HDU 1002A + B Problem II

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#permutation #c #div #iostream #delete #up

本文详细介绍了几种不同类型的大数运算模板，包括加法、减法、乘法、除法等基本运算，以及大数的平方根、长度计算、末尾0个数计算等高级功能，并给出了完整的C++代码实现。

1002解题报告：A + B Problem II

代码：

#include<stdio.h> #include<string.h> #define N 1005 char A[N],B[N],sum[N]; int main() { int T,i,j,k,x,sign; while(scanf("%d",&T)!=EOF) { for(i=0;i<T;i++) { if(i) printf("/n"); scanf("%s%s",&A,&B); j=strlen(A)-1,k=strlen(B)-1; for(x=0,sign=0;(j+1)&&(k+1);j--,k--,x++) { if((A[j]-'0')+(B[k]-'0')+sign<10) { sum[x]=(A[j]-'0')+(B[k]-'0')+sign; sign=0; } else { sum[x]=(A[j]-'0')+(B[k]-'0')+sign-10; sign=1; } } if(j+1) { for(;j>=0;j--,x++) { if(A[j]-'0'+sign<10) { sum[x]=(A[j]-'0')+sign; sign=0; } else { sum[x]=0; sign=1; } } } else if(k+1) { for(;k>=0;k--,x++) { if(B[k]-'0'+sign<10) { sum[x]=(B[k]-'0')+sign; sign=0; } else { sum[x]=0; sign=1; } } } if(sign) sum[x]=1; else x--; printf("Case %d:/n",i+1); printf("%s + %s = ",A,B); while(x>-1) printf("%d",sum[x--]); printf("/n"); } } return 0; }

相关资料整理如下：

（1）c++大数类模板：＃i nclude<iostream> ＃i nclude<string> ＃i nclude<iomanip> ＃i nclude<algorithm> using namespace std; #define MAXN 9999 #define DLEN 4 class BigNum{ private: int a[300];//DLEN digs for a position int len; public: BigNum(){len = 1;memset(a,0,sizeof(a));} BigNum(const int b); BigNum(const BigNum & T); bool Bigger(const BigNum &) const; BigNum & operator=(const BigNum &); BigNum & Add(const BigNum &); BigNum & Sub(const BigNum &); BigNum operator+(const BigNum &) const; BigNum operator-(const BigNum &) const; BigNum operator*(const BigNum &) const; BigNum operator/(const int &) const; void Print(); }; 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 BigNum & T) : len(T.len) { int i; memset(a,0,sizeof(a)); for(i = 0 ; i < len ; i++) a[i] = T.a[i]; } bool BigNum::Bigger(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; } 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::Add(const BigNum & T) { int i,big; big = T.len > len ? T.len : len; for(i = 0 ; i < big ; i++) { a[i] = a[i] + T.a[i]; if(a[i] > MAXN) { a[i + 1]++; a[i] = a[i] - MAXN - 1; } } if(a[big] != 0) len = big + 1; else len = big; return *this; } BigNum & BigNum::Sub(const BigNum & T) { int i,j,big; big = T.len > len ? T.len : len; for(i = 0 ; i < big ; i++){ if(a[i] < T.a[i]){ j = i + 1; while(a[j] == 0) j++; a[j--]--; while(j > i) a[j--] += MAXN; a[i] = a[i] + MAXN + 1 - T.a[i]; } else a[i] -= T.a[i]; } len = big; while(a[len - 1] == 0 && len > 1) len--; return *this; } BigNum BigNum::operator+(const BigNum & n) const { BigNum a = *this; a.Add(n); return a; } BigNum BigNum::operator-(const BigNum & T) const { BigNum b = *this; b.Sub(T); return b; } 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--; return ret; } void BigNum::Print() { int i; cout << a[len - 1]; for(i = len - 2 ; i >= 0 ; i--){ cout.width(DLEN); cout.fill('0'); cout << a[i]; } cout << endl; }

模板二： class BigNum { public: void output( ); BigNum( ) { len = 1; num[ 0 ] = 0; } BigNum &operator = ( const BigNum & ); BigNum &operator = ( const int & ); friend bool operator <= ( const BigNum & , const BigNum & ); friend bool operator < ( const BigNum & , const BigNum & ); friend bool operator == ( const BigNum & , const BigNum & ); friend bool operator == ( const BigNum & , const int & ); friend bool operator != ( const BigNum & , const BigNum & ); friend bool operator != ( const BigNum & , const int & ); friend BigNum operator + ( const BigNum & , const BigNum & ); friend BigNum operator - ( const BigNum & , const BigNum & ); friend BigNum operator * ( const BigNum & , const BigNum & ); friend BigNum operator / ( const BigNum & , const BigNum & ); friend BigNum operator % ( const BigNum & , const BigNum & ); friend BigNum operator + ( const BigNum & , const int & ); friend BigNum operator - ( const BigNum & , const int & ); friend BigNum operator * ( const BigNum & , const int & ); friend BigNum operator / ( const BigNum & , const int & ); friend BigNum operator % ( const BigNum & , const int & ); friend void operator += ( BigNum & , const BigNum & ); friend void operator -= ( BigNum & , const BigNum & ); friend void operator *= ( BigNum & , const BigNum & ); friend void operator /= ( BigNum & , const BigNum & ); friend void operator %= ( BigNum & , const BigNum & ); friend void operator += ( BigNum & , const int & ); friend void operator -= ( BigNum & , const int & ); friend void operator *= ( BigNum & , const int & ); friend void operator /= ( BigNum & , const int & ); friend void operator %= ( BigNum & , const int & ); private: int len, num[ 300 ]; }; void BigNum::output( ) { int i; printf("%d", num[ len - 1 ]); for ( i = len - 2; i >= 0; i-- ) printf("%04d", num[ i ]); } BigNum &BigNum::operator = ( const BigNum &a ) { int i; len = a.len; for ( i = 0; i < a.len; i++ ) num[ i ] = a.num[ i ]; return *this; } BigNum &BigNum::operator = ( const int &b ) { int a = b; len = 0; num[ 0 ] = 0; while ( a ) { num[ len++ ] = a % 10000; a /= 10000; } if ( !len ) len = 1; return *this; } bool operator <= ( const BigNum &a, const BigNum &b ) { if ( a.len < b.len ) return true; if ( a.len > b.len ) return false; int i; for ( i = a.len - 1; i >= 0; i-- ) { if ( a.num[ i ] < b.num[ i ] ) return true; if ( a.num[ i ] > b.num[ i ] ) return false; } return true; } bool operator < ( const BigNum &a, const BigNum &b ) { if ( a.len < b.len ) return true; if ( a.len > b.len ) return false; int i; for ( i = a.len - 1; i >= 0; i-- ) { if ( a.num[ i ] < b.num[ i ] ) return true; if ( a.num[ i ] > b.num[ i ] ) return false; } return false; } bool operator == ( const BigNum &a, const BigNum &b ) { if ( a.len != b.len ) return false; int i; for ( i = 0; i < a.len; i++ ) if ( a.num[ i ] != b.num[ i ] ) return false; return true; } bool operator == ( const BigNum &a, const int &b ) { BigNum c; c = b; return a == c; } bool operator != ( const BigNum &a, const BigNum &b ) { if ( a.len != b.len ) return true; int i; for ( i = 0; i < a.len; i++ ) if ( a.num[ i ] != b.num[ i ] ) return true; return false; } bool operator != ( const BigNum &a, const int &b ) { BigNum c; c = b; return a != c; } BigNum operator + ( const BigNum &c, const BigNum &b ) { int i, j; BigNum a; a = c; for ( i = 0; i < b.len; i++ ) { if ( i < a.len ) a.num[ i ] += b.num[ i ]; else { a.num[ i ] = a.num[ i ]; a.len++; } } for ( i = 0; i < a.len; i++ ) if ( a.num[ i ] >= 10000 ) { if ( i == a.len - 1 ) { a.len++; a.num[ i + 1 ] = 0; } a.num[ i + 1 ] += a.num[ i ] / 10000; a.num[ i ] %= 10000; } return a; } //notice that a must larger than b BigNum operator - ( const BigNum &c, const BigNum &b ) { int i, j; BigNum a; a = c; for ( i = b.len - 1; i >= 0; i-- ) { a.num[ i ] -= b.num[ i ]; if ( a.num[ i ] < 0 ) { a.num[ i ] += 10000; a.num[ i + 1 ]--; if ( i + 2 == a.len && a.num[ i + 1 ] == 0 ) a.len--; } if ( i == a.len - 1 && a.num[ i ] == 0 ) a.len--; } return a; } BigNum operator * ( const BigNum &a, const BigNum &b ) { BigNum c; int i, j; c.len = a.len + b.len - 1; for ( i = 0; i < c.len; i++ ) c.num[ i ] = 0; for ( i = 0; i < b.len; i++ ) for ( j = 0; j < a.len; j++ ) c.num[ i + j ] += a.num[ j ] * b.num[ i ]; for ( i = 0; i < c.len; i++ ) if ( c.num[ i ] >= 10000 ) { if ( i == c.len - 1 ) { c.len++; c.num[ i + 1 ] = 0; } c.num[ i + 1 ] += c.num[ i ] / 10000; c.num[ i ] %= 10000; } while ( !c.num[ c.len - 1 ] && c.len > 1 ) c.len--; return c; } BigNum operator / ( const BigNum &e, const BigNum &b ) { int i, t1, t2; BigNum c, d, a; a = e; for ( i = a.len - 1; i >= 0; i-- ) { c *= 10000; c += a.num[ i ]; if ( b <= c ) { t2 = b.num[ b.len - 1 ]; if ( c.len > b.len ) t1 = c.num[ c.len - 1 ] * 10000 + c.num[ c.len - 2 ]; else t1 = c.num[ c.len - 1 ]; t1 /= t2; d = b * t1; while ( c < d ) { d -= b; t1--; } a.num[ i ] = t1; c -= d; } else { a.num[ i ] = 0; if ( i == a.len - 1 ) a.len--; } } return a; } BigNum operator % ( const BigNum &a, const BigNum &b ) { int i, t1, t2; BigNum c, d; for ( i = a.len - 1; i >= 0; i-- ) { c *= 10000; c += a.num[ i ]; if ( b <= c ) { t2 = b.num[ b.len - 1 ]; if ( c.len > b.len ) t1 = c.num[ c.len - 1 ] * 10000 + c.num[ c.len - 2 ]; else t1 = c.num[ c.len - 1 ]; t1 /= t2; d = b * t1; while ( c < d ) { d -= b; t1--; } c -= d; } } return c; } BigNum operator + ( const BigNum &a, const int &b ) { BigNum c; c = b; return a + c; } BigNum operator - ( const BigNum &a, const int &b ) { BigNum c; c = b; return a - c; } BigNum operator * ( const BigNum &a, const int &b ) { BigNum c; c = b; return a * c; } BigNum operator / ( const BigNum &a, const int &b ) { BigNum c; c = b; return a / c; } BigNum operator % ( const BigNum &a, const int &b ) { BigNum c; c = b; return a % c; } void operator += ( BigNum &a, const BigNum &b ) { int i, j; for ( i = 0; i < b.len; i++ ) { if ( i < a.len ) a.num[ i ] += b.num[ i ]; else { a.num[ i ] = a.num[ i ]; a.len++; } } for ( i = 0; i < a.len; i++ ) if ( a.num[ i ] >= 10000 ) { if ( i == a.len - 1 ) { a.len++; a.num[ i + 1 ] = 0; } a.num[ i + 1 ] += a.num[ i ] / 10000; a.num[ i ] %= 10000; } } //notice that a must larger than b void operator -= ( BigNum &a, const BigNum &b ) { int i, j; for ( i = b.len - 1; i >= 0; i-- ) { a.num[ i ] -= b.num[ i ]; if ( a.num[ i ] < 0 ) { a.num[ i ] += 10000; a.num[ i + 1 ]--; if ( i + 2 == a.len && a.num[ i + 1 ] == 0 ) a.len--; } if ( i == a.len - 1 && a.num[ i ] == 0 ) a.len--; } } void operator *= ( BigNum &a, const BigNum &b ) { BigNum c; int i, j; c.len = a.len + b.len - 1; for ( i = 0; i < c.len; i++ ) c.num[ i ] = 0; for ( i = 0; i < b.len; i++ ) for ( j = 0; j < a.len; j++ ) c.num[ i + j ] += a.num[ j ] * b.num[ i ]; for ( i = 0; i < c.len; i++ ) if ( c.num[ i ] >= 10000 ) { if ( i == c.len - 1 ) { c.len++; c.num[ i + 1 ] = 0; } c.num[ i + 1 ] += c.num[ i ] / 10000; c.num[ i ] %= 10000; } while ( !c.num[ c.len - 1 ] && c.len > 1 ) c.len--; a = c; } void operator /= ( BigNum &a, const BigNum &b ) { int i, t1, t2; BigNum c, d; for ( i = a.len - 1; i >= 0; i-- ) { c *= 10000; c += a.num[ i ]; if ( b <= c ) { t2 = b.num[ b.len - 1 ]; if ( c.len > b.len ) t1 = c.num[ c.len - 1 ] * 10000 + c.num[ c.len - 2 ]; else t1 = c.num[ c.len - 1 ]; t1 /= t2; d = b * t1; while ( c < d ) { d -= b; t1--; } a.num[ i ] = t1; c -= d; } else { a.num[ i ] = 0; if ( i == a.len - 1 ) a.len--; } } } void operator %= ( BigNum &a, const BigNum &b ) { int i, t1, t2; BigNum c, d; for ( i = a.len - 1; i >= 0; i-- ) { c *= 10000; c += a.num[ i ]; if ( b <= c ) { t2 = b.num[ b.len - 1 ]; if ( c.len > b.len ) t1 = c.num[ c.len - 1 ] * 10000 + c.num[ c.len - 2 ]; else t1 = c.num[ c.len - 1 ]; t1 /= t2; d = b * t1; while ( c < d ) { d -= b; t1--; } c -= d; } } a = c; } void operator += ( BigNum &a, const int &b ) { BigNum c; c = b; a += c; } void operator -= ( BigNum &a, const int &b ) { BigNum c; c = b; a -= c; } void operator *= ( BigNum &a, const int &b ) { BigNum c; c = b; a *= c; } void operator /= ( BigNum &a, const int &b ) { BigNum c; c = b; a /= c; } void operator %= ( BigNum &a, const int &b ) { BigNum c; c = b; a %= c; }

模板三：

此模板只能处理正数的大数，包含四则运算、平方根、求末尾0个数、求长度等以及int型的组合排列。下面会有介绍模板的一些使用，就我目前所知道的使用方法。首先看下排列和组合的含义：

排列：组合：

模板如下： view plaincopy to clipboardprint? #include <iostream> #include <cstring> using namespace std; #define DIGIT 4 //四位隔开,即万进制 #define DEPTH 10000 //万进制 #define MAX 100 typedef int bignum_t[MAX+1]; /************************************************************************/ /* 读取操作数，对操作数进行处理存储在数组里 */ /************************************************************************/ int read(bignum_t a,istream&is=cin) { char buf[MAX*DIGIT+1],ch ; int i,j ; memset((void*)a,0,sizeof(bignum_t)); if(!(is>>buf))return 0 ; for(a[0]=strlen(buf),i=a[0]/2-1;i>=0;i--) ch=buf[i],buf[i]=buf[a[0]-1-i],buf[a[0]-1-i]=ch ; for(a[0]=(a[0]+DIGIT-1)/DIGIT,j=strlen(buf);j<a[0]*DIGIT;buf[j++]='0'); for(i=1;i<=a[0];i++) for(a[i]=0,j=0;j<DIGIT;j++) a[i]=a[i]*10+buf[i*DIGIT-1-j]-'0' ; for(;!a[a[0]]&&a[0]>1;a[0]--); return 1 ; } void write(const bignum_t a,ostream&os=cout) { int i,j ; for(os<<a[i=a[0]],i--;i;i--) for(j=DEPTH/10;j;j/=10) os<<a[i]/j%10 ; } int comp(const bignum_t a,const bignum_t b) { int i ; if(a[0]!=b[0]) return a[0]-b[0]; for(i=a[0];i;i--) if(a[i]!=b[i]) return a[i]-b[i]; return 0 ; } int comp(const bignum_t a,const int b) { int c[12]= { 1 } ; for(c[1]=b;c[c[0]]>=DEPTH;c[c[0]+1]=c[c[0]]/DEPTH,c[c[0]]%=DEPTH,c[0]++); return comp(a,c); } int comp(const bignum_t a,const int c,const int d,const bignum_t b) { int i,t=0,O=-DEPTH*2 ; if(b[0]-a[0]<d&&c) return 1 ; for(i=b[0];i>d;i--) { t=t*DEPTH+a[i-d]*c-b[i]; if(t>0)return 1 ; if(t<O)return 0 ; } for(i=d;i;i--) { t=t*DEPTH-b[i]; if(t>0)return 1 ; if(t<O)return 0 ; } return t>0 ; } /************************************************************************/ /* 大数与大数相加 */ /************************************************************************/ void add(bignum_t a,const bignum_t b) { int i ; for(i=1;i<=b[0];i++) if((a[i]+=b[i])>=DEPTH) a[i]-=DEPTH,a[i+1]++; if(b[0]>=a[0]) a[0]=b[0]; else for(;a[i]>=DEPTH&&i<a[0];a[i]-=DEPTH,i++,a[i]++); a[0]+=(a[a[0]+1]>0); } /************************************************************************/ /* 大数与小数相加 */ /************************************************************************/ void add(bignum_t a,const int b) { int i=1 ; for(a[1]+=b;a[i]>=DEPTH&&i<a[0];a[i+1]+=a[i]/DEPTH,a[i]%=DEPTH,i++); for(;a[a[0]]>=DEPTH;a[a[0]+1]=a[a[0]]/DEPTH,a[a[0]]%=DEPTH,a[0]++); } /************************************************************************/ /* 大数相减(被减数>=减数) */ /************************************************************************/ void sub(bignum_t a,const bignum_t b) { int i ; for(i=1;i<=b[0];i++) if((a[i]-=b[i])<0) a[i+1]--,a[i]+=DEPTH ; for(;a[i]<0;a[i]+=DEPTH,i++,a[i]--); for(;!a[a[0]]&&a[0]>1;a[0]--); } /************************************************************************/ /* 大数减去小数(被减数>=减数) */ /************************************************************************/ void sub(bignum_t a,const int b) { int i=1 ; for(a[1]-=b;a[i]<0;a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEPTH*DEPTH,i++); for(;!a[a[0]]&&a[0]>1;a[0]--); } void sub(bignum_t a,const bignum_t b,const int c,const int d) { int i,O=b[0]+d ; for(i=1+d;i<=O;i++) if((a[i]-=b[i-d]*c)<0) a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEPTH*DEPTH ; for(;a[i]<0;a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEPTH*DEPTH,i++); for(;!a[a[0]]&&a[0]>1;a[0]--); } /************************************************************************/ /* 大数相乘，读入被乘数a，乘数b，结果保存在c[] */ /************************************************************************/ void mul(bignum_t c,const bignum_t a,const bignum_t b) { int i,j ; memset((void*)c,0,sizeof(bignum_t)); for(c[0]=a[0]+b[0]-1,i=1;i<=a[0];i++) for(j=1;j<=b[0];j++) if((c[i+j-1]+=a[i]*b[j])>=DEPTH) c[i+j]+=c[i+j-1]/DEPTH,c[i+j-1]%=DEPTH ; for(c[0]+=(c[c[0]+1]>0);!c[c[0]]&&c[0]>1;c[0]--); } /************************************************************************/ /* 大数乘以小数，读入被乘数a，乘数b，结果保存在被乘数 */ /************************************************************************/ void mul(bignum_t a,const int b) { int i ; for(a[1]*=b,i=2;i<=a[0];i++) { a[i]*=b ; if(a[i-1]>=DEPTH) a[i]+=a[i-1]/DEPTH,a[i-1]%=DEPTH ; } for(;a[a[0]]>=DEPTH;a[a[0]+1]=a[a[0]]/DEPTH,a[a[0]]%=DEPTH,a[0]++); for(;!a[a[0]]&&a[0]>1;a[0]--); } void mul(bignum_t b,const bignum_t a,const int c,const int d) { int i ; memset((void*)b,0,sizeof(bignum_t)); for(b[0]=a[0]+d,i=d+1;i<=b[0];i++) if((b[i]+=a[i-d]*c)>=DEPTH) b[i+1]+=b[i]/DEPTH,b[i]%=DEPTH ; for(;b[b[0]+1];b[0]++,b[b[0]+1]=b[b[0]]/DEPTH,b[b[0]]%=DEPTH); for(;!b[b[0]]&&b[0]>1;b[0]--); } /**************************************************************************/ /* 大数相除,读入被除数a，除数b，结果保存在c[]数组 */ /* 需要comp()函数 */ /**************************************************************************/ void div(bignum_t c,bignum_t a,const bignum_t b) { int h,l,m,i ; memset((void*)c,0,sizeof(bignum_t)); c[0]=(b[0]<a[0]+1)?(a[0]-b[0]+2):1 ; for(i=c[0];i;sub(a,b,c[i]=m,i-1),i--) for(h=DEPTH-1,l=0,m=(h+l+1)>>1;h>l;m=(h+l+1)>>1) if(comp(b,m,i-1,a))h=m-1 ; else l=m ; for(;!c[c[0]]&&c[0]>1;c[0]--); c[0]=c[0]>1?c[0]:1 ; } void div(bignum_t a,const int b,int&c) { int i ; for(c=0,i=a[0];i;c=c*DEPTH+a[i],a[i]=c/b,c%=b,i--); for(;!a[a[0]]&&a[0]>1;a[0]--); } /************************************************************************/ /* 大数平方根，读入大数a，结果保存在b[]数组里 */ /* 需要comp()函数 */ /************************************************************************/ void sqrt(bignum_t b,bignum_t a) { int h,l,m,i ; memset((void*)b,0,sizeof(bignum_t)); for(i=b[0]=(a[0]+1)>>1;i;sub(a,b,m,i-1),b[i]+=m,i--) for(h=DEPTH-1,l=0,b[i]=m=(h+l+1)>>1;h>l;b[i]=m=(h+l+1)>>1) if(comp(b,m,i-1,a))h=m-1 ; else l=m ; for(;!b[b[0]]&&b[0]>1;b[0]--); for(i=1;i<=b[0];b[i++]>>=1); } /************************************************************************/ /* 返回大数的长度 */ /************************************************************************/ int length(const bignum_t a) { int t,ret ; for(ret=(a[0]-1)*DIGIT,t=a[a[0]];t;t/=10,ret++); return ret>0?ret:1 ; } /************************************************************************/ /* 返回指定位置的数字，从低位开始数到第b位，返回b位上的数 */ /************************************************************************/ int digit(const bignum_t a,const int b) { int i,ret ; for(ret=a[(b-1)/DIGIT+1],i=(b-1)%DIGIT;i;ret/=10,i--); return ret%10 ; } /************************************************************************/ /* 返回大数末尾0的个数 */ /************************************************************************/ int zeronum(const bignum_t a) { int ret,t ; for(ret=0;!a[ret+1];ret++); for(t=a[ret+1],ret*=DIGIT;!(t%10);t/=10,ret++); return ret ; } void comp(int*a,const int l,const int h,const int d) { int i,j,t ; for(i=l;i<=h;i++) for(t=i,j=2;t>1;j++) while(!(t%j)) a[j]+=d,t/=j ; } void convert(int*a,const int h,bignum_t b) { int i,j,t=1 ; memset(b,0,sizeof(bignum_t)); for(b[0]=b[1]=1,i=2;i<=h;i++) if(a[i]) for(j=a[i];j;t*=i,j--) if(t*i>DEPTH) mul(b,t),t=1 ; mul(b,t); } /************************************************************************/ /* 组合数 */ /************************************************************************/ void combination(bignum_t a,int m,int n) { int*t=new int[m+1]; memset((void*)t,0,sizeof(int)*(m+1)); comp(t,n+1,m,1); comp(t,2,m-n,-1); convert(t,m,a); delete[]t ; } /************************************************************************/ /* 排列数 */ /************************************************************************/ void permutation(bignum_t a,int m,int n) { int i,t=1 ; memset(a,0,sizeof(bignum_t)); a[0]=a[1]=1 ; for(i=m-n+1;i<=m;t*=i++) if(t*i>DEPTH) mul(a,t),t=1 ; mul(a,t); } #define SGN(x) ((x)>0?1:((x)<0?-1:0)) #define ABS(x) ((x)>0?(x):-(x)) int read(bignum_t a,int&sgn,istream&is=cin) { char str[MAX*DIGIT+2],ch,*buf ; int i,j ; memset((void*)a,0,sizeof(bignum_t)); if(!(is>>str))return 0 ; buf=str,sgn=1 ; if(*buf=='-')sgn=-1,buf++; for(a[0]=strlen(buf),i=a[0]/2-1;i>=0;i--) ch=buf[i],buf[i]=buf[a[0]-1-i],buf[a[0]-1-i]=ch ; for(a[0]=(a[0]+DIGIT-1)/DIGIT,j=strlen(buf);j<a[0]*DIGIT;buf[j++]='0'); for(i=1;i<=a[0];i++) for(a[i]=0,j=0;j<DIGIT;j++) a[i]=a[i]*10+buf[i*DIGIT-1-j]-'0' ; for(;!a[a[0]]&&a[0]>1;a[0]--); if(a[0]==1&&!a[1])sgn=0 ; return 1 ; } struct bignum { bignum_t num ; int sgn ; public : inline bignum() { memset(num,0,sizeof(bignum_t)); num[0]=1 ; sgn=0 ; } inline int operator!() { return num[0]==1&&!num[1]; } inline bignum&operator=(const bignum&a) { memcpy(num,a.num,sizeof(bignum_t)); sgn=a.sgn ; return*this ; } inline bignum&operator=(const int a) { memset(num,0,sizeof(bignum_t)); num[0]=1 ; sgn=SGN (a); add(num,sgn*a); return*this ; } ; inline bignum&operator+=(const bignum&a) { if(sgn==a.sgn)add(num,a.num); else if (sgn&&a.sgn) { int ret=comp(num,a.num); if(ret>0)sub(num,a.num); else if(ret<0) { bignum_t t ; memcpy(t,num,sizeof(bignum_t)); memcpy(num,a.num,sizeof(bignum_t)); sub (num,t); sgn=a.sgn ; } else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ; } else if(!sgn) memcpy(num,a.num,sizeof(bignum_t)),sgn=a.sgn ; return*this ; } inline bignum&operator+=(const int a) { if(sgn*a>0)add(num,ABS(a)); else if(sgn&&a) { int ret=comp(num,ABS(a)); if(ret>0)sub(num,ABS(a)); else if(ret<0) { bignum_t t ; memcpy(t,num,sizeof(bignum_t)); memset(num,0,sizeof(bignum_t)); num[0]=1 ; add(num,ABS (a)); sgn=-sgn ; sub(num,t); } else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ; } else if (!sgn)sgn=SGN(a),add(num,ABS(a)); return*this ; } inline bignum operator+(const bignum&a) { bignum ret ; memcpy(ret.num,num,sizeof (bignum_t)); ret.sgn=sgn ; ret+=a ; return ret ; } inline bignum operator+(const int a) { bignum ret ; memcpy(ret.num,num,sizeof (bignum_t)); ret.sgn=sgn ; ret+=a ; return ret ; } inline bignum&operator-=(const bignum&a) { if(sgn*a.sgn<0)add(num,a.num); else if (sgn&&a.sgn) { int ret=comp(num,a.num); if(ret>0)sub(num,a.num); else if(ret<0) { bignum_t t ; memcpy(t,num,sizeof(bignum_t)); memcpy(num,a.num,sizeof(bignum_t)); sub(num,t); sgn=-sgn ; } else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ; } else if(!sgn)add (num,a.num),sgn=-a.sgn ; return*this ; } inline bignum&operator-=(const int a) { if(sgn*a<0)add(num,ABS(a)); else if(sgn&&a) { int ret=comp(num,ABS(a)); if(ret>0)sub(num,ABS(a)); else if(ret<0) { bignum_t t ; memcpy(t,num,sizeof(bignum_t)); memset(num,0,sizeof(bignum_t)); num[0]=1 ; add(num,ABS(a)); sub(num,t); sgn=-sgn ; } else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ; } else if (!sgn)sgn=-SGN(a),add(num,ABS(a)); return*this ; } inline bignum operator-(const bignum&a) { bignum ret ; memcpy(ret.num,num,sizeof(bignum_t)); ret.sgn=sgn ; ret-=a ; return ret ; } inline bignum operator-(const int a) { bignum ret ; memcpy(ret.num,num,sizeof(bignum_t)); ret.sgn=sgn ; ret-=a ; return ret ; } inline bignum&operator*=(const bignum&a) { bignum_t t ; mul(t,num,a.num); memcpy(num,t,sizeof(bignum_t)); sgn*=a.sgn ; return*this ; } inline bignum&operator*=(const int a) { mul(num,ABS(a)); sgn*=SGN(a); return*this ; } inline bignum operator*(const bignum&a) { bignum ret ; mul(ret.num,num,a.num); ret.sgn=sgn*a.sgn ; return ret ; } inline bignum operator*(const int a) { bignum ret ; memcpy(ret.num,num,sizeof (bignum_t)); mul(ret.num,ABS(a)); ret.sgn=sgn*SGN(a); return ret ; } inline bignum&operator/=(const bignum&a) { bignum_t t ; div(t,num,a.num); memcpy (num,t,sizeof(bignum_t)); sgn=(num[0]==1&&!num[1])?0:sgn*a.sgn ; return*this ; } inline bignum&operator/=(const int a) { int t ; div(num,ABS(a),t); sgn=(num[0]==1&&!num [1])?0:sgn*SGN(a); return*this ; } inline bignum operator/(const bignum&a) { bignum ret ; bignum_t t ; memcpy(t,num,sizeof(bignum_t)); div(ret.num,t,a.num); ret.sgn=(ret.num[0]==1&&!ret.num[1])?0:sgn*a.sgn ; return ret ; } inline bignum operator/(const int a) { bignum ret ; int t ; memcpy(ret.num,num,sizeof(bignum_t)); div(ret.num,ABS(a),t); ret.sgn=(ret.num[0]==1&&!ret.num[1])?0:sgn*SGN(a); return ret ; } inline bignum&operator%=(const bignum&a) { bignum_t t ; div(t,num,a.num); if(num[0]==1&&!num[1])sgn=0 ; return*this ; } inline int operator%=(const int a) { int t ; div(num,ABS(a),t); memset(num,0,sizeof (bignum_t)); num[0]=1 ; add(num,t); return t ; } inline bignum operator%(const bignum&a) { bignum ret ; bignum_t t ; memcpy(ret.num,num,sizeof(bignum_t)); div(t,ret.num,a.num); ret.sgn=(ret.num[0]==1&&!ret.num [1])?0:sgn ; return ret ; } inline int operator%(const int a) { bignum ret ; int t ; memcpy(ret.num,num,sizeof(bignum_t)); div(ret.num,ABS(a),t); memset(ret.num,0,sizeof(bignum_t)); ret.num[0]=1 ; add(ret.num,t); return t ; } inline bignum&operator++() { *this+=1 ; return*this ; } inline bignum&operator--() { *this-=1 ; return*this ; } ; inline int operator>(const bignum&a) { return sgn>0?(a.sgn>0?comp(num,a.num)>0:1):(sgn<0?(a.sgn<0?comp(num,a.num)<0:0):a.sgn<0); } inline int operator>(const int a) { return sgn>0?(a>0?comp(num,a)>0:1):(sgn<0?(a<0?comp(num,-a)<0:0):a<0); } inline int operator>=(const bignum&a) { return sgn>0?(a.sgn>0?comp(num,a.num)>=0:1):(sgn<0?(a.sgn<0?comp(num,a.num)<=0:0):a.sgn<=0); } inline int operator>=(const int a) { return sgn>0?(a>0?comp(num,a)>=0:1):(sgn<0?(a<0?comp(num,-a)<=0:0):a<=0); } inline int operator<(const bignum&a) { return sgn<0?(a.sgn<0?comp(num,a.num)>0:1):(sgn>0?(a.sgn>0?comp(num,a.num)<0:0):a.sgn>0); } inline int operator<(const int a) { return sgn<0?(a<0?comp(num,-a)>0:1):(sgn>0?(a>0?comp(num,a)<0:0):a>0); } inline int operator<=(const bignum&a) { return sgn<0?(a.sgn<0?comp(num,a.num)>=0:1):(sgn>0?(a.sgn>0?comp(num,a.num)<=0:0):a.sgn>=0); } inline int operator<=(const int a) { return sgn<0?(a<0?comp(num,-a)>=0:1): (sgn>0?(a>0?comp(num,a)<=0:0):a>=0); } inline int operator==(const bignum&a) { return(sgn==a.sgn)?!comp(num,a.num):0 ; } inline int operator==(const int a) { return(sgn*a>=0)?!comp(num,ABS(a)):0 ; } inline int operator!=(const bignum&a) { return(sgn==a.sgn)?comp(num,a.num):1 ; } inline int operator!=(const int a) { return(sgn*a>=0)?comp(num,ABS(a)):1 ; } inline int operator[](const int a) { return digit(num,a); } friend inline istream&operator>>(istream&is,bignum&a) { read(a.num,a.sgn,is); return is ; } friend inline ostream&operator<<(ostream&os,const bignum&a) { if(a.sgn<0) os<<'-' ; write(a.num,os); return os ; } friend inline bignum sqrt(const bignum&a) { bignum ret ; bignum_t t ; memcpy(t,a.num,sizeof(bignum_t)); sqrt(ret.num,t); ret.sgn=ret.num[0]!=1||ret.num[1]; return ret ; } friend inline bignum sqrt(const bignum&a,bignum&b) { bignum ret ; memcpy(b.num,a.num,sizeof(bignum_t)); sqrt(ret.num,b.num); ret.sgn=ret.num[0]!=1||ret.num[1]; b.sgn=b.num[0]!=1||ret.num[1]; return ret ; } inline int length() { return :: length(num); } inline int zeronum() { return :: zeronum(num); } inline bignum C(const int m,const int n) { combination(num,m,n); sgn=1 ; return*this ; } inline bignum P(const int m,const int n) { permutation(num,m,n); sgn=1 ; return*this ; } }; #include <iostream> #include <cstring> using namespace std; #define DIGIT 4 //四位隔开,即万进制 #define DEPTH 10000 //万进制 #define MAX 100 typedef int bignum_t[MAX+1]; /************************************************************************/ /* 读取操作数，对操作数进行处理存储在数组里 */ /************************************************************************/ int read(bignum_t a,istream&is=cin) { char buf[MAX*DIGIT+1],ch ; int i,j ; memset((void*)a,0,sizeof(bignum_t)); if(!(is>>buf))return 0 ; for(a[0]=strlen(buf),i=a[0]/2-1;i>=0;i--) ch=buf[i],buf[i]=buf[a[0]-1-i],buf[a[0]-1-i]=ch ; for(a[0]=(a[0]+DIGIT-1)/DIGIT,j=strlen(buf);j<a[0]*DIGIT;buf[j++]='0'); for(i=1;i<=a[0];i++) for(a[i]=0,j=0;j<DIGIT;j++) a[i]=a[i]*10+buf[i*DIGIT-1-j]-'0' ; for(;!a[a[0]]&&a[0]>1;a[0]--); return 1 ; } void write(const bignum_t a,ostream&os=cout) { int i,j ; for(os<<a[i=a[0]],i--;i;i--) for(j=DEPTH/10;j;j/=10) os<<a[i]/j%10 ; } int comp(const bignum_t a,const bignum_t b) { int i ; if(a[0]!=b[0]) return a[0]-b[0]; for(i=a[0];i;i--) if(a[i]!=b[i]) return a[i]-b[i]; return 0 ; } int comp(const bignum_t a,const int b) { int c[12]= { 1 } ; for(c[1]=b;c[c[0]]>=DEPTH;c[c[0]+1]=c[c[0]]/DEPTH,c[c[0]]%=DEPTH,c[0]++); return comp(a,c); } int comp(const bignum_t a,const int c,const int d,const bignum_t b) { int i,t=0,O=-DEPTH*2 ; if(b[0]-a[0]<d&&c) return 1 ; for(i=b[0];i>d;i--) { t=t*DEPTH+a[i-d]*c-b[i]; if(t>0)return 1 ; if(t<O)return 0 ; } for(i=d;i;i--) { t=t*DEPTH-b[i]; if(t>0)return 1 ; if(t<O)return 0 ; } return t>0 ; } /************************************************************************/ /* 大数与大数相加 */ /************************************************************************/ void add(bignum_t a,const bignum_t b) { int i ; for(i=1;i<=b[0];i++) if((a[i]+=b[i])>=DEPTH) a[i]-=DEPTH,a[i+1]++; if(b[0]>=a[0]) a[0]=b[0]; else for(;a[i]>=DEPTH&&i<a[0];a[i]-=DEPTH,i++,a[i]++); a[0]+=(a[a[0]+1]>0); } /************************************************************************/ /* 大数与小数相加 */ /************************************************************************/ void add(bignum_t a,const int b) { int i=1 ; for(a[1]+=b;a[i]>=DEPTH&&i<a[0];a[i+1]+=a[i]/DEPTH,a[i]%=DEPTH,i++); for(;a[a[0]]>=DEPTH;a[a[0]+1]=a[a[0]]/DEPTH,a[a[0]]%=DEPTH,a[0]++); } /************************************************************************/ /* 大数相减(被减数>=减数) */ /************************************************************************/ void sub(bignum_t a,const bignum_t b) { int i ; for(i=1;i<=b[0];i++) if((a[i]-=b[i])<0) a[i+1]--,a[i]+=DEPTH ; for(;a[i]<0;a[i]+=DEPTH,i++,a[i]--); for(;!a[a[0]]&&a[0]>1;a[0]--); } /************************************************************************/ /* 大数减去小数(被减数>=减数) */ /************************************************************************/ void sub(bignum_t a,const int b) { int i=1 ; for(a[1]-=b;a[i]<0;a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEPTH*DEPTH,i++); for(;!a[a[0]]&&a[0]>1;a[0]--); } void sub(bignum_t a,const bignum_t b,const int c,const int d) { int i,O=b[0]+d ; for(i=1+d;i<=O;i++) if((a[i]-=b[i-d]*c)<0) a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEPTH*DEPTH ; for(;a[i]<0;a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEPTH*DEPTH,i++); for(;!a[a[0]]&&a[0]>1;a[0]--); } /************************************************************************/ /* 大数相乘，读入被乘数a，乘数b，结果保存在c[] */ /************************************************************************/ void mul(bignum_t c,const bignum_t a,const bignum_t b) { int i,j ; memset((void*)c,0,sizeof(bignum_t)); for(c[0]=a[0]+b[0]-1,i=1;i<=a[0];i++) for(j=1;j<=b[0];j++) if((c[i+j-1]+=a[i]*b[j])>=DEPTH) c[i+j]+=c[i+j-1]/DEPTH,c[i+j-1]%=DEPTH ; for(c[0]+=(c[c[0]+1]>0);!c[c[0]]&&c[0]>1;c[0]--); } /************************************************************************/ /* 大数乘以小数，读入被乘数a，乘数b，结果保存在被乘数 */ /************************************************************************/ void mul(bignum_t a,const int b) { int i ; for(a[1]*=b,i=2;i<=a[0];i++) { a[i]*=b ; if(a[i-1]>=DEPTH) a[i]+=a[i-1]/DEPTH,a[i-1]%=DEPTH ; } for(;a[a[0]]>=DEPTH;a[a[0]+1]=a[a[0]]/DEPTH,a[a[0]]%=DEPTH,a[0]++); for(;!a[a[0]]&&a[0]>1;a[0]--); } void mul(bignum_t b,const bignum_t a,const int c,const int d) { int i ; memset((void*)b,0,sizeof(bignum_t)); for(b[0]=a[0]+d,i=d+1;i<=b[0];i++) if((b[i]+=a[i-d]*c)>=DEPTH) b[i+1]+=b[i]/DEPTH,b[i]%=DEPTH ; for(;b[b[0]+1];b[0]++,b[b[0]+1]=b[b[0]]/DEPTH,b[b[0]]%=DEPTH); for(;!b[b[0]]&&b[0]>1;b[0]--); } /**************************************************************************/ /* 大数相除,读入被除数a，除数b，结果保存在c[]数组 */ /* 需要comp()函数 */ /**************************************************************************/ void div(bignum_t c,bignum_t a,const bignum_t b) { int h,l,m,i ; memset((void*)c,0,sizeof(bignum_t)); c[0]=(b[0]<a[0]+1)?(a[0]-b[0]+2):1 ; for(i=c[0];i;sub(a,b,c[i]=m,i-1),i--) for(h=DEPTH-1,l=0,m=(h+l+1)>>1;h>l;m=(h+l+1)>>1) if(comp(b,m,i-1,a))h=m-1 ; else l=m ; for(;!c[c[0]]&&c[0]>1;c[0]--); c[0]=c[0]>1?c[0]:1 ; } void div(bignum_t a,const int b,int&c) { int i ; for(c=0,i=a[0];i;c=c*DEPTH+a[i],a[i]=c/b,c%=b,i--); for(;!a[a[0]]&&a[0]>1;a[0]--); } /************************************************************************/ /* 大数平方根，读入大数a，结果保存在b[]数组里 */ /* 需要comp()函数 */ /************************************************************************/ void sqrt(bignum_t b,bignum_t a) { int h,l,m,i ; memset((void*)b,0,sizeof(bignum_t)); for(i=b[0]=(a[0]+1)>>1;i;sub(a,b,m,i-1),b[i]+=m,i--) for(h=DEPTH-1,l=0,b[i]=m=(h+l+1)>>1;h>l;b[i]=m=(h+l+1)>>1) if(comp(b,m,i-1,a))h=m-1 ; else l=m ; for(;!b[b[0]]&&b[0]>1;b[0]--); for(i=1;i<=b[0];b[i++]>>=1); } /************************************************************************/ /* 返回大数的长度 */ /************************************************************************/ int length(const bignum_t a) { int t,ret ; for(ret=(a[0]-1)*DIGIT,t=a[a[0]];t;t/=10,ret++); return ret>0?ret:1 ; } /************************************************************************/ /* 返回指定位置的数字，从低位开始数到第b位，返回b位上的数 */ /************************************************************************/ int digit(const bignum_t a,const int b) { int i,ret ; for(ret=a[(b-1)/DIGIT+1],i=(b-1)%DIGIT;i;ret/=10,i--); return ret%10 ; } /************************************************************************/ /* 返回大数末尾0的个数 */ /************************************************************************/ int zeronum(const bignum_t a) { int ret,t ; for(ret=0;!a[ret+1];ret++); for(t=a[ret+1],ret*=DIGIT;!(t%10);t/=10,ret++); return ret ; } void comp(int*a,const int l,const int h,const int d) { int i,j,t ; for(i=l;i<=h;i++) for(t=i,j=2;t>1;j++) while(!(t%j)) a[j]+=d,t/=j ; } void convert(int*a,const int h,bignum_t b) { int i,j,t=1 ; memset(b,0,sizeof(bignum_t)); for(b[0]=b[1]=1,i=2;i<=h;i++) if(a[i]) for(j=a[i];j;t*=i,j--) if(t*i>DEPTH) mul(b,t),t=1 ; mul(b,t); } /************************************************************************/ /* 组合数 */ /************************************************************************/ void combination(bignum_t a,int m,int n) { int*t=new int[m+1]; memset((void*)t,0,sizeof(int)*(m+1)); comp(t,n+1,m,1); comp(t,2,m-n,-1); convert(t,m,a); delete[]t ; } /************************************************************************/ /* 排列数 */ /************************************************************************/ void permutation(bignum_t a,int m,int n) { int i,t=1 ; memset(a,0,sizeof(bignum_t)); a[0]=a[1]=1 ; for(i=m-n+1;i<=m;t*=i++) if(t*i>DEPTH) mul(a,t),t=1 ; mul(a,t); } #define SGN(x) ((x)>0?1:((x)<0?-1:0)) #define ABS(x) ((x)>0?(x):-(x)) int read(bignum_t a,int&sgn,istream&is=cin) { char str[MAX*DIGIT+2],ch,*buf ; int i,j ; memset((void*)a,0,sizeof(bignum_t)); if(!(is>>str))return 0 ; buf=str,sgn=1 ; if(*buf=='-')sgn=-1,buf++; for(a[0]=strlen(buf),i=a[0]/2-1;i>=0;i--) ch=buf[i],buf[i]=buf[a[0]-1-i],buf[a[0]-1-i]=ch ; for(a[0]=(a[0]+DIGIT-1)/DIGIT,j=strlen(buf);j<a[0]*DIGIT;buf[j++]='0'); for(i=1;i<=a[0];i++) for(a[i]=0,j=0;j<DIGIT;j++) a[i]=a[i]*10+buf[i*DIGIT-1-j]-'0' ; for(;!a[a[0]]&&a[0]>1;a[0]--); if(a[0]==1&&!a[1])sgn=0 ; return 1 ; } struct bignum { bignum_t num ; int sgn ; public : inline bignum() { memset(num,0,sizeof(bignum_t)); num[0]=1 ; sgn=0 ; } inline int operator!() { return num[0]==1&&!num[1]; } inline bignum&operator=(const bignum&a) { memcpy(num,a.num,sizeof(bignum_t)); sgn=a.sgn ; return*this ; } inline bignum&operator=(const int a) { memset(num,0,sizeof(bignum_t)); num[0]=1 ; sgn=SGN (a); add(num,sgn*a); return*this ; } ; inline bignum&operator+=(const bignum&a) { if(sgn==a.sgn)add(num,a.num); else if (sgn&&a.sgn) { int ret=comp(num,a.num); if(ret>0)sub(num,a.num); else if(ret<0) { bignum_t t ; memcpy(t,num,sizeof(bignum_t)); memcpy(num,a.num,sizeof(bignum_t)); sub (num,t); sgn=a.sgn ; } else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ; } else if(!sgn) memcpy(num,a.num,sizeof(bignum_t)),sgn=a.sgn ; return*this ; } inline bignum&operator+=(const int a) { if(sgn*a>0)add(num,ABS(a)); else if(sgn&&a) { int ret=comp(num,ABS(a)); if(ret>0)sub(num,ABS(a)); else if(ret<0) { bignum_t t ; memcpy(t,num,sizeof(bignum_t)); memset(num,0,sizeof(bignum_t)); num[0]=1 ; add(num,ABS (a)); sgn=-sgn ; sub(num,t); } else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ; } else if (!sgn)sgn=SGN(a),add(num,ABS(a)); return*this ; } inline bignum operator+(const bignum&a) { bignum ret ; memcpy(ret.num,num,sizeof (bignum_t)); ret.sgn=sgn ; ret+=a ; return ret ; } inline bignum operator+(const int a) { bignum ret ; memcpy(ret.num,num,sizeof (bignum_t)); ret.sgn=sgn ; ret+=a ; return ret ; } inline bignum&operator-=(const bignum&a) { if(sgn*a.sgn<0)add(num,a.num); else if (sgn&&a.sgn) { int ret=comp(num,a.num); if(ret>0)sub(num,a.num); else if(ret<0) { bignum_t t ; memcpy(t,num,sizeof(bignum_t)); memcpy(num,a.num,sizeof(bignum_t)); sub(num,t); sgn=-sgn ; } else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ; } else if(!sgn)add (num,a.num),sgn=-a.sgn ; return*this ; } inline bignum&operator-=(const int a) { if(sgn*a<0)add(num,ABS(a)); else if(sgn&&a) { int ret=comp(num,ABS(a)); if(ret>0)sub(num,ABS(a)); else if(ret<0) { bignum_t t ; memcpy(t,num,sizeof(bignum_t)); memset(num,0,sizeof(bignum_t)); num[0]=1 ; add(num,ABS(a)); sub(num,t); sgn=-sgn ; } else memset(num,0,sizeof(bignum_t)),num[0]=1,sgn=0 ; } else if (!sgn)sgn=-SGN(a),add(num,ABS(a)); return*this ; } inline bignum operator-(const bignum&a) { bignum ret ; memcpy(ret.num,num,sizeof(bignum_t)); ret.sgn=sgn ; ret-=a ; return ret ; } inline bignum operator-(const int a) { bignum ret ; memcpy(ret.num,num,sizeof(bignum_t)); ret.sgn=sgn ; ret-=a ; return ret ; } inline bignum&operator*=(const bignum&a) { bignum_t t ; mul(t,num,a.num); memcpy(num,t,sizeof(bignum_t)); sgn*=a.sgn ; return*this ; } inline bignum&operator*=(const int a) { mul(num,ABS(a)); sgn*=SGN(a); return*this ; } inline bignum operator*(const bignum&a) { bignum ret ; mul(ret.num,num,a.num); ret.sgn=sgn*a.sgn ; return ret ; } inline bignum operator*(const int a) { bignum ret ; memcpy(ret.num,num,sizeof (bignum_t)); mul(ret.num,ABS(a)); ret.sgn=sgn*SGN(a); return ret ; } inline bignum&operator/=(const bignum&a) { bignum_t t ; div(t,num,a.num); memcpy (num,t,sizeof(bignum_t)); sgn=(num[0]==1&&!num[1])?0:sgn*a.sgn ; return*this ; } inline bignum&operator/=(const int a) { int t ; div(num,ABS(a),t); sgn=(num[0]==1&&!num [1])?0:sgn*SGN(a); return*this ; } inline bignum operator/(const bignum&a) { bignum ret ; bignum_t t ; memcpy(t,num,sizeof(bignum_t)); div(ret.num,t,a.num); ret.sgn=(ret.num[0]==1&&!ret.num[1])?0:sgn*a.sgn ; return ret ; } inline bignum operator/(const int a) { bignum ret ; int t ; memcpy(ret.num,num,sizeof(bignum_t)); div(ret.num,ABS(a),t); ret.sgn=(ret.num[0]==1&&!ret.num[1])?0:sgn*SGN(a); return ret ; } inline bignum&operator%=(const bignum&a) { bignum_t t ; div(t,num,a.num); if(num[0]==1&&!num[1])sgn=0 ; return*this ; } inline int operator%=(const int a) { int t ; div(num,ABS(a),t); memset(num,0,sizeof (bignum_t)); num[0]=1 ; add(num,t); return t ; } inline bignum operator%(const bignum&a) { bignum ret ; bignum_t t ; memcpy(ret.num,num,sizeof(bignum_t)); div(t,ret.num,a.num); ret.sgn=(ret.num[0]==1&&!ret.num [1])?0:sgn ; return ret ; } inline int operator%(const int a) { bignum ret ; int t ; memcpy(ret.num,num,sizeof(bignum_t)); div(ret.num,ABS(a),t); memset(ret.num,0,sizeof(bignum_t)); ret.num[0]=1 ; add(ret.num,t); return t ; } inline bignum&operator++() { *this+=1 ; return*this ; } inline bignum&operator--() { *this-=1 ; return*this ; } ; inline int operator>(const bignum&a) { return sgn>0?(a.sgn>0?comp(num,a.num)>0:1):(sgn<0?(a.sgn<0?comp(num,a.num)<0:0):a.sgn<0); } inline int operator>(const int a) { return sgn>0?(a>0?comp(num,a)>0:1):(sgn<0?(a<0?comp(num,-a)<0:0):a<0); } inline int operator>=(const bignum&a) { return sgn>0?(a.sgn>0?comp(num,a.num)>=0:1):(sgn<0?(a.sgn<0?comp(num,a.num)<=0:0):a.sgn<=0); } inline int operator>=(const int a) { return sgn>0?(a>0?comp(num,a)>=0:1):(sgn<0?(a<0?comp(num,-a)<=0:0):a<=0); } inline int operator<(const bignum&a) { return sgn<0?(a.sgn<0?comp(num,a.num)>0:1):(sgn>0?(a.sgn>0?comp(num,a.num)<0:0):a.sgn>0); } inline int operator<(const int a) { return sgn<0?(a<0?comp(num,-a)>0:1):(sgn>0?(a>0?comp(num,a)<0:0):a>0); } inline int operator<=(const bignum&a) { return sgn<0?(a.sgn<0?comp(num,a.num)>=0:1):(sgn>0?(a.sgn>0?comp(num,a.num)<=0:0):a.sgn>=0); } inline int operator<=(const int a) { return sgn<0?(a<0?comp(num,-a)>=0:1): (sgn>0?(a>0?comp(num,a)<=0:0):a>=0); } inline int operator==(const bignum&a) { return(sgn==a.sgn)?!comp(num,a.num):0 ; } inline int operator==(const int a) { return(sgn*a>=0)?!comp(num,ABS(a)):0 ; } inline int operator!=(const bignum&a) { return(sgn==a.sgn)?comp(num,a.num):1 ; } inline int operator!=(const int a) { return(sgn*a>=0)?comp(num,ABS(a)):1 ; } inline int operator[](const int a) { return digit(num,a); } friend inline istream&operator>>(istream&is,bignum&a) { read(a.num,a.sgn,is); return is ; } friend inline ostream&operator<<(ostream&os,const bignum&a) { if(a.sgn<0) os<<'-' ; write(a.num,os); return os ; } friend inline bignum sqrt(const bignum&a) { bignum ret ; bignum_t t ; memcpy(t,a.num,sizeof(bignum_t)); sqrt(ret.num,t); ret.sgn=ret.num[0]!=1||ret.num[1]; return ret ; } friend inline bignum sqrt(const bignum&a,bignum&b) { bignum ret ; memcpy(b.num,a.num,sizeof(bignum_t)); sqrt(ret.num,b.num); ret.sgn=ret.num[0]!=1||ret.num[1]; b.sgn=b.num[0]!=1||ret.num[1]; return ret ; } inline int length() { return :: length(num); } inline int zeronum() { return :: zeronum(num); } inline bignum C(const int m,const int n) { combination(num,m,n); sgn=1 ; return*this ; } inline bignum P(const int m,const int n) { permutation(num,m,n); sgn=1 ; return*this ; } }; 主函数调用如下： view plaincopy to clipboardprint? int main() { bignum a,b,c; cin>>a>>b; cout<<"加法:"<<a+b<<endl; cout<<"减法:"<<a-b<<endl; cout<<"乘法:"<<a*b<<endl; cout<<"除法:"<<a/b<<endl; c=sqrt(a); cout<<"平方根:"<<c<<endl; cout<<"a的长度:"<<a.length()<<endl; cout<<"a的末尾0个数:"<<a.zeronum()<<endl<<endl; cout<<"组合: 从10个不同元素取3个元素组合的所有可能性为"<<c.C(10,3)<<endl; cout<<"排列: 从10个不同元素取3个元素排列的所有可能性为"<<c.P(10,3)<<endl; return 0 ; }

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