + next) % ;
next = (bit[i] + n.bit[i] + next) / ;
}
return bi;
}
BigInt BigInt::absoluteMinus(const BigInt& n)const
{
BigInt bi(*this);
; i>=; --i) {
if (bi.bit[i]>=n.bit[i]) bi.bit[i] -= n.bit[i];
else {//借位
;//借位位
) ++borrow;
--bi.bit[borrow];
; j<borrow; ++j) bi.bit[j] = ;
bi.bit[i] = bi.bit[i] + - n.bit[i];
}
}
return bi;
}
bool BigInt::absoluteEqual(const BigInt& n)const
{
; i<MAXBIT; ++i) {
if (bit[i] != n.bit[i]) return false;
}
return true;
}
bool BigInt::absoluteGreater(const BigInt& n)const
{
; i>=; --i) {
if (bit[i]>n.bit[i]) return true;
else if (bit[i]<n.bit[i]) return false;
}
return false;
}
bool BigInt::absoluteEqualGreater(const BigInt& n)const
{
; i>=; --i) {
if (bit[i]>n.bit[i]) return true;
else if (bit[i]<n.bit[i]) return false;
}
return true;
}
代码调用也挺方便，如下例子：
#include "BigInt.h"
int main()
{
BigInt m = ;
BigInt n("-32143542");
if (m >= n) puts("m >= n");
n = m + n;
n = n * ;
n.print();
;
}
模板写成后特地去poj刷了大数相加和大数相乘两道水题，一次ac的满足感可是杠杠的~
欢迎大家参考，测试，批评指正bug和不足之处，感谢~
---------------------------------------------------------------------------------------------
2014/10/15更新
添加了重载负号，+=,-=,*=,/=,%=，还有string()函数返回值的字符串功能
/*BigInt.h*/
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#define MAXBIT 1007
#define BITTYPE int
class BigInt {
private:
BITTYPE bit[MAXBIT];
bool negative;//负数标志
public:
BigInt(); //默认构造函数，值为0
BigInt(const int); //构造函数
BigInt(const char *); //构造函数
BigInt(const BigInt &); //复制构造函数
/*重载赋值运算符*/
BigInt& operator=(const BigInt&);
BigInt& operator=(const int );
/*重载算数运算符*/
BigInt operator+(const BigInt& )const;
BigInt operator+(const int )const;
BigInt operator+=(const BigInt& );
BigInt operator+=(const int );
BigInt operator-(const BigInt& )const;
BigInt operator-(const int )const;
BigInt operator-=(const BigInt& );
BigInt operator-=(const int );
BigInt operator-( )const;
BigInt operator*(const BigInt& )const;
BigInt operator*(const int )const;
BigInt operator*=(const BigInt& );
BigInt operator*=(const int );
BigInt operator/(const int )const;
BigInt operator/=(const int );
int operator%(const int )const;
BigInt operator%=(const int );
/*重载比较运算符*/
bool operator>(const BigInt& )const;
bool operator>(const int )const;
bool operator>=(const BigInt& )const;
bool operator>=(const int )const;
bool operator<(const BigInt& )const;
bool operator<(const int )const;
bool operator<=(const BigInt& )const;
bool operator<=(const int )const;
bool operator==(const BigInt& )const;
bool operator==(const int )const;
bool operator!=(const BigInt& )const;
bool operator!=(const int )const;
void print() const;//输出数值
char *string() const;//返回数值字符串
bool isZero() const;//是否为0
bool isPositive() const;//是否为正数
bool isNegative() const;//是否为负数
bool nonNegative() const;//是否为非负数
private:
BigInt opposite()const;//取相反数
BigInt absoluteAdd(const BigInt&)const;//加上绝对值
BigInt absoluteMinus(const BigInt&)const;//减去绝对值小于自身的数的绝对值
bool absoluteEqual(const BigInt&)const;//绝对值等于
bool absoluteGreater(const BigInt&)const;//绝对值大于
bool absoluteEqualGreater(const BigInt&)const;//绝对值大于等于
};
BigInt::BigInt()
{
memset(bit,,sizeof(bit));
negative = false;
}
BigInt::BigInt(const int n)
{
memset(bit,,sizeof(bit));
int nn = n;
) negative = false;
else {
negative = true;
nn = -nn;
}
;
while (nn) {
bit[pos++] = nn % ;
nn /= ;
}
}
BigInt::BigInt(const char *s)
{
int len = strlen(s);
bool valid = true;//符合数字格式
) {
]!=]!=])) valid = false;
; i<len; ++i) {
if (!isdigit(s[i])) valid = false;
}
}
) {
])) valid = false;
}
|| !valid) {
memset(bit,,sizeof(bit));
negative = false;
return;
}
, end = len-;
] == '+') {
negative = false;
++beg;
}
] == '-') {
bool zeroFlag = true;
; i<len; ++i) {
') {
zeroFlag = false;
break;
}
}
if (zeroFlag) negative = false;
else negative = true;
++beg;
}
else negative = false;
memset(bit,,sizeof(bit));
for (int i=beg; i<=end; ++i) {
bit[len--i] = s[i] - ';
}
}
BigInt::BigInt(const BigInt& n)
{
memcpy(bit,n.bit,sizeof(bit));
negative = n.negative;
}
BigInt& BigInt::operator=(const BigInt& n)
{
memcpy(bit,n.bit,sizeof(bit));
negative = n.negative;
return *this;
}
BigInt& BigInt::operator=(const int n)
{
return *this = BigInt(n);
}
BigInt BigInt::operator+(const BigInt& n)const
{
if ((!negative && !n.negative) || (negative && n.negative)) {
return this->absoluteAdd(n);
}
else {
if (absoluteEqual(n)) return BigInt();
else if (absoluteEqualGreater(n)) return this->absoluteMinus(n);
else return n.absoluteMinus(*this);
}
}
BigInt BigInt::operator+(const int n)const
{
return *this + BigInt(n);
}
BigInt BigInt::operator+=(const BigInt& n)
{
return *this = *this + n;
}
BigInt BigInt::operator+=(const int n)
{
return *this = *this + n;
}
BigInt BigInt::operator-(const BigInt& n)const
{
return *this + n.opposite();
}
BigInt BigInt::operator-(const int n)const
{
return *this - BigInt(n);
}
BigInt BigInt::operator-=(const BigInt& n)
{
return *this = *this - n;
}
BigInt BigInt::operator-=(const int n)
{
return *this = *this - n;
}
BigInt BigInt::operator-()const
{
BigInt bi(*this);
if (!this->isZero()) bi.negative = !bi.negative;
return bi;
}
BigInt BigInt::operator*(const BigInt& n)const
{
if (isZero() || n.isZero()) return BigInt();
BigInt bi = BigInt();
if ((!negative && !n.negative) || (negative && n.negative)) {
bi.negative = false;
}
else bi.negative = true;
; i<MAXBIT; ++i) ; j<MAXBIT-i; ++j) {
bi.bit[i+j] += bit[i] * n.bit[j];
}
; i<MAXBIT-; ++i) {//进位
bi.bit[i+] += bi.bit[i] / ;
bi.bit[i] %= ;
}
return bi;
}
BigInt BigInt::operator*(const int n)const
{
return *this * BigInt(n);
}
BigInt BigInt::operator*=(const BigInt& n)
{
return *this = *this - n;
}
BigInt BigInt::operator*=(const int n)
{
return *this = *this * n;
}
BigInt BigInt::operator/(const int n)const
{//除以0直接返回0
) return BigInt();
BigInt bi = BigInt();
) || (negative && n<)) {
bi.negative = false;
}
else bi.negative = true;
;//累计除数
; i>=; --i) {
div = div * + bit[i];
bi.bit[i] = div / n;
div %= n;
}
return bi;
}
BigInt BigInt::operator/=(const int n)
{//除以0直接返回0
) return BigInt();
else return *this = *this / n;
}
int BigInt::operator%(const int n)const
{
;//累计余数
; i>=; --i) {
//mod = ((mod*(MAXBIT+1/*??*/)) + bit[i]) % n;
mod = ((mod*) + bit[i]) % n;
}
return mod;
}
BigInt BigInt::operator%=(const int n)
{
;//累计余数
; i>=; --i) {
//mod = ((mod*(MAXBIT+1/*??*/)) + bit[i]) % n;
mod = ((mod*) + bit[i]) % n;
}
return *this = BigInt(mod);
}
bool BigInt::operator>(const BigInt& n)const
{
if (!negative && n.negative) return true;
else if (negative && !n.negative) return false;
else if (!negative && !n.negative) return absoluteGreater(n);
else return n.absoluteGreater(*this);
}
bool BigInt::operator>(const int n)const
{
return *this > BigInt(n);
}
bool BigInt::operator>=(const BigInt& n)const
{
if (!negative && n.negative) return true;
else if (negative && !n.negative) return false;
else if (!negative && !n.negative) return absoluteEqualGreater(n);
else return n.absoluteEqualGreater(*this);
}
bool BigInt::operator>=(const int n)const
{
return *this >= BigInt(n);
}
bool BigInt::operator<(const BigInt& n)const
{
return n > *this;
}
bool BigInt::operator<(const int n)const
{
return *this < BigInt(n);
}
bool BigInt::operator<=(const BigInt& n)const
{
return n >= *this;
}
bool BigInt::operator<=(const int n)const
{
return *this <= BigInt(n);
}
bool BigInt::operator==(const BigInt& n)const
{
if (negative != n.negative) return false;
; i<MAXBIT; ++i) {
if (bit[i] != n.bit[i]) return false;
}
return true;
}
bool BigInt::operator==(const int n)const
{
return *this == BigInt(n);
}
bool BigInt::operator!=(const BigInt& n)const
{
if (negative != n.negative) return true;
; i<MAXBIT; ++i) {
if (bit[i] != n.bit[i]) return true;
}
return false;
}
bool BigInt::operator!=(const int n)const
{
return *this != BigInt(n);
}
void BigInt::print()const
{
if (negative) printf("-");
;
; --pos) {
if (bit[pos]) break;
}
; --i) printf("%d",bit[i]);
}
char *BigInt::string()const
{
];
;
if (negative) content[posi++] = '-';
;
; --pos) {
if (bit[pos]) break;
}
//printf("pos = %d\n",pos);
; --i) {
content[posi++] = bit[i] + ';
//printf("bit[%d] = %d\n",i,bit[i]);
}
content[posi] = '\0';
return content;
}
bool BigInt::isZero()const
{
bool zeroFlag = true;
; i<MAXBIT; ++i) {
) {
zeroFlag = false;
break;
}
}
return zeroFlag;
}
bool BigInt::isPositive()const
{
return !negative && !isZero();
}
bool BigInt::isNegative()const
{
return negative;
}
bool BigInt::nonNegative()const
{
return !negative;
}
BigInt BigInt::opposite()const
{
BigInt n(*this);
if (!n.isZero()) n.negative = !n.negative;
return n;
}
BigInt BigInt::absoluteAdd(const BigInt& n)const
{
BigInt bi(*this);
;//进位
; i<MAXBIT; ++i) {
bi.bit[i] = (bit[i] + n.bit[i] + next) % ;
next = (bit[i] + n.bit[i] + next) / ;
}
return bi;
}
BigInt BigInt::absoluteMinus(const BigInt& n)const
{
BigInt bi(*this);
; i>=; --i) {
if (bi.bit[i]>=n.bit[i]) bi.bit[i] -= n.bit[i];
else {//借位
;//借位位
) ++borrow;
--bi.bit[borrow];
; j<borrow; ++j) bi.bit[j] = ;
bi.bit[i] = bi.bit[i] + - n.bit[i];
}
}
return bi;
}
bool BigInt::absoluteEqual(const BigInt& n)const
{
; i<MAXBIT; ++i) {
if (bit[i] != n.bit[i]) return false;
}
return true;
}
bool BigInt::absoluteGreater(const BigInt& n)const
{
; i>=; --i) {
if (bit[i]>n.bit[i]) return true;
else if (bit[i]<n.bit[i]) return false;
}
return false;
}
bool BigInt::absoluteEqualGreater(const BigInt& n)const
{
; i>=; --i) {
if (bit[i]>n.bit[i]) return true;
else if (bit[i]<n.bit[i]) return false;
}
return true;
}