C++ 大数操作类

最新推荐文章于 2022-04-13 17:52:03 发布

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#c++ #up #class #c

本文介绍了一个用于处理大整数运算的C++类BigNum的实现细节。该类支持基本的大数加减乘除等操作，并提供了输入输出重载以方便使用。通过对大数的特殊存储方式和运算逻辑的设计，使得在计算机中可以有效地处理超出标准整型变量范围的数值。

class BigNum; istream& operator>>(istream&, BigNum&); ostream& operator<<(ostream&, BigNum&); #define MAXN 9999 #define MAXSIZE 1000 #define DLEN 4 class BigNum { public: int a[MAXSIZE]; int len; public: BigNum(){len = 1;memset(a,0,sizeof(a));} BigNum(const int); BigNum(const char*); BigNum(const BigNum &); BigNum &operator=(const BigNum &); friend istream& operator>>(istream&, BigNum&); friend ostream& operator<<(ostream&, BigNum&); BigNum operator+(const BigNum &) const; BigNum operator-(const BigNum &) const; BigNum operator*(const BigNum &) const; BigNum operator/(const int &) const; BigNum operator^(const int &) const; int operator%(const int &) const; bool operator>(const BigNum & T)const; bool operator==(const BigNum & T)const; bool operator==(const int & t)const; bool operator>(const int & t)const; }; istream& operator>>(istream & in, BigNum & b) { char ch[MAXSIZE*4]; int i = -1; in>>ch; int l=strlen(ch); int count=0,sum=0; for(i=l-1;i>=0;) { sum = 0; int t=1; for(int j=0;j<4&&i>=0;j++,i--,t*=10) { sum+=(ch[i]-'0')*t; } b.a[count]=sum; count++; } b.len =count++; return in; } ostream& operator<<(ostream& out, BigNum& b) { int i; cout << b.a[b.len - 1]; for(i = b.len - 2 ; i >= 0 ; i--) { cout.width(DLEN); cout.fill('0'); cout << b.a[i]; } return out; } BigNum::BigNum(const int b) { int c,d = b; len = 0; memset(a,0,sizeof(a)); while(d > MAXN) { c = d - (d / (MAXN + 1)) * (MAXN + 1); d = d / (MAXN + 1); a[len++] = c; } a[len++] = d; } BigNum::BigNum(const char*s) { int t,k,index,l; memset(a,0,sizeof(a)); l=strlen(s); len=l/DLEN; if(l%DLEN)len++; index=0; for(int i=l-1;i>=0;i-=DLEN) { t=0;k=i-DLEN+1; if(k<0)k=0; for(int j=k;j<=i;j++) t=t*10+s[j]-'0'; a[index++]=t; } } BigNum::BigNum(const BigNum & T) : len(T.len) { int i; memset(a,0,sizeof(a)); for(i = 0 ; i < len ; i++) a[i] = T.a[i]; } BigNum & BigNum::operator=(const BigNum & n) { len = n.len; memset(a,0,sizeof(a)); for(int i = 0 ; i < len ; i++) a[i] = n.a[i]; return *this; } BigNum BigNum::operator+(const BigNum & T) const { BigNum t(*this); int i,big; big = T.len > len ? T.len : len; for(i = 0 ; i < big ; i++) { t.a[i] +=T.a[i]; if(t.a[i] > MAXN) { t.a[i + 1]++; t.a[i] -=MAXN+1; } } if(t.a[big] != 0) t.len = big + 1; else t.len = big; return t; } BigNum BigNum::operator-(const BigNum & T) const { int i,j,big; bool flag; BigNum t1,t2; if(*this>T) { t1=*this; t2=T; flag=0; } else { t1=T; t2=*this; flag=1; } big=t1.len; for(i = 0 ; i < big ; i++) { if(t1.a[i] < t2.a[i]) { j = i + 1; while(t1.a[j] == 0) j++; t1.a[j--]--; while(j > i) t1.a[j--] += MAXN; t1.a[i] += MAXN + 1 - t2.a[i]; } else t1.a[i] -= t2.a[i]; } t1.len = big; while(t1.a[len - 1] == 0 && t1.len > 1) { t1.len--; big--; } if(flag)t1.a[big-1]=0-t1.a[big-1]; return t1; } BigNum BigNum::operator*(const BigNum & T) const { BigNum ret; int i,j,up; int temp,temp1; for(i = 0 ; i < len ; i++) { up = 0; for(j = 0 ; j < T.len ; j++) { temp = a[i] * T.a[j] + ret.a[i + j] + up; if(temp > MAXN) { temp1 = temp - temp / (MAXN + 1) * (MAXN + 1); up = temp / (MAXN + 1); ret.a[i + j] = temp1; } else { up = 0; ret.a[i + j] = temp; } } if(up != 0) ret.a[i + j] = up; } ret.len = i + j; while(ret.a[ret.len - 1] == 0 && ret.len > 1) ret.len--; return ret; } BigNum BigNum::operator/(const int & b) const { BigNum ret; int i,down = 0; for(i = len - 1 ; i >= 0 ; i--) { ret.a[i] = (a[i] + down * (MAXN + 1)) / b; down = a[i] + down * (MAXN + 1) - ret.a[i] * b; } ret.len = len; while(ret.a[ret.len - 1] == 0 && ret.len > 1) ret.len--; return ret; } int BigNum::operator %(const int & b) const { int i,d=0; for (i = len-1; i>=0; i--) { d = ((d * (MAXN+1))% b + a[i])% b; } return d; } BigNum BigNum::operator^(const int & n) const { BigNum t,ret(1); int i; if(n<0)exit(-1); if(n==0)return 1; if(n==1)return *this; int m=n; while(m>1) { t=*this; for( i=1;i<<1<=m;i<<=1){ t=t*t; } m-=i; ret=ret*t; if(m==1)ret=ret*(*this); } return ret; } bool BigNum::operator>(const BigNum & T) const { int ln; if(len > T.len) return true; else if(len == T.len) { ln = len - 1; while(a[ln] == T.a[ln] && ln >= 0) ln--; if(ln >= 0 && a[ln] > T.a[ln]) return true; else return false; } else return false; } bool BigNum::operator==(const BigNum & T) const { int ln; if(len != T.len) return false; else { ln = len - 1; while(a[ln] == T.a[ln] && ln-- ); if(ln < 0) return true; else return false; } } bool BigNum::operator >(const int & t) const { BigNum b(t); return *this>b; } bool BigNum::operator==(const int & t) const { BigNum b(t); return *this==b; }