usaco——fractions to Decimals

Fractions to Decimals

Write a program that will accept a fraction of the form N/D, where N is the numerator and D is the denominator and print the decimal representation. If the decimal representation has a repeating sequence of digits, indicate the sequence by enclosing it in brackets. For example, 1/3 = .33333333...is denoted as 0.(3), and 41/333 = 0.123123123...is denoted as 0.(123). Use xxx.0 to denote an integer. Typical conversions are:

1/3     =  0.(3)
22/5    =  4.4
1/7     =  0.(142857)
2/2     =  1.0
3/8     =  0.375
45/56   =  0.803(571428)

PROGRAM NAME: fracdec

INPUT FORMAT

A single line with two space separated integers, N and D, 1 <= N,D <= 100000.

SAMPLE INPUT (file fracdec.in)

45 56

OUTPUT FORMAT

The decimal expansion, as detailed above. If the expansion exceeds 76 characters in length, print it on multiple lines with 76 characters per line.

SAMPLE OUTPUT (file fracdec.out)

0.803(571428)
/* 
ID: guangxue1    
PROG: fracdec   
LANG: C++    
*/
#include <fstream>
using namespace std;

int memory[100000];
int result[100000];
int core(int N, int D,int i,int &A,int &B)
{
 if(N==0) return i;
 result[i]=N*10/D;
   if(memory[N]!=0)
       {A=memory[N]-1,B=i; return -1;}
    memory[N]=i+1;   
 core(N*10%D, D, ++i,A,B);
}
int main()
{
  ifstream fin("fracdec.in");
  ofstream fout("fracdec.out");
  int length=0;
  int N,D;
  int A,B;
  fin>>N>>D;
  fout<<N/D;
  int NN=N;
  do
   ++length;
  while(NN=NN/D);
  fout<<'.';
  ++length;
  if(N%D==0)
  { fout<<0<<endl;
  return 0;}
  else
   {
     int sign;
     sign=core(N%D,D,0,A,B);
     if(sign==-1)
     {
      for(int i=0; i<A; ++i)
       {fout<<result[i];++length; if(length==76) {fout<<endl; length=0;}}
      fout<<'(';
      ++length;
      if(length==76)
      {fout<<endl; length=0;}
      for(int i=A; i<B; ++i)
      {fout<<result[i]; ++length; if(length==76) {fout<<endl; length=0;}}
      fout<<')'<<endl;
     }
     else
     { 
       for(int i=0; i<sign; ++i)
         { fout<<result[i]; ++length; if(length==76) {fout<<endl; length=0;}}
          fout<<endl;
      }
    }    
   return 0;  
} 

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>

#define MAXDIGIT 100100

char dec[MAXDIGIT];
int lastrem[MAXDIGIT];
char buf[MAXDIGIT];

void
main(void)
{
    FILE *fin, *fout;
    int n, d, k, i, rem, len;

    fin = fopen("fracdec.in", "r");
    fout = fopen("fracdec.out", "w");
    assert(fin != NULL && fout != NULL);

    fscanf(fin, "%d %d", &n, &d);
    sprintf(buf, "%d.", n/d);

	/* long division keeping track of if we've seem a remainder before */
    for(i=0; i<MAXDIGIT; i++)
	lastrem[i] = -1;

    rem = n % d;
    for(i=0;; i++) {
	if(rem == 0) {
	    if(i == 0)
		sprintf(buf+strlen(buf), "0");
	    else
		sprintf(buf+strlen(buf), "%s", dec);
	    break;
	}
	if(lastrem[rem] != -1) {
	    k = lastrem[rem];
	    sprintf(buf+strlen(buf), "%.*s(%s)", k, dec, dec+k);
	    break;
	}

	lastrem[rem] = i;
	n = rem * 10;
	dec[i] = n/d + '0';
	rem = n%d;
    }

    /* print buf 76 chars per line */
    len = strlen(buf);
    for(i=0; i<len; i+=76) {
    	fprintf(fout, "%.76s/n", buf+i);
    }
    exit(0);
}
 

#include <iostream.h>
#include <fstream.h>
#include <math.h>
ofstream out("fracdec.out");

int colcount=0;

int numBeforeRepeat(int n, int d) {
    int c2=0, c5=0;
    if (n == 0) return 1;
    while (d%2==0) { d/=2; c2++; }
    while (d%5==0) { d/=5; c5++; }
    while (n%2==0) { n/=2; c2--; } /* can go negative */
    while (n%5==0) { n/=5; c5--; } /* can go negative */
    if (c2>c5)
        if (c2>0) return c2;
        else return 0;
    else
        if (c5>0) return c5;
        else return 0;
}

void print (char c) {
    if (colcount==76) {
        out<<endl;
        colcount=0;
    }
    out<<c;
    colcount++;
}

void print (int n) {
    if (n>=10) print (n/10);
    print ((char)('0'+(n%10)));
}

int main() {
    int n, d;
    ifstream in("fracdec.in");
    in>>n>>d;
    in.close();

    print (n/d);
    print ('.');
    n=n%d;
    int m=numBeforeRepeat(n,d);
    for(int i=0;i<m;i++) {
        n*=10;
	print (n/d);
        n%=d;
    }
    int r=n;
    if(r!=0) {
	print ('(');
        do {
            n*=10;
	    print (n/d);
            n%=d;
        } while (n!=r);
	print (')');
    }
    out<<endl;
    out.close();
    exit (0);
}