10494 - If We Were a Child Again大总结

大整数问题之终结篇，除法运算最为复杂

主要操作：

①字符数组转置，头部存储个位，这样可使操作更为方便一些

②头置零的处理，但需要保证单个零的完整输出

③字符和整数，切勿混淆‘0’和0

④估算最后结果大致为多少位，定义MAXN

注意：①处有补充！初始化时要注意一下

//未通过

#include <iostream>#include <string>int const MAXN=1000;using namespace std;class BigNumber{public:BigNumber();BigNumber(int num);BigNumber(const char *num);BigNumber operator=(const char *num);BigNumber operator=(int num);BigNumber operator+(const BigNumber &c)const;BigNumber operator-(const BigNumber &c)const;BigNumber operator*(const BigNumber &c)const;BigNumber operator/(const BigNumber &c)const;BigNumber operator%(const BigNumber &c)const;BigNumber operator+=(const BigNumber &c){*this=*this+c;return *this;}BigNumber operator-=(const BigNumber &c){*this=*this-c;return *this;}BigNumber operator*=(const BigNumber &c){*this=*this*c;return *this;}BigNumber operator/=(const BigNumber &c){*this=*this/c;return *this;}BigNumber operator%=(const BigNumber &c){*this=*this%c;return *this;}bool operator<(const BigNumber &c)const;bool operator>(const BigNumber &c)const{return c<*this;}bool operator<=(const BigNumber &c)const{return !(*this>c);}bool operator>=(const BigNumber &c)const{return !(*this<c);}bool operator==(const BigNumber &c)const{return (*this<=c)&&(*this>=c);}bool operator!=(const BigNumber &c)const{return !(*this<c)&&!(*this>c);}void cleanLeadZero();//void divisionTen(int n);//void mutiplyTen(int n);string str()const;BigNumber getSub(int n)const;friend istream & operator>>(istream &in,BigNumber &c);friend ostream & operator<<(ostream &in,BigNumber &c);private:int s[MAXN];int len;};BigNumber::BigNumber(){memset(s,0,sizeof(s));len=1;//这样设置使初始化的值为零}BigNumber::BigNumber(const char *num){*this=num;}BigNumber::BigNumber(int num){*this=num;}string BigNumber::str()const{string r="";for(int i=0;i<len;i++)r=(char)(s[i]+'0')+r;if(r=="") r="0";return r;}BigNumber BigNumber::operator=(const char *num){len=strlen(num);//①前面加一句memset(num,0,sizeof(num));效果会很好for(int i=0;i<len;i++)s[i]=num[len-1-i]-'0';return *this;}BigNumber BigNumber::operator=(int num){char r[MAXN];sprintf(r,"%d",num);*this=r;return *this;}void BigNumber::cleanLeadZero(){while(len>1 && !s[len-1])//此处注意len>1，保证单个0的输出len--;}BigNumber BigNumber::operator+(const BigNumber &c)const{BigNumber r;r.len=0;int up=0;int maxlen=len>c.len?len:c.len;for(int i=0;up || i<maxlen;i++){int temp=up;if(i<len) temp+=s[i];//###,这里需要判断的是i<len，而不是s[i]是否为零if(i<c.len) temp+=c.s[i];r.s[r.len++]=temp%10;up=temp/10;}r.cleanLeadZero();return r;}//a-b时要确保，a>bBigNumber BigNumber::operator-(const BigNumber &c)const{BigNumber r;r.len=0;int down=0;for(int i=0;i<len;i++){int temp=s[i]-down;if(i<c.len) temp-=c.s[i];//这里是-；if(temp>=0)down=0;else{down=1;temp+=10;}r.s[r.len++]=temp;}r.cleanLeadZero();return r;}BigNumber BigNumber::operator*(const BigNumber &c)const//大整数问题的另外一种操作，不需要中间变量{BigNumber r;r.len=len+c.len;for(int i=0;i<len;i++){for(int j=0;j<c.len;j++){r.s[i+j]+=s[i]*c.s[j];//###,+=}}for(int i=0;i<r.len-1;i++){r.s[i+1]+=r.s[i]/10;r.s[i]%=10;}r.cleanLeadZero();return r;}BigNumber BigNumber::getSub(int n)const//###“BigNumber::getSub”: 不能将“this”指针从“const BigNumber”转换为“BigNumber &”//出现这个错误后，将函数设置成const即可{BigNumber r;r.len=0;for(int i=0;i<n;i++){r.s[r.len++]=s[len-n+i];}return r;}BigNumber BigNumber::operator/(const BigNumber &c)const{BigNumber r;r.len=0;BigNumber temp=getSub(c.len-1);for(int i=len-c.len;i>=0;i--){temp=temp*10+s[i];if(temp<c)r.s[r.len++]=0;else{int j;for(j=1;j<=10;j++)//这里最大值可以取到10if(c*j>temp)//c要放到*的前面，这样才可以调用operator*函数break;r.s[r.len++]=j-1;temp=temp-(c*(j-1));}}for(int i=0;i<r.len/2;i++){char mid=r.s[i];r.s[i]=r.s[r.len-1-i];r.s[r.len-1-i]=mid;}r.cleanLeadZero();return r;}BigNumber BigNumber::operator%(const BigNumber &c)const{BigNumber r;r=*this/c;r=*this-r*c;return r;}bool BigNumber::operator<(const BigNumber &c)const{if(len!=c.len) return len<c.len;else{for(int i=len-1;i>=0;i--)//一失足成千古恨，i--if(s[i]!=c.s[i])return s[i]<c.s[i];}return false;}istream & operator>>(istream &in,BigNumber &c){string str;in>>str;c=str.c_str();return in;}ostream & operator<<(ostream &out,BigNumber &c){out<<c.str();return out;}char a[1000];char b[100];char op;int main(){while(scanf("%s %c %s",a,&op,b)==3){BigNumber f1(a);BigNumber f2(b);if(op=='/')cout<<f1/f2<<endl;else if(op=='%')cout<<f1%f2<<endl;}return 0;}

第二次做：Runtime error

#include <iostream>#include <cstdio>#include <cstring>using namespace std;const int nMax=100;class BigNumber{private:int f[nMax];int len;public:BigNumber(){len=1;memset(f,0,sizeof(f));}BigNumber(int a);BigNumber(char *ch);BigNumber operator=(char *ch);BigNumber operator+(const BigNumber &c)const;BigNumber operator-(const BigNumber &c)const;BigNumber operator*(const BigNumber &c)const;BigNumber operator/(const BigNumber &c)const;BigNumber operator%(const BigNumber &c)const;bool operator<(const BigNumber &c)const;bool operator>(const BigNumber &c)const{return c<*this;}bool operator==(const BigNumber &c)const{return !(*this<c) && !(c<*this);}bool operator<=(const BigNumber &c)const{return *this<c || *this==c;}friend ostream &operator<<(ostream &out,const BigNumber &c);void clearLeadZero();BigNumber getSub(int len)const;};BigNumber BigNumber::operator=(char *ch){len=strlen(ch);for(int i=0;i<len;i++)f[len-1-i]=ch[i]-'0';clearLeadZero();return *this;}void BigNumber::clearLeadZero(){while(len>0 && !f[len-1]) len--;if(len==0)len=1,f[0]=0;}BigNumber::BigNumber(char *ch){memset(f,0,sizeof(f));*this=ch;}BigNumber::BigNumber(int a){char ch[nMax];sprintf(ch,"%d",a);memset(f,0,sizeof(f));*this=ch;}bool BigNumber::operator<(const BigNumber &c)const{if(len!=c.len)return len<c.len;elsefor(int i=len-1;i>=0;i--)if(f[i]!=c.f[i])return f[i]<c.f[i];return 0;}BigNumber BigNumber::operator+(const BigNumber &c)const{int i,up;BigNumber z;for(i=0,up=0;i<len || i<c.len || up;i++){int p=up+f[i]+c.f[i];z.f[i]=p%10;up=p/10;}z.len=i;z.clearLeadZero();return z;}//保证被减数比减数大BigNumber BigNumber::operator-(const BigNumber &c)const{int i,down;BigNumber z;for(i=0,down=0;i<len;i++){int p=down+f[i]-c.f[i];if(p>=0)down=0,z.f[i]=p%10;elsedown=-1,z.f[i]=10+p;}z.len=i;z.clearLeadZero();return z;}BigNumber BigNumber::operator*(const BigNumber &c)const{int i,j,up;BigNumber z;for(i=0;i<len;i++){up=0;for(j=0;j<c.len || up;j++){int p=up+f[i]*c.f[j]+z.f[i+j];z.f[i+j]=p%10;up=p/10;}}z.len=i+j;z.clearLeadZero();return z;}BigNumber BigNumber::getSub(int sub_len)const{BigNumber z;for(int i=0;i<sub_len;i++)z.f[i]=f[len-sub_len+i];z.len=sub_len;z.clearLeadZero();return z;}BigNumber BigNumber::operator/(const BigNumber &c)const{if(*this<c) return BigNumber(0);BigNumber z,temp;temp=getSub(c.len-1);for(int i=len-c.len;i>=0;i--){temp=temp*10+f[i];int k=0;while(k<10 && c*k<=temp) k++;z.f[z.len++]=k-1;}for(int i=0;i<z.len/2;i++){int temp=z.f[i];z.f[i]=z.f[z.len-1-i];z.f[z.len-1-i]=temp;}z.clearLeadZero();return z;}BigNumber BigNumber::operator%(const BigNumber &c)const{BigNumber z;z=(*this)-c*((*this)/c);z.clearLeadZero();return z;}ostream &operator<<(ostream &out,const BigNumber &c){for(int i=c.len-1;i>=0;i--)out<<c.f[i];return out;}int main(){//freopen("f:/data.in","r",stdin);char c1[nMax],opt,c2[nMax];while(scanf("%s %c %s",c1,&opt,c2)==3){BigNumber f1(c1);BigNumber f2(c2);if(opt=='/') cout<<f1/f2<<endl;else if(opt=='%') cout<<f1%f2<<endl;}return 0;}