我正在尝试编写一个简单的重复十进制算法。现在，我已经非常接近找到有用的东西了。

我尝试使用这个算法:How to know the repeating decimal in a fraction?

"A very simple algorithm is this: implement long division. Record every intermediate division you do. As soon as you see a division identical to the one you've done before, you have what's being repeated."

除了检测重复的小数模式并将其放在括号中外，我能够执行上述所有操作。

对于分数 7/13，我的输出应该是 0。[538461]现在是 0,5,3,8,4,6,1,5,3,8,4,6,1,5,3,8,4,6,1,5。

关于如何使用我上面提到的算法实现检测重复小数模式并将其放在括号中的任何建议？我知道有类似的问题，但我想用我当前的代码使用我上面提到的算法来实现它。

<script>
// All the prime numbers under 1,000
var primeNumbers = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997];

// Finds all the prime factors of a non-zero integer
// a = integer
function primeFactors(a) {
    var primeFactors = new Array(); 

    // Trial division algorithm
    for (var i = 0, p = primeNumbers[i]; i < primeNumbers.length && p * p <= a; i++, p = primeNumbers[i]) {
        while (a % p == 0) {         
                primeFactors.push(p);

                a /= p;
        }
    }

    if (a > 1) {
        primeFactors.push(a);
    }

    return primeFactors;
}

// Converts a fraction to a decimal
// i = number
// n = numerator
// d = denominator
function fractionToDecimal(n, d) {
    var pFS = primeFactors(d);

    for (var i = 0; i < pFS.length; i++) { // Go through each of the denominators prime factors

        if (pFS[i] !== 2 && pFS[i] !== 5) { // We have a repeating decimal

            var output = new Array();

            // Let's find the repeating decimal
            // Repeating decimal algorithm - uses long division
            for (var i = 0; i < 20; i++) { // For now find 20 spots, ideally this should stop after it finds the repeating decimal

                // How many times does the denominator go into the numerator evenly
                var temp2 = parseInt(n / d);

                output.push(temp2);

                var n = n % d;

                n += "0";
            }

            return "Repeating decimal: " + output;
        }
    }

    // Terminating decimal
    return "Terminating decimal: " + n / d;
}

document.write(fractionToDecimal(7, 13));
</script>

最佳答案

您已经了解了大部分内容，只缺少 2 个部分:

1. 检查长除法的分子是否重复并停止循环。当分子重复时，表示我们找到了重复小数。

2. 将数组转换为不带逗号的字符串，这可以使用 join('') 轻松实现。

这是实现了上述两点的代码的相关部分:

function fractionToDecimal(n, d) {
    var pFS = primeFactors(d);
    for (var i = 0; i < pFS.length; i++) { // Go through each of the denominators prime factors

        if (pFS[i] !== 2 && pFS[i] !== 5) { // We have a repeating decimal

            var output = new Array();
            var ns = new Array();

            // Let's find the repeating decimal
            // Repeating decimal algorithm - uses long division
            for (var i = 0; i < 20; i++) { // For now find 20 spots, ideally this should stop after it finds the repeating decimal
                // How many times does the denominator go into the numerator evenly
                var temp2 = parseInt(n / d);

                if (ns[n] === undefined) {
                    ns[n] = i;
                } else {
                    return "Repeating decimal: " + 
                        output.slice(0, 1).join('') +
                        '.' +
                        output.slice(1, ns[n]).join('') +
                        '[' + output.slice(ns[n]).join('') + ']'
                    ;
                }

                output.push(temp2);
                var n = n % d;
                n += "0";
            }           
            return "Repeating decimal: " + output;
        }
    }

    // Terminating decimal
    return "Terminating decimal: " + n / d;
}

jsFiddle 完整代码:http://jsfiddle.net/49Xks/

关于javascript - 重复小数算法，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/14533222/