（注意，_string 你用C++ std::string 代替就行）
加法：
/// <summary>
/// 无符号的两个整数相加 (参考自星飞星火）
/// </summary>
/// <param name="num1"></param>
/// <param name="num2"></param>
/// <returns></returns>
/// 创建时间：2024-04-21 最后一次修改时间：2024-04-28
_string _Integer::Add(const _string& num1, const _string& num2)
{
/*
std::string add(const std::string &num1, const std::string &num2) {
int len1 = num1.size();
int len2 = num2.size();
int maxLen = std::max(len1, len2);
std::string result(maxLen + 1, '0');
int carry = 0;
for (int i = 0; i < maxLen; i++) {
int sum = carry;
if (i < len1) {
sum += num1[len1 - 1 - i] - '0';
}
if (i < len2) {
sum += num2[len2 - 1 - i] - '0';
}
carry = sum / 10;
sum %= 10;
result[maxLen - i] = sum + '0';
}
if (carry > 0) {
result[0] = carry + '0';
} else {
result.erase(result.begin());
}
return result;
}
*/
int len1 = num1.std_size();
int len2 = num2.std_size();
int maxLen = _Math::Max(len1, len2);
_string result(maxLen + 1, _t('0'));
int carry = 0;
for (int i = 0; i < maxLen; i++) {
int sum = carry;
if (i < len1) {
sum += num1[len1 - 1 - i] - _t('0');
}
if (i < len2) {
sum += num2[len2 - 1 - i] - _t('0');
}
carry = sum / 10;
sum %= 10;
result[maxLen - i] = sum + _t('0');
}
if (carry > 0) {
result[0] = carry + _t('0');
}
else {
//result.std_erase(result.std_begin());
return result.SubStr(1, result.Length - 1);
}
return result;
}减法：
/// <summary>
/// 无符号的两个整数相减，部分算法参考自星飞星火，但星火
/// 算的结果只有同位数相减才正确，注意：这里是假定是无符
/// 号两个整数相减。
/// 【中文】：两个数相减
/// 【英文】：Subtract two numbers
/// 百度文心一言和星飞星火结果不对。
/// </summary>
/// <param name="num1"></param>
/// <param name="num2"></param>
/// <returns></returns>
/// 创建时间：2024-04-21 最后一次修改时间：2024-04-25 （已测试）
_string _Integer::Subtract(const _string& num1, const _string& num2, bool isCheckForamt)
{
if (isCheckForamt){ Check(num1); Check(num2);}
/*
* 星火给出的代码：
*
int len1 = num1.size();
int len2 = num2.size();
int maxLen = std::max(len1, len2);
std::string result(maxLen, '0');
int iBorrow = 0;
for (int i = 0; i < maxLen; i++) {
int iDiff = num1[len1 - 1 - i] - num2[len2 - 1 - i] - iBorrow;
if (iDiff < 0) {
iDiff += 10;
iBorrow = 1;
}
else {
iBorrow = 0;
}
result[maxLen - 1 - i] = iDiff + '0';
}
result.erase(std::find_if(result.rbegin(), result.rend(), [](char ch) { return ch != '0'; }).base(), result.end());
return result;
*/
int len1 = num1.Length;
int len2 = num2.Length;
int maxLen = _Math::Max(len1, len2);
_string sResult(_t(""), maxLen + 1);
//这里先比较字符串长度（数字位数）的大小
if (len1 > len2){ //num1 > num2
int iBorrow = 0;
for (int i = 0; i < len2; i++) {
int iDiff = num1[len1 - 1 - i] - num2[len2 - 1 - i] - iBorrow;
if (iDiff < 0) {
iDiff += 10;
iBorrow = 1;
}
else {
iBorrow = 0;
}
sResult.Add(iDiff + _t('0'));
}
if (iBorrow != 0){
bool bBorrow = false;
for (int i = len2; i < len1; i++){
_char c = num1[len1 - i - 1];
if (!bBorrow){
if (c == _t('0')) {
sResult.Add(_t('9'));
}else{
sResult.Add(c - 1);
bBorrow = true;
}
}else{
sResult.Add(c);
}
}
}else{
for (int i = len2; i < len1; i++){
_char c = num1[len1 - i - 1];
sResult.Add(c);
}
}
sResult.TrimRight(_t('0')); //除去尾部的0
return sResult.Reversal();
}else if(len1 == len2){//字符长度相等
if (num1 > num2){
int iBorrow = 0;
for (int i = 0; i < len2; i++) {
int iDiff = num1[len1 - 1 - i] - num2[len2 - 1 - i] - iBorrow;
if (iDiff < 0) {
iDiff += 10;
iBorrow = 1;
}
else {
iBorrow = 0;
}
sResult.Add(iDiff + _t('0'));
}
sResult.TrimRight(_t('0')); //除去尾部的0
return sResult.Reversal();
}else if(num1 == num2){
return _t("0");
}else{
int iBorrow = 0;
for (int i = 0; i < len2; i++) {
int iDiff = num2[len1 - 1 - i] - num1[len2 - 1 - i] - iBorrow;
if (iDiff < 0) {
iDiff += 10;
iBorrow = 1;
}
else {
iBorrow = 0;
}
sResult.Add(iDiff + _t('0'));
}
sResult.TrimRight(_t('0')); //除去尾部的0
sResult.Add(_t('-'));
return sResult.Reversal();
}
}else{ //len1 < len2 小数减大数
int iBorrow = 0;
for (int i = 0; i < len1; i++) {
int iDiff = num2[len2 - 1 - i] - num1[len1 - 1 - i] - iBorrow;
if (iDiff < 0) {
iDiff += 10;
iBorrow = 1;
}
else {
iBorrow = 0;
}
sResult.Add(iDiff + _t('0'));
}
if (iBorrow != 0) { //还需借一位
bool bBorrow = false;
for (int i = len1; i < len2; i++) {
_char c = num2[len2 - i - 1];
if (!bBorrow) {
if (c == _t('0')) {
sResult.Add(_t('9'));
}
else {
sResult.Add(c - 1);
bBorrow = true;
}
}
else {
sResult.Add(c);
}
}
}
else {
for (int i = len1; i < len2; i++) {
_char c = num2[len2 - i - 1];
sResult.Add(c);
}
}
sResult.TrimRight(_t('0'));
sResult.Add(_t("-"));
return sResult.Reversal();
}
}乘法
/// <summary>
/// 无符号的两个整数相剩 (参考自星飞星火）
/// 【中文】：两个数相乘
/// 【英文】：Multiplication of two numbers
/// </summary>
/// <param name="sNum1"></param>
/// <param name="sNum2"></param>
/// <returns></returns>
/// 创建时间：2024-04-21 最后一次修改时间：2024-04-21 （已测试）
_string _Integer::Multiplication(const _string& sNum1, const _string& sNum2, bool isCheckForamt)
{
if (isCheckForamt) { Check(sNum2); Check(sNum2); }
/*
int len1 = num1.size();
int len2 = num2.size();
std::vector<int> result(len1 + len2, 0);
for (int i = len1 - 1; i >= 0; i--) {
for (int j = len2 - 1; j >= 0; j--) {
int product = (num1[i] - '0') * (num2[j] - '0');
int sum = result[i + j + 1] + product;
result[i + j + 1] = sum % 10;
result[i + j] += sum / 10;
}
}
std::string res;
for (int num : result) {
if (!res.empty() || num != 0) {
res.push_back(num + '0');
}
}
return res.empty() ? "0" : res;
*/
size_t len1 = sNum1.Length;
size_t len2 = sNum2.Length;
_Array<_byte> result(len1 + len2); //设置缓冲长度为 len1 + len2
result.ZeroBufferAll(); //把缓冲区初始为0
result.ResetLength(len1 + len2); //重设长度
/*
123
11
33 (3) i = 2 j = 1（个位+3） i + j = 3 刚好是第4位 (3) i = 2 j = 0 （十位加3）
22
11
________
1353
*/
for (int i = len1 - 1; i >= 0; i--) {
for (int j = len2 - 1; j >= 0; j--) {
int product = (sNum1[i] - '0') * (sNum2[j] - '0'); //总量 n * n
int sum = result[i + j + 1] + product; //
result[i + j + 1] = sum % 10;
result[i + j] += sum / 10;
}
}
_string sTmp(_t(""), result.Length);
/*
//15*15 = 0225 (第一位是0）
size_t nStart = (*result.Data == 0) ? 1 : 0;
for(size_t n = nStart; n < result.Length; ++n)
sTmp.Add( *(result.Data + n) + 48);
*/
for (_byte b : result) {
if (sTmp.Length > 0 || b != 0) { //如果前面有非零的数字，则添加
sTmp.Add(b + 48);
}
}
return sTmp.Length == 0 ? _t("0") : sTmp;
}小整数整除
/// <summary>
/// sNum1 / sNum2 ，sNum1 的倍数受制于int所能表达的最大值
/// </summary>
/// <param name="sNum1"></param>
/// <param name="sNum2"></param>
/// <param name="isCheckForamt"></param>
/// <returns></returns>
/// 创建时间：2024-04-26 最后一次修改时间：2024-04-27 （已测试）
_Pair<int, _string> _Integer::SmallDiv(const _string& sNum1, const _string& sNum2, bool isCheckForamt)
{
if (isCheckForamt) { Check(sNum1); Check(sNum2); }
if (sNum2 == _t("0"))
{
d.PrintError(_t("除数不能为零"), _t("_Integer::SmallDiv"));
assert(false);
}
if (sNum1.Length < sNum2.Length)
return _Pair<int, _string>(0, sNum1);
if (sNum1.Length == sNum2.Length)
{
if (sNum1 > sNum2)
{
int nNear = (sNum1[0] - 48) / (sNum2[0] - 48 ) + 1;
for (int n = nNear; n > 0; --n)
{
_string sn = ga.intToString(n);
_string s = _Integer::Multiplication(sNum2, sn, false); //乘积
_string r = _Integer::Subtract(sNum1, s, false); //余数
if (r[0] == _t('-'))
{
}
else if (r == _t("0"))
{
return _Pair<int, _string>(n, _t("0"));
}
else
{
if (r.Length < sNum2.Length)
{
return _Pair<int, _string>(n, r);
}
else if (r.Length == sNum2.Length)
{
if (r < sNum2)
{
return _Pair<int, _string>(n, r);
}
else if (r == sNum2)
{
return _Pair<int, _string>(n + 1, _t("0"));
}
}
}
}
}
else if (sNum1 == sNum2)
{
return _Pair<int, _string>(1, _t("0"));
}
else
{
return _Pair<int, _string>(0, sNum1);
}
}
else //sNum1.Length > sNum2.Length
{
int nNear = _Math::pow(10, sNum1.Length - sNum2.Length) * (sNum1[0] -48 + 1) - 1;
//_pin(nNear);
for (int n = nNear; n > 0; --n)
{
_string sn = ga.intToString(n);
_string s = _Integer::Multiplication(sNum2, sn, false); //乘积
_string r = _Integer::Subtract(sNum1, s, false); //余数
if (r[0] == _t('-'))
{
}
else if (r == _t("0"))
{
return _Pair<int, _string>(n, _t("0"));
}
else
{
if (r.Length < sNum2.Length)
{
return _Pair<int, _string>(n, r);
}
else if (r.Length == sNum2.Length)
{
if (r < sNum2)
{
return _Pair<int, _string>(n, r);
}
else if (r == sNum2)
{
return _Pair<int, _string>(n + 1, _t("0"));
}
}
}
}
}
std::wcout << _t("错误：\n");
_pcn(sNum1);
_pcn(sNum2);
assert(false);
return _Pair<int, _string>(0, _t("错误！"));
}大整数整除
/// <summary>
/// 【单词中英文对照】：两个数相除 - Divide two numbers
///
/// 百度文心一言和星飞星火结果不对。
/// </summary>
/// 创建时间：2024-04-25 最后一次修改时间：2024-04-27 (已测式，这个函数用了大约1整天时间，搞死人）
_string _Integer::Divide(const _string& sNum1, const _string& sNum2,bool isCheckForamt)
{
if (isCheckForamt) { Check(sNum1); Check(sNum2); }
if (sNum2 == _t("0"))
{
_string sError = _t("_string _Integer::Divide: 除数 sNum2 不能为零不能为 0 ！");
_cout << sError <<"\n";
assert(false);
}
_string sResult(_t(""), sNum1.Length);
//2024/4 nPos = 4-1 = 3 sSub = 24 Point = 2 - 1 - 1(2<4) = 0 s = sSub ""
//2124/4 nPos = 4-1 = 3
//2124/23 nPos = 4-2 - 1 = 1
_string sSub = sNum1.SubStr(0, sNum2.Length); //除数
auto p = SmallDiv(sSub, sNum2, false);
int nStart = sNum2.Length;
//获取第一位，确保第一次 p.Fist不等于0
if (p.First == 0) {
sSub = sNum1.SubStr(0, sNum2.Length + 1);
p = SmallDiv(sSub, sNum2, false);
nStart = sNum2.Length + 1;
}
for( int i = nStart; i <= sNum1.Length; ++i){
if (p.First > 0) {//商不为0
sResult.Add(_tostr(p.First));
if (p.Second == _t("0")) { //商不为0，余数为0
sSub = sNum1.SubStr(i, 1);
}else{ //商不为0，余数不为0
sSub = p.Second + sNum1.SubStr(i, 1);
}
if(sSub.Length > 0)
p = SmallDiv(sSub, sNum2, false);
}else { //--------------------------------商为零
sResult.Add(_t("0"));
if (p.Second == _t("0")) { //--------------商为0，余数为0
sSub = sNum1.SubStr(i, 1);
}
else { //----------------------------商为0，余数不为0
sSub = p.Second + sNum1.SubStr(i, 1);
}
if (sSub.Length > 0)
p = SmallDiv(sSub, sNum2, false);
}
}
return sResult;
}例子：
int main()
{
for (int i = 1; i < 100; ++i)
{
_string s = _Integer::Divide(_t("2024"), _tostr(i));
std::wcout << _t("2024/") << i << _t("\t\t");
std::wcout << s << "\t";
std::wcout << 2024 / i << "\n";
}
_string s1 = "88888888888888888888888888888888888888888888888888888888";
_string s2 = "44444444444444444444444444444444444444444444444444444444";
_string s3 = "23";
_pcn(s1);
_pcn(s2);
_pcn(s3);
_pcn(_Integer::Divide(s1,s2));
_pcn(_Integer::Divide(s1, s3));
_string s4 = _Integer::Divide(s1, s3);
_pcn(s4);
_pcn(_Integer::Divide(s2,s4));
_pcn(_Integer::Multiplication(s4, s3));
return 0;
}执行结果：
