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Is there a way to avoid number to string conversion & nested loops for performance?

I just took a coding test online and this one question really bothered me. My solution was correct but was rejected for being unoptimized. The question is as following:
Write a function combineTheGivenNumber taking two arguments:
numArray: number[]
num: a number
The function should check all the concatenation pairs that can result in making a number equal to num and return their count.
E.g. if numArray = [1, 212, 12, 12] & num = 1212 then we will have return value of 3 from combineTheGivenNumber
The pairs are as following:
numArray[0]+numArray[1]
numArray[2]+numArray[3]
numArray[3]+numArray[2]
The function I wrote for this purpose is as following:
function combineTheGivenNumber(numArray, num) {
//convert all numbers to strings for easy concatenation
numArray = numArray.map(e => e+'');
//also convert the `hay` to string for easy comparison
num = num+'';
let pairCounts = 0;
// itereate over the array to get pairs
numArray.forEach((e,i) => {
numArray.forEach((f,j) => {
if(i!==j && num === (e+f)) {
pairCounts++;
}
});
});
return pairCounts;
}
console.log('Test 1: ', combineTheGivenNumber([1,212,12,12],1212));
console.log('Test 2: ', combineTheGivenNumber([4,21,42,1],421));
From my experience, I know conversion of number to string is slow in JS, but I am not sure whether my approach is wrong/lack of knowledge or does the tester is ignorant of this fact. Can anyone suggest further optimization of the code snipped?
Elimination of string to number to string will be a significant speed boost but I am not sure how to check for concatenated numbers otherwise.

Elimination of string to number to string will be a significant speed boost
No, it won't.
Firstly, you're not converting strings to numbers anywhere, but more importantly the exercise asks for concatenation so working with strings is exactly what you should do. No idea why they're even passing numbers. You're doing fine already by doing the conversion only once for each number input, not every time your form a pair. And last but not least, avoiding the conversion will not be a significant improvement.
To get a significant improvement, you should use a better algorithm. #derpirscher is correct in his comment: "[It's] the nested loop checking every possible combination which hits the time limit. For instance for your example, when the outer loop points at 212 you don't need to do any checks, because regardless, whatever you concatenate to 212, it can never result in 1212".
So use
let pairCounts = 0;
numArray.forEach((e,i) => {
if (num.startsWith(e)) {
//^^^^^^^^^^^^^^^^^^^^^^
numArray.forEach((f,j) => {
if (i !== j && num === e+f) {
pairCounts++;
}
});
}
});
You might do the same with suffixes, but it becomes more complicated to rule out concatenation to oneself there.
Optimising further, you can even achieve a linear complexity solution by putting the strings in a lookup structure, then when finding a viable prefix just checking whether the missing part is an available suffix:
function combineTheGivenNumber(numArray, num) {
const strings = new Map();
for (const num of numArray) {
const str = String(num);
strings.set(str, 1 + (strings.get(str) ?? 0));
}
const whole = String(num);
let pairCounts = 0;
for (const [prefix, pCount] of strings) {
if (!whole.startsWith(prefix))
continue;
const suffix = whole.slice(prefix.length);
if (strings.has(suffix)) {
let sCount = strings.get(suffix);
if (suffix == prefix) sCount--; // no self-concatenation
pairCounts += pCount*sCount;
}
}
return pairCounts;
}
(the proper handling of duplicates is a bit difficile)

I like your approach of going to strings early. I can suggest a couple of simple optimizations.
You only need the numbers that are valid "first parts" and those that are valid "second parts"
You can use the javascript .startsWith and .endsWith to test for those conditions. All other strings can be thrown away.
The lengths of the strings must add up to the length of the desired answer
Suppose your target string is 8 digits long. If you have 2 valid 3-digit "first parts", then you only need to know how many valid 5-digit "second parts" you have. Suppose you have 9 of them. Those first parts can only combine with those second parts, and give you 2 * 9 = 18 valid pairs.
You don't actually need to keep the strings!
It struck me that if you know you have 2 valid 3-digit "first parts", you don't need to keep those actual strings. Knowing that they are valid 2-digit first parts is all you need to know.
So let's build an array containing:
How many valid 1-digit first parts do we have?,
How many valid 2-digit first parts do we have?,
How many valid 3-digit first parts do we have?,
etc.
And similarly an array containing the number of valid 1-digit second parts, etc.
X first parts and Y second parts can be combined in X * Y ways
Except if the parts are the same length, in which case we are reusing the same list, and so it is just X * (Y-1).
So not only do we not need to keep the strings, but we only need to do the multiplication of the appropriate elements of the arrays.
5 1-char first parts & 7 3-char second parts = 5 * 7 = 35 pairs
6 2-char first part & 4 2-char second parts = 6 * (4-1) = 18 pairs
etc
So this becomes extremely easy. One pass over the strings, tallying the "first part" and "second part" matches of each length. This can be done with an if and a ++ of the relevant array element.
Then one pass over the lengths, which will be very quick as the array of lengths will be very much shorter than the array of actual strings.
function combineTheGivenNumber(numArray, num) {
const sElements = numArray.map(e => "" + e);
const sTarget = "" + num;
const targetLength = sTarget.length
const startsByLen = (new Array(targetLength)).fill(0);
const endsByLen = (new Array(targetLength)).fill(0);
sElements.forEach(sElement => {
if (sTarget.startsWith(sElement)) {
startsByLen[sElement.length]++
}
if (sTarget.endsWith(sElement)) {
endsByLen[sElement.length]++
}
})
// We can now throw away the strings. We have two separate arrays:
// startsByLen[1] is the count of strings (without attempting to remove duplicates) which are the first character of the required answer
// startsByLen[2] similarly the count of strings which are the first 2 characters of the required answer
// etc.
// and endsByLen[1] is the count of strings which are the last character ...
// and endsByLen[2] is the count of strings which are the last 2 characters, etc.
let pairCounts = 0;
for (let firstElementLength = 1; firstElementLength < targetLength; firstElementLength++) {
const secondElementLength = targetLength - firstElementLength;
if (firstElementLength === secondElementLength) {
pairCounts += startsByLen[firstElementLength] * (endsByLen[secondElementLength] - 1)
} else {
pairCounts += startsByLen[firstElementLength] * endsByLen[secondElementLength]
}
}
return pairCounts;
}
console.log('Test 1: ', combineTheGivenNumber([1, 212, 12, 12], 1212));
console.log('Test 2: ', combineTheGivenNumber([4, 21, 42, 1], 421));

Depending on a setup, the integer slicing can be marginally faster
Although in the end it falls short
Also, when tested on higher N values, the previous answer exploded in jsfiddle. Possibly a memory error.
As far as I have tested with both random and hand-crafted values, my solution holds. It is based on an observation, that if X, Y concantenated == Z, then following must be true:
Z - Y == X * 10^(floor(log10(Y)) + 1)
an example of this:
1212 - 12 = 1200
12 * 10^(floor((log10(12)) + 1) = 12 * 10^(1+1) = 12 * 100 = 1200
Now in theory, this should be faster then manipulating strings. And in many other languages it most likely would be. However in Javascript as I just learned, the situation is a bit more complicated. Javascript does some weird things with casting that I haven't figured out yet. In short - when I tried storing the numbers(and their counts) in a map, the code got significantly slower making any possible gains from this logarithm shenanigans evaporate. Furthermore, storing them in a custom-crafted data structure isn't guaranteed to be faster since you have to build it etc. Also it would be quite a lot of work.
As it stands this log comparison is ~ 8 times faster in a case without(or with just a few) matches since the quadratic factor is yet to kick in. As long as the possible postfix count isn't too high, it will outperform the linear solution. Unfortunately it is still quadratic in nature with the breaking point depending on a total number of strings as well as their length.
So if you are searching for a needle in a haystack - for example you are looking for a few pairs in a huge heap of numbers, this can help. In the other case of searching for many matches, this won't help. Similarly, if the input array was sorted, you could use binary search to push the breaking point further up.
In the end, unless you manage to figure out how to store ints in a map(or some custom implementation of it) in a way that doesn't completely kill the performance, the linear solution of the previous answer will be faster. It can still be useful even with the performance hit if your computation is going to be memory heavy. Storing numbers takes less space then storing strings.
var log10 = Math.log(10)
function log10floored(num) {
return Math.floor(Math.log(num) / log10)
}
function combineTheGivenNumber(numArray, num) {
count = 0
for (var i=0; i!=numArray.length; i++) {
let portion = num - numArray[i]
let removedPart = Math.pow(10, log10floored(numArray[i]))
if (portion % (removedPart * 10) == 0) {
for (var j=0; j!=numArray.length; j++) {
if (j != i && portion / (removedPart * 10) == numArray[j] ) {
count += 1
}
}
}
}
return count
}
//The previous solution, that I used for timing, comparison and check purposes
function combineTheGivenNumber2(numArray, num) {
const strings = new Map();
for (const num of numArray) {
const str = String(num);
strings.set(str, 1 + (strings.get(str) ?? 0));
}
const whole = String(num);
let pairCounts = 0;
for (const [prefix, pCount] of strings) {
if (!whole.startsWith(prefix))
continue;
const suffix = whole.slice(prefix.length);
if (strings.has(suffix)) {
let sCount = strings.get(suffix);
if (suffix == prefix) sCount--; // no self-concatenation
pairCounts += pCount*sCount;
}
}
return pairCounts;
}
var myArray = []
for (let i =0; i!= 10000000; i++) {
myArray.push(Math.floor(Math.random() * 1000000))
}
var a = new Date()
t1 = a.getTime()
console.log('Test 1: ', combineTheGivenNumber(myArray,15285656));
var b = new Date()
t2 = b.getTime()
console.log('Test 2: ', combineTheGivenNumber2(myArray,15285656));
var c = new Date()
t3 = c.getTime()
console.log('Test1 time: ', t2 - t1)
console.log('test2 time: ', t3 - t2)
Small update
As long as you are willing to take a performance hit with the setup and settle for the ~2 times performance, using a simple "hashing" table can help.(Hashing tables are nice and tidy, this is a simple modulo lookup table. The principle is similar though.)
Technically this isn't linear, practicaly it is enough for the most cases - unless you are extremely unlucky and all your numbers fall in the same bucket.
function combineTheGivenNumber(numArray, num) {
count = 0
let size = 1000000
numTable = new Array(size)
for (var i=0; i!=numArray.length; i++) {
let idx = numArray[i] % size
if (numTable[idx] == undefined) {
numTable[idx] = [numArray[i]]
} else {
numTable[idx].push(numArray[i])
}
}
for (var i=0; i!=numArray.length; i++) {
let portion = num - numArray[i]
let removedPart = Math.pow(10, log10floored(numArray[i]))
if (portion % (removedPart * 10) == 0) {
if (numTable[portion / (removedPart * 10) % size] != undefined) {
let a = numTable[portion / (removedPart * 10) % size]
for (var j=0; j!=a.length; j++) {
if (j != i && portion / (removedPart * 10) == a[j] ) {
count += 1
}
}
}
}
}
return count
}

Here's a simplified, and partially optimised approach with 2 loops:
// let's optimise 'combineTheGivenNumber', where
// a=array of numbers AND n=number to match
const ctgn = (a, n) => {
// convert our given number to a string using `toString` for clarity
// this isn't entirely necessary but means we can use strict equality later
const ns = n.toString();
// reduce is an efficient mechanism to return a value based on an array, giving us
// _=[accumulator], na=[array number] and i=[index]
return a.reduce((_, na, i) => {
// convert our 'array number' to an 'array number string' for later concatenation
const nas = na.toString();
// iterate back over our array of numbers ... we're using an optimised/reverse loop
for (let ii = a.length - 1; ii >= 0; ii--) {
// skip the current array number
if (i === ii) continue;
// string + number === string, which lets us strictly compare our 'number to match'
// if there's a match we increment the accumulator
if (a[ii] + nas === ns) ++_;
}
// we're done
return _;
}, 0);
}

Random lottery number generator

What I'm trying to do is generate 6 random numbers, five in a range of 1-45 and one in a range of 1-25 for a Greek lottery game (Tzoker). The first 5 numbers should be unique. By pressing a button, I want to add these numbers to a div using jQuery (I have some working code for this part).
I thought it would be pretty easy using a loop, but I've found myself unable to check if the number generated already exists. The loop would only contain the first 5 numbers, because the last number can be equal to one of the other 5.

Let me propose you some simpler solution.
Make a list of all numbers from 1 to 45.
Sort the list using Math.random (plus minus something, read the docs of Array.sort to find out) as the comparison function. You will get the list in random order.
Take 5 first items from the list.
Then, when you already have the numbers, put them all into your div.
This way you don't mix your logic (getting the numbers) with your presentation (putting stuff into the DOM).
I leave the implementation as an exercise for the reader. :)

Like this?
$(function() {
$('button').on('click', function(e) {
e.preventDefault();
var numArray = [];
while( numArray.length < 5 ) {
var number = Math.floor((Math.random() * 45 ) + 1);
if( $.inArray( number, numArray ) == -1 ) {
numArray.push( number );
}
}
numArray.push( Math.floor((Math.random() * 25 ) + 1) );
$('div').html( numArray.join("<br />") );
});
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<button>Generate</button>
<div></div>

While this might be not exactly what you were asking for, if you would use lodash, this would be as simple as:
_.sample(_.range(1, 46), 5) // the 5 numbers from 1..45
_.random(1, 26) // one more from 1..25
This is why functional programming is so cool. You can read for example Javascript Allonge to find out more.

http://jsfiddle.net/015d05uu/
var tzoker = $("#tzoker");
var results = $("#results");
tzoker.click(function() {
results.empty();
var properResults = [];
var rand = 0;
var contains = false;
for (i = 1; i < 7; i++) {
do
{
(rand = Math.floor((Math.random() * (i != 6 ? 45 : 25)) + 1));
contains = properResults.indexOf(rand) > -1;
} while(contains)
results.append("<br />", rand, "<br />");
properResults.push(rand);
}
});
Here is the main idea of a solution. You can define the max value as a parameter for the random.
Then, check the existence of the item in a simple array with only the data you want.

You may use a general function which generates random numbers from 1 to maxValue, and adds them to an array only if they don't exist. Then, to display, cycle through the array items and append them to #randomNumbers.
HTML
<div id="randomNumbers"></div>
JS (with jQuery)
var randomNumbersArray = [];
$(function() {
generateRandomNumbers();
displayRandomNumbers();
});
function generateRandomNumbers() {
for (i = 0; i < 5; i++) {
generateRandomNumberFrom1To(45);
}
generateRandomNumberFrom1To(25);
}
function generateRandomNumberFrom1To(maxValue) {
var randomNumber;
do {
randomNumber = Math.ceil(Math.random() * maxValue);
} while ($.inArray(randomNumber, randomNumbersArray) > -1);
randomNumbersArray.push(randomNumber);
}
function displayRandomNumbers() {
for (i in randomNumbersArray) {
$("#randomNumbers").append(randomNumbersArray[i] + "<br>");
}
}

Need help writing code to convert decimal to binary without the use of the toString

I'm trying to create my own decimal to binary converter with the method of decrementing the inputted variable (decimal value), by dividing it by 2 and storing the remainder (like 2nd grade math remainder), which is always either 0 or 1. Each of the remainder values i thin should be stored in an array and I think maybe put in backwards so that the most significant digit is first in the array (this is because when decrementing the remainer values are filled in left to right). Soooo yea i dont really know how to store the remainder values in an array using a function
Thanks in advance and if something is confusing then feel free to ask because im not even sure if this is the best method of doing this its just what i came up with
function decimalToBinary(num) {
var bin = 0;
while (num > 0) {
bin = num % 2 + bin;
num >>= 1; // basically /= 2 without remainder if any
}
alert("That decimal in binary is " + bin);
}

Your code is almost correct. The main problem is that bin starts out as 0; when you add a digit, they are added numerically, so your code ends up just counting the binary 1s: in this manner, 10 is initial 0, and +1+0+1+0, resulting in 2. You want to handle it as a string: ""+1+0+1+0 results in 1010. So, the only needed change is:
var bin = "";
If you want to solve it using arrays, with minimal changes to your code, it would be:
function decimalToBinary(num) {
var bin = [];
while (num > 0) {
bin.unshift(num % 2);
num >>= 1; // basically /= 2 without remainder if any
}
alert("That decimal in binary is " + bin.join(''));
}
Here, I use .unshift to add an element to the head of the array (and renumbering the remaining elements); .join() to collect them all into a string.
Or this:
function decimalToBinary(num) {
var bin = [];
while (num > 0) {
bin[bin.length] = num % 2;
num >>= 1; // basically /= 2 without remainder if any
}
alert("That decimal in binary is " + bin.reverse().join(''));
}
This is not as good, but illustrates some more things you can do with arrays: taking their length, setting an arbitrary element, and flipping them around.

I have written a custom Decimal to Binary method:
function toBinary (input) {
let options = [1];
let max = 0;
let i = 1;
while(i) {
max = Math.pow(2, i);
if (max > input) break;
options.push(max);
i++;
}
let j = options.length;
let result = new Array(j);
result.fill("0");
while(j >= 0) {
if (options[j] <= input) {
result[j] = "1"
input = input - options[j];
}
j--;
}
return [...result].reverse().join("");
}
//Test the toBin method with built-in toString(2)
toBinary(100) === (100).toString(2) // true
toBinary(1) === (1).toString(2) // true
toBinary(128) === (128).toString(2) // true

Fibonacci Sequence - Find the number of digits - JavaScript

So, I have successfully written the Fibonacci sequence to create an array with the sequence of numbers, but I need to know the length (how many digits) the 500th number has.
I've tried the below code, but its finding the length of the scientific notation (22 digits), not the proper 105 it should be returning.
Any ideas how to convert a scientific notation number into an actual integer?
var fiblength = function fiblength(nth) {
var temparr = [0,1];
for(var i = 2; i<=nth; i++){
var prev = temparr[temparr.length-2],
cur = temparr[temparr.length-1],
next = prev + cur;
temparr.push(next);
}
var final = temparr[temparr.length-1].toString().length;
console.log(temparr[temparr.length-1]);
return final;
};
a = fiblength(500);
console.log(a);

Why not use the simple procedure of dividing the number by 10 until the number is less than 1.
Something as simple as this should work (a recursive def obv works as well)
function getDigits(n) {
var digits = 0;
while(n >= 1) {
n/=10;
digits += 1;
}
return digits;
}
getDigits(200);//3
getDigits(3.2 * 10e20);//=>22

Here's a solution in constant time:
function fiblength(n) {
return Math.floor((n>1)?n*.2089+.65051:1);
}
Let's explain how I arrived to it.
All previous solutions will probably not work for N>300 unless you have a BigNumber library in place. Also they're pretty inneficient.
There is a formula to get any Fibonacci number, which uses PHI (golden ratio number), it's very simple:
F(n) = ABS((PHI^n)/sqrt(5))
Where PHI=1.61803399 (golden ratio, found all over the fibonacci sequence)
If you want to know how many digits a number has, you calculate the log base 10 and add 1 to that. Let's call that function D(n) = log10(n) + 1
So what you want fiblength to be is in just the following function
fiblength(n) = D(F(n)) // number of digits of a fibonacci number...
Let's work it out, so you see what the one liner code will be like once you use math.
Substitute F(n)
fiblength(n) = D(ABS((PHI^n)/sqrt(5)))
Now apply D(n) on that:
fiblength(n) = log10(ABS((PHI^n)/sqrt(5))) + 1
So, since log(a/b) = log(a) - log(b)
fiblength(n) = log10(ABS((PHI^n))) - log10(sqrt(5))) + 1
and since log(a^n) = n * log(a)
fiblength(n) = n*log10(PHI) - log10(sqrt(5))) + 1
Then we evaluate those logarithms since they're all on constants
and add the special cases of n=0 and n=1 to return 1
function fiblength(n) {
return Math.floor((n>1)?n*.2089+.65051:1);
}
Enjoy :)
fiblength(500) => 105 //no iterations necessary.

Most of the javascript implementations, internally use 64 bit numbers. So, if the number we are trying to represent is very big, it uses scientific notation to represent those numbers. So, there is no pure "javascript numbers" based solution for this. You may have to look for other BigNum libraries.
As far as your code is concerned, you want only the 500th number, so you don't have to store the entire array of numbers in memory, just previous and current numbers are enough.
function fiblength(nth) {
var previous = 0, current = 1, temp;
for(var i = 2; i<=nth; i++){
temp = current;
current = previous + current;
previous = temp;
}
return current;
};

My Final Solution
function fiblength(nth) {
var a = 0, b = 1, c;
for(var i=2;i<=nth;i++){
c=b;
b=a+b;
a=c;
}
return Math.floor(Math.log(b)/Math.log(10))+1;
}
console.log(fiblength(500));
Thanks for the help!!!

The problem is because the resulting number was converted into a string before any meaningful calculations could be made. Here's how it could have been solved in the original code:
var fiblength = function fiblength(nth) {
var temparr = [0,1];
for(var i = 2; i<=nth; i++){
var prev = temparr[temparr.length-2],
cur = temparr[temparr.length-1],
next = prev + cur;
temparr.push(next);
}
var x = temparr[temparr.length-1];
console.log(x);
var length = 1;
while (x > 1) {
length = length + 1;
x = x/10;
}
return length;
};
console.log ( fiblength(500) );

Small Straight (Yahtzee) Algorithm

I have created a working javascript function to check an array of 5 numbers for a small straight, in a Yahtzee game I'm making. I've tested it to no end and I'm confident it works 100% of the time, but it is also probably the worst algorithm of all time in terms of being efficient. Here is what it looks like:
function calcSmstraight() {
var sum = 0;
var r = new Array();
var r2 = new Array();
var counter = 0;
var temp;
var bool = false;
var bool2 = false;
r[0] = document.getElementById('setKeep1').value;
r[1] = document.getElementById('setKeep2').value;
r[2] = document.getElementById('setKeep3').value;
r[3] = document.getElementById('setKeep4').value;
r[4] = document.getElementById('setKeep5').value;
// Move non-duplicates to new array
r2[0] = r[0];
for(var i=0; i<r.length; i++) {
for(var j=0; j<r2.length; j++) {
if(r[i] == r2[j]) {
bool2 = true; // Already in new list
}
}
// Add to new list if not already in it
if(!bool2) {
r2.push(r[i]);
}
bool2 = false;
}
// Make sure list has at least 4 different numbers
if(r2.length >= 4) {
// Sort dice from least to greatest
while(counter < r2.length) {
if(r2[counter] > r2[counter+1]) {
temp = r2[counter];
r2[counter] = r2[counter+1];
r2[counter+1] = temp;
counter = 0;
} else {
counter++;
}
}
// Check if the dice are in order
if(((r2[0] == (r2[1]-1)) && (r2[1] == (r2[2]-1)) && (r2[2] == (r2[3]-1)))
|| ((r2[1] == (r2[2]-1)) && (r2[2] == (r2[3]-1)) && (r2[3] == (r2[4]-1)))) {
bool = true;
}
}
if(bool) {
// If small straight give 30 points
sum = 30;
}
return sum;
}
My strategy is to:
1) Remove duplicates by adding numbers to a new array as they occur
2) Make sure the new array is at least 4 in length (4 different numbers)
3) Sort the array from least to greatest
4) Check if the first 4 OR last 4 (if 5 in length) numbers are in order
My question:
Does anyone know a way that I can improve this method? It seems ridiculously terrible to me but I can't think of a better way to do this and it at least works.

Given that you're implementing a Yahtzee game you presumably need to test for other patterns beyond just small straights, so it would be better to create the array of values before calling the function so that you can use them in all tests, rather than getting the values from the DOM elements inside the small straight test.
Anyway, here's the first way that came to my mind to test for a small straight within an array representing the values of five six-sided dice:
// assume r is an array with the values from the dice
r.sort();
if (/1234|2345|3456/.test(r.join("").replace(/(.)\1/,"$1") {
// is a small straight
}
Note that you can sort an array of numbers using this code:
r2.sort(function(a,b){return a-b;});
...but in your case the values in the array are strings because they came from the .value attribute of DOM elements, so a default string sort will work with r2.sort(). Either way you don't need your own sort routine, because JavaScript provides one.
EDIT: If you assume that you can just put the five values as a string as above you can implement tests for all possible combinations as a big if/else like this:
r.sort();
r = r.join("");
if (/(.)\1{4}/.test(r)) {
alert("Five of a Kind");
} else if (/(.)\1{3}/.test(r)) {
alert("Four of a Kind");
} else if (/(.)\1{2}(.)\2|(.)\3(.)\4{2}/.test(r)) {
alert("Full House");
} else if (/(.)\1{2}/.test(r)) {
alert("Three of a Kind");
} else if (/1234|2345|3456/.test( r.replace(/(.)\1/,"$1") ) {
alert("Small Straight");
} // etc.
Demo: http://jsfiddle.net/4Qzfw/

Why don't you just have a six-element array of booleans indicating whether a number is present, then check 1-4, 2-5, and 3-6 for being all true? In pseudocode:
numFlags = array(6);
foreach(dice)
numFlags[die.value-1] = true;
if(numFlags[0] && numFlags[1] && numFlags[2] && numFlags[3]) return true
//Repeat for 1-4 and 2-5
return false
This wouldn't be a useful algorithm if you were using million-sided dice, but for six-siders there are only three possible small straights to check for, so it's simple and straightforward.

I do not play Yahtzee, but I do play cards, and it would appear the algorithm might be similar. This routine, written in ActionScript (my JavaScript is a bit rusty) has been compiled but not tested. It should accept 5 cards for input, and return a message for either straights greater than 3 cards or pairs or higher.
private function checkCards(card1:int,card2:int,card3:int,card4:int,card5:int):String
{
// Assumes that the 5 cards have a value between 0-12 (Ace-King)
//The key to the routine is using the card values as pointers into an array of possible card values.
var aryCardValues:Array = new Array(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
aryCardValues[card1] += 1;
aryCardValues[card1] += 1;
aryCardValues[card1] += 1;
aryCardValues[card1] += 1;
aryCardValues[card1] += 1;
var aryCardNames:Array = new Array("Ace", "2", "3", "4", "5", "6", "7", "8", "9", "10", "Jack", "Queen", "King");
var strOutMessage:String;
var intCardCount:int = 0;
var strSeperator:String;
var strHighCard:String;
for (var i:int = 0;i < aryCardValues.length;i++)
{
//Check for runs of three of a kind or greater.
if (aryCardValues[i] >= 2)
{
strOutMessage = strOutMessage + strSeperator + i + "-" + aryCardNames[i] + "s";
strSeperator = " & ";
}
//Check for values in a straight.
if (aryCardValues[i] > 0)
{
intCardCount++;
if (intCardCount > 3)strHighCard = aryCardNames[i];
}
else
{
if (intCardCount < 3)intCardCount = 0;
}
}
if (intCardCount > 3) strOutMessage = intCardCount + " run " + strHighCard + " High."
return strOutMessage;
}
It may not be as concise as the regular expressions used above, but it might be more readable and easily modified. One change that could be made is to pass in an array of cards rather than discrete variables for each card.