factorial.js

/*jshint node:true, white:true*/
var assert = require('assert');

/**
 * 大数
 * @class BigNumber
 * @param {Number} num
 */
function BigNumber(num) {
    this.digits = this._serialize(num);
}
BigNumber.prototype._serialize = function (num) {
    var digits = [];
    while (num > 0) {
        digits.push(num % 10);
        num = Math.floor(num / 10);
    }
    return digits;
};
BigNumber.prototype.multiply = function (num) {
    var digits = this.digits,
        nums = this._serialize(num),
        i, j, len = digits.length, lenNums = nums.length,
        product, carry,
        result = [];

    for (i = 0; i < lenNums; ++i) {
        for (j = 0; j < len; ++j) {
            product = nums[i] * digits[j] + (result[i + j] || 0);
            carry = Math.floor(product / 10);
            result[i + j] = product % 10;
            if (carry > 0) {
                result[i + j + 1] = carry + (result[i + j + 1] || 0);
            }
        }
    }
    this.digits = result;

    return this;
};
BigNumber.prototype.format = function () {
    return this.digits.concat().reverse().join('');
};

/**
 * 求阶乘
 * @method factorial
 * @param {Number} num
 * @return {String}
 */
function factorial(num) {
    var n = new BigNumber(num);
    while (--num > 0) {
        n.multiply(num);
    }
    return n.format();
}


var bigNumber = new BigNumber(1234);
assert.deepEqual(bigNumber.digits, [4, 3, 2, 1], '_serialize failed');
assert.deepEqual(bigNumber.multiply(56).digits, [4, 0, 1, 9, 6], 'multiply failed');
assert.deepEqual(bigNumber.format(), '69104', 'format failed');
assert.deepEqual(factorial(1000), '402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000', 'factorial failed');