UVA202循环小数Repeating Decimals

Repeating Decimals

The decimal expansion of the fraction 1/33 is , where the is used to indicate that the cycle 03 repeats indefinitely with no intervening digits. In fact, the decimal expansion of every rational number (fraction) has a repeating cycle as opposed to decimal expansions of irrational numbers, which have no such repeating cycles.

Examples of decimal expansions of rational numbers and their repeating cycles are shown below. Here, we use parentheses to enclose the repeating cycle rather than place a bar over the cycle.

Write a program that reads numerators and denominators of fractions and determines their repeating cycles.

For the purposes of this problem, define a repeating cycle of a fraction to be the first minimal length string of digits to the right of the decimal that repeats indefinitely with no intervening digits. Thus for example, the repeating cycle of the fraction 1/250 is 0, which begins at position 4 (as opposed to 0 which begins at positions 1 or 2 and as opposed to 00 which begins at positions 1 or 4).

Input

Each line of the input file consists of an integer numerator, which is nonnegative, followed by an integer denominator, which is positive. None of the input integers exceeds 3000. End-of-file indicates the end of input.

Output

For each line of input, print the fraction, its decimal expansion through the first occurrence of the cycle to the right of the decimal or 50 decimal places (whichever comes first), and the length of the entire repeating cycle.

In writing the decimal expansion, enclose the repeating cycle in parentheses when possible. If the entire repeating cycle does not occur within the first 50 places, place a left parenthesis where the cycle begins - it will begin within the first 50 places - and place ``...)" after the 50th digit.

Print a blank line after every test case.

Sample Input

76 25
5 43
1 397

Sample Output

76/25 = 3.04(0)
1 = number of digits in repeating cycle

5/43 = 0.(116279069767441860465)
21 = number of digits in repeating cycle

1/397 = 0.(00251889168765743073047858942065491183879093198992...)
99 = number of digits in repeating cycle

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;

const int MAX = 3000;
int y[MAX];  //数组 存储 余数
int s[MAX];  //数组 存储 商
int bj[MAX];  //标记 数字i 是否出现

int main()
{
int a, b;

while (cin >> a >> b)
{
memset(y, 0, sizeof(y));
memset(s, 0, sizeof(s));
memset(bj, 0, sizeof(bj));

int a_temp = a;             //保存a的值
int cnt = 0;                //
s[cnt++] = a / b;              //存ab相除的 商（整数部分）
a = a%b;                    //求ab相除的余数
while (a&&!bj[a])   //a不为0 &&  a在标记数组没有出现过
{
bj[a] = 1;              //标记 余数a
s[cnt] = 10 * a / b;        //循环存 商
y[cnt] = a;            //循环 存 余数
a = 10 * a%b;
cnt++;              //最后一次循环时，cnt已经多加了一次。
}
cout << a_temp << "/" << b << "=" << s[0] << ".";

if (a == 0)
{
for (int i = 1; i<cnt; i++)
cout << s[i];
cout << "(0)" << endl;
cout << "1=number of digits in repeating cycle" << endl;

}
else
{
int pos;
for (int i = 1; i <= 50 && i<cnt; i++)
{
if (y[i] == a)      //找到数值a在余数数组的位置
{
cout << "(";
pos = i;
}
cout << s[i];    //循环输出 循环部分的 数字
}
if (cnt>50)
cout << "....)" << endl;
else
cout << ")" << endl;
cout << cnt - pos << "=number of digits in repeating cycle" << endl;

}

}
getchar();
getchar();
return 0;
}