Repeating decimal algorithm

Question

I am trying to write a simple repeating decimal algorithm. Now I'm almost close to what works.

I tried to use this algorithm: How to find out the repeated decimal number in a fraction?

"A very simple algorithm: implement a long division. Each intermediate division you do. As soon as you see a section identical to the one you did before, you have what was repeated."

I was able to do all of the above except detecting a repeating decimal pattern and placing it in brackets.

For fraction 7/13, my conclusion should be 0. [538461] right now it's 0.5,3,8,4,6,1,5,3,8,4,6,1,5,3,8,4 6.1.5.

Any suggestions on how to implement duplicate decimal pattern detection and put it in brackets using the algorithm mentioned above? I know there are similar questions, but I would like to implement it with my current code using the algorithm mentioned above.

<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 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> 

Answer 1

You have most of them, only two parts are missing:

• Make sure the long division numerator repeats and stops the cycle. When the numerator is repeated, it means that we have found a repeating decimal number.

• Converting an array to a comma-free string, which is easily achievable with join('') .

Here the corresponding part of your code is executed with the above two points:

 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 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 with full code: http://jsfiddle.net/49Xks/