(algorithm) to accurately represent decimals

Topic:

Given a positive integer n, ask for a decimal representation of 1/n, such as:

1/2=0.5

1/3=0. (3)

1/6=0.1 (6)

1/7=0. (142857)

Where parentheses represent the loop portion of the decimal.

Ideas:

Consider the process of the division operation:

When the remainder is duplicated with the previous operation, then the loop has already begun, so a hash table can be used to record the position of the remainder.

Dividend divisor remainder quotient

1 7 1 0

1*10 7 3 1

3*10 7 2 4

2*10 7 6 2

6*10 7 4 8

4*10 7 5 5

5*10 7 1 7

1*10 7 3 1

3*10 7 2 4

2*10 7 6 2

6*10 7 4 8

4*10 7 5 5

5*10 7 1　　　7　

Code:

#include <iostream>#include<map>#include<sstream>using namespacestd;stringDecimalrepresent (intN) {Map<int,int>MP; intnum=Ten; intResidue=1; stringMulti; intidx=0;  while(Mp.find (residue) = =Mp.end ()) {        if(residue==0) {StringStream ss; stringtmp; SS<<1.0/N; SS>>tmp; returntmp; } Mp[residue]=idx;        StringStream Sstr; stringstr; Sstr<<num/N; Sstr>>str; Multi=multi+str; IDX++; Residue=num%N; Num=residue*Ten; }        stringresult="0."+MULTI.SUBSTR (0, Mp[residue]) +"("+multi.substr (Mp[residue]) +")"; returnresult;}intMain () {intN;  while(cin>>N) {cout<<"The result of 1/"<<n<<": "<<Endl; cout<<decimalrepresent (n) <<Endl; }    return 0;}

(algorithm) to accurately represent decimals