大数乘法、大数加法实现

<span style="font-size:14px;">#include <iostream>
#include <stack>
#include <queue>
#include <algorithm>
#include <string.h>
#include <cstdio>
#include <stdlib.h>
#include <cctype>
using namespace std;

// 实现两个数的加法

// 判断一个字符串是否为有效的数
bool isValidNumber( const string &s )
{
bool ret = true;
int len = s.length();

if( len <= 0 )
{
ret = false;
return ret;
}

if( 1 == len && ( '+' == s[0] || '-' == s[0] ) )
{
ret = false;
return ret;
}

for( int i = 0; i < len; i++ )
{
if( 0 == isdigit( s[i] ) )
{
if( 0 == i && ( '+' == s[0] || '-' == s[0] ) )
{
continue;
}
else
{
ret = false;
break;
}
}
}

return ret;
}

// 实现两个正数的加法
string twoPositivePlus( const string &lhs, const string &rhs )
{
string result = "";

if( !isValidNumber( lhs ) || !isValidNumber( rhs ) )
{
return result;
}

int len1 = lhs.length();
int len2 = rhs.length();

int len = len1 > len2 ? len1 + 2 : len2 + 2;

result.resize(len);

string lhs1 = lhs;
string rhs1 = rhs;

if( '+' == lhs[0] )
{
lhs1.assign( lhs, 1, len1 - 1 );
}

if( '+' == rhs[0] )
{
rhs1.assign( rhs, 1, len2 - 1 );
}

int len11 = lhs1.length();
int len22 = rhs1.length();
int i = 0;
int j = 0;
int up = 0;
int idx = 0;

for( i = len11 - 1, j = len22 - 1; i >= 0 && j >= 0; i--, j-- )
{
int add = ( lhs1[i] - '0' ) + ( rhs1[j] - '0' ) + up;

if( add >= 10 )
{
add = add - 10;
result[ idx++ ] = add + '0';
up = 1;
}
else
{
result[ idx++ ] = add + '0';
up = 0;
}

}

while( i >= 0 )
{
int add = ( lhs1[i] - '0' ) + up;

if( add >= 10 )
{
add = add - 10;
result[ idx++ ] = add + '0';
up = 1;
}
else
{
result[ idx++ ] = add + '0';
up = 0;
}

i--;
}

while( j >= 0 )
{
int add = ( rhs1[j] - '0' ) + up;

if( add >= 10 )
{
add = add - 10;
result[ idx++ ] = add + '0';
up = 1;
}
else
{
result[ idx++ ] = add + '0';
up = 0;
}

j--;
}

if( 1 == up )
{
result[ idx++ ] = '1';
}

result[idx] = '\0';
result.resize( idx + 1 );
//result.reverse();
for( i = 0, j = idx - 1; i < j; i++, j-- )
{
char ch = result[i];
result[i] = result[j];
result[j] = ch;
}

return result;

}

// 正数加上负数
string posiveAddNegative( const string &lhs, const string &rhs )
{
string result = "";

if( !isValidNumber( lhs ) || !isValidNumber( rhs ) )
{
return result;
}

int len1 = lhs.length();
int len2 = rhs.length();

int len = len1 > len2 ? len1 + 2 : len2 + 2;

result.resize(len);
string lhs1 = lhs;
string rhs1 = rhs;

if( '+' == lhs[0] )
{
lhs1.assign( lhs, 1, len1 - 1 );
}

if( '-' == rhs[0] )
{
rhs1.assign( rhs, 1, len2 - 1 );
}

int flag = lhs1.compare( rhs1 );

if( 0 == flag )
{
return "0";
}

int isMinus = 0;

int len11 = lhs1.length();
int len22 = rhs1.length();

if( ( len11 == len22 && flag < 0 ) || len11 < len22 )
{
string tmp = lhs1;
lhs1 = rhs1;
rhs1 = tmp;
isMinus = 1;
}

int up = 0;
int idx = 0;
int i = 0;
int j = 0;

len11 = lhs1.length();
len22 = rhs1.length();
//cout << lhs1 << ' ' << rhs1 << endl;

for( i = len11 - 1, j = len22 - 1; i >= 0 && j >= 0; i--, j-- )
{
int minus = ( lhs1[i] - '0' - up ) - ( rhs1[j] - '0' );

if( minus < 0 )
{
up = 1;
result[ idx++ ] = minus + 10 + '0';

}
else
{
up = 0;
result[ idx++ ] = minus + '0';

}

}

//cout << i << ' ' << j << ' ' << result[0] << endl;

while( i >= 0 )
{
int minus = ( lhs1[i] - '0' - up );
//cout << minus << endl;
if( minus < 0 )
{
up = 1;
result[ idx++ ] = minus + 10 + '0';
}
else
{
up = 0;
result[ idx++ ] = minus + '0';
}

i--;
}

while( j >= 0 )
{
int minus = ( rhs1[j] - '0' - up );

if( minus < 0 )
{
up = 1;
result[ idx++ ] = minus + 10 + '0';
}
else
{
up = 0;
result[ idx++ ] = minus + '0';
}

j--;
}

result[idx] = '\0';
//result.resize( idx + 1 );
//cout << "result=" << result << endl;

for( i = 0, j = idx - 1; i < j; i++, j-- ) //逆置一下
{
char ch = result[i];
result[i] = result[j];
result[j] = ch;
}

//cout << idx << ' ' <<  "result=" << result << endl; // 0001

int k = 0;
int cur = 0;

while( '0' == result[k] )
{
k++;
}

while( k <= idx )
{
result[ cur++ ] = result[ k++ ];
}

result[cur] = '\0';
result.resize( cur + 1 ); //预留一个字符给符号位

//cout << result << " sf" << ' ' << cur << endl;
idx = cur;

if( 1 == isMinus ) //结果为负数
{

for( i = idx - 1; i >= 0; i-- )
{
result[ i + 1 ] = result[i];
}

result[0] = '-';
result[ idx + 1 ] = '\0';
result.resize( idx + 2 );
}

//cout << result << endl;
return result;
}

int judgeAddType( const string &s1, const string &s2 )
{
int type = 0;

if( !isValidNumber(s1) || !isValidNumber(s2) )
{
type = -1;
return type;
}

if( s1[0] != '-' && s2[0] != '-' )
{
type = 0;
}
else if( s1[0] != '-' && '-' == s2[0] )
{
type = 1;
}
else if( '-' == s1[0] && s2[0] != '-' )
{
type = 2;
}
else if( '-' == s1[0] && '-' == s2[0] )
{
type = 3;
}

return type;
}

// 大数乘法
/*

思想：
0  1  2  3  4
0  1  2
-----------------------
20  21  22  23  24
10  11  12  13  14
00  01  02  03  04
------------------------------------

*/

string multipy( const string &s1, const string &s2 )
{
string ret = "";

if( !isValidNumber(s1) || !isValidNumber(s2) )
{
cout << "multipy func: err -1, !isValidNumber(s1) || !isValidNumber(s2)" << endl;
return ret;
}

// 任意元素为0，乘积为0
if( ( 1 == s1.length() && '0' == s1[0] ) || ( 1 == s2.length() && '0' == s2[0] ) )
{
return "0";
}

bool isPositive = true;

if( ( '-' == s1[0] && s2[0] != '-' ) || ( s1[0] != '-' && '-' == s2[0] ) )
{
isPositive = false;
}

string ss1 = s1;
string ss2 = s2;

if( !isdigit(s1[0]) )
{
ss1.assign( s1, 1, s1.length() - 1 );
}

if( !isdigit(s2[0]) )
{
ss2.assign( s2, 1, s2.length() - 1 );
}

int len1 = ss1.length();
int len2 = ss2.length();
int *pResult = new int[ len1 + len2 ];

if( NULL == pResult )
{
cout << "multipy func: err -1, NULL==pResult" << endl;
return ret;
}

for( int i = 0; i < len1 + len2; i++ )
{
pResult[i] = 0;
}

for( int i = len1 - 1; i >= 0; i-- )
{
for( int j = len2 - 1; j >= 0; j-- )
{
pResult[ i + j + 1 ] += ( ss1[i] - '0' ) * ( ss2[j] - '0' );
}
}

for( int i = len1 + len2 - 1; i >= 1; i-- )
{
if( pResult[i] >= 10 )
{
pResult[ i - 1 ] += pResult[i] / 10;
pResult[i] %= 10;
}
}

char *pch = new char[ len1 + len2 + 1 ];

if( NULL == pch )
{
cout << "multipy func: err -1, NULL == pch" << endl;
}

int k = 0;

while( 0 == pResult[k] ) // 跳过头部0元素
{
k++;
}

int idx = 0;

if( !isPositive )
{
idx = 1;
}

for( ; k < len1 + len2; k++ )
{
pch[ idx++ ] = pResult[k] + '0';
}

pch[idx] = '\0';

if( !isPositive )
{
pch[0] = '-';
}

string result(pch);

delete []pch;
pch = NULL;
delete []pResult;
pResult = NULL;

return result;
}

int main()
{
int ret = 0;

string s1;
string s2;

while( cin >> s1 >> s2 )
{
cout << multipy( s1, s2 ) << endl;

int type = judgeAddType( s1, s2 );

if( -1 == type )
{
cout << "error input" << endl;
ret = -1;
return ret;
}
else if( 0 == type ) // 正+正
{
cout << twoPositivePlus( s1, s2 ) << endl;
}
else if( 1 == type ) // 正+负
{
cout << posiveAddNegative( s1, s2 ) << endl;
}
else if( 2 == type ) // 负+正
{
cout << posiveAddNegative( s2, s1 ) << endl;
}
else if( 3 == type ) // 负+负
{
string tmp1;
tmp1.assign( s1, 1, s1.length() - 1 );

string tmp2;
tmp2.assign( s2, 1, s2.length() - 1 );

cout << "-" << twoPositivePlus( tmp1, tmp2 ) << endl;
}
}

return ret;
}

</span>