高精度除法

求  M/N 的商的整数部分。

 

M/N = A

M = N * A + res(余数)

A可以用二进制表示

M = N * ( 2^p1 + 2^ p2+ ... +2^pk ) + res

 

所以设 t[i] =  N * 2^i

从高到低   如果 M > t[i]

M -= t[i]

ans += 2^i

直到M < N*1 (此时M是余数)。因此只需要高精度加，减，比较大小

 

#include <iostream>using namespace std;const int _DEF_MAXSIZE = 300;const int _DEF_ZS = 300;//指数 2^300int _ga[_DEF_MAXSIZE],_gb[_DEF_MAXSIZE],_gc[_DEF_MAXSIZE],_gans[_DEF_MAXSIZE];int _gzs[_DEF_ZS][_DEF_MAXSIZE],_gt[_DEF_ZS][_DEF_MAXSIZE];void _ftoNum( char *str,int *n ){n[0] = strlen(str);for( int i = 1,move = n[0]-1;i <= n[0];++i,--move )n[i] = str[move]-'0';}int _fmax( int a,int b ){return a > b ? a : b;}int _fmin( int a,int b ){return a < b ? a : b;}void _fadd( int *a,int *b,int *c ){c[0] = _fmax( a[0],b[0] ),c[ c[0]+1 ] = 0;int *p,end;if( a[0] > b[0] )end = b[0],p = a;elseend = a[0],p = b;for( int i = 1;i <= end;++i )c[i] = a[i] + b[i];for( int i = end+1;i <= c[0];++i )c[i] = p[i];for( int i = 1;i <= c[0];++i )if( c[i] >= 10 )++c[i+1],c[i] %= 10;if( c[c[0]+1] )++c[0];}void _fsub( int *a,int *b,int *c )//保证a >= b {c[0] = a[0];for( int i = 1;i <= b[0];++i )c[i] = a[i] - b[i];for( int i = b[0]+1;i <= a[0];++i )c[i] = a[i];for( int i = 1;i <= a[0];++i )if( c[i] < 0 )c[i] += 10,--c[i+1];while( !c[c[0]] && c[0] > 0 )--c[0];}int _fcomp( int *a,int *b ){if( a[0] < b[0] )return -1;if( b[0] < a[0] )return 1;for( int i = a[0];i >= 1;--i ){if( a[i] < b[i] )return -1;if( b[i] < a[i] )return 1;}return 1;}void _fprint( int *p ){for( int i = p[0];i >= 1;--i )cout << p[i];cout << endl;}int main(){char str[_DEF_MAXSIZE+1];cin >> str;_ftoNum( str,_ga );cin >> str;_ftoNum( str,_gb );memcpy( _gt[0],_gb,sizeof(_gb) );_gzs[0][0] = 1,_gzs[0][1] = 1;for( int i = 1;i < _DEF_ZS;++i ){_fadd( _gt[i-1],_gt[i-1],_gt[i] );_fadd( _gzs[i-1],_gzs[i-1],_gzs[i] );}_gans[0] = 0;for( int i = _DEF_ZS-1;i >= 0;--i ){if( _fcomp( _ga,_gt[i] ) == 1 ){_fsub( _ga,_gt[i],_gc );memcpy( _ga,_gc,sizeof(_gc) );_fadd( _gzs[i],_gans,_gc );memcpy( _gans,_gc,sizeof(_gc) );}}_fprint( _gans );system("pause");return 0;}