zoukankan      html  css  js  c++  java
  • Repeating Decimals, ACM/ICPC World Finals 1990, UVa202

                                                                                        Repeating Decimals

    Description

    The decimal expansion of the fraction 1/33 is tex2html_wrap_inline43 , where the tex2html_wrap_inline45 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.

    tabular23

    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
    

    输出a/b的循环小数表示以及循环节长度。
    用变量c存储小数点之前的结果,用afterpoint【3000】、mod【3000】分别存储小数点之后的数、a%b(余数);
    模拟除法,每除一次,查找余数是否在前面出现过,如果出现过,则mod【j】~mod【i】为循环节。
    #include<stdio.h>
    int main()
    {
        int a, b;
        while(scanf("%d%d", &a, &b)!=EOF)
        {
            int c = a/b, afterpoint[3000], mod[3000], i, j, k, flag=0;
            printf("%d/%d = ", a, b);
            for(i=0; i<b; i++)
            {
                a = a%b;
                mod[i] = a;
                a *= 10;
                afterpoint[i] = a/b;
                for(j=0; j<i; j++)
                  if(mod[j] == mod[i]) {
                        flag = 1;
                        break;
                    }
                if(flag == 1) break;
            }
            printf("%d.", c);
            for(k=0; k<j; k++)
                printf("%d", afterpoint[k]);
            printf("(");
            if(i-j >50){
                for(k=j; k< j+50; k++)
                    printf("%d", afterpoint[k]);
                printf("...");
            }
            else {
                for(k=j; k<i; k++)
                    printf("%d", afterpoint[k]);
            }
            printf(")
    ");
            printf("   %d = number of digits in repeating cycle
    
    ", i-j);
        }
        return 0;
    }


  • 相关阅读:
    嵌入式成长轨迹5 【嵌入式环境及基础】【嵌入式Linux软件开发入门】【变量和运算符】
    嵌入式成长轨迹3 【嵌入式环境及基础】【嵌入式Linux软件开发入门】【VI编辑器的使用】
    嵌入式成长轨迹8 【嵌入式环境及基础】【Linux shell强化】【文本过滤】
    嵌入式成长轨迹7 【(转)十年后嵌入式设计技术将不再是独立的技术门类】
    浏览器加载和渲染html的顺序
    IE9/火狐4.0/Chrome 10 三足鼎立的浏览器之争
    为什么要叫我“美工”?
    可用性测试启发式评估十条原则介绍
    为何用户体验无法被设计,如何为用户体验设计
    浅谈web标准、可用性、可访问性
  • 原文地址:https://www.cnblogs.com/Genesis2018/p/9079919.html
Copyright © 2011-2022 走看看