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Fibonacci sequence generator not working for 1 or 2 as inputs but it works for the rest of the sequence?

Can someone explain to me why my fibonacciGenerator function doesn't work with this code? I understand why it works with the second code tho but I just don't get why the first one doesn't.
function fibonacciGenerator(n) {
if (n > 0) {
var fArray = [];
fArray.push(0);
if (n >= 2) {
fArray.push(1);
}
for (var i = 0; i < n; i++) {
fArray.push(fArray[i] + fArray[i + 1]);
}
console.log(fArray);
}
}
fibonacciGenerator(1);
fibonacciGenerator(2);
Second code working :
function fibonacciGenerator(n) {
if (n > 0) {
var fArray = [];
fArray.push(0);
if (n >= 2) {
fArray.push(1);
}
for (var i = 2; i < n; i++) {
fArray.push(fArray[i - 1] + fArray[i - 2]);
}
console.log(fArray);
}
}
fibonacciGenerator(1);
fibonacciGenerator(2);

The first code is printing 2 extra Fibonacci number this is because:
you are first pushing 0 and 1 into the array as:
var fArray = [];
fArray.push(0);
if (n >=2 ){
fArray.push(1);
}
and then you loop over again till n times. Because of this reason it prints two extra Fibonacci numbers.
the solution is to either loop over n-2 time or to use the second code.

var fArray = [];
fArray.push(0);
if (n >= 2) {
fArray.push(1);
}
The initial condition is to cover n=1: [0] and n=2: [0,1]
The 2nd code is working because the loop only starts when n is greater than i, so means it skips the loop with n < 2.
For your problem, you don't skip the loop when n < 2.
for (var i = 0; i < n; i++) {
fArray.push(fArray[i] + fArray[i + 1]);
}
You can imagine the result will be like below when n < 2 with your loop.
Note that the inital value is fArray = [0]
fArray.push(fArray[0] + fArray[1]); //fArray[1] is undefined because you only have 1 item in your array
In this case fArray[0] + fArray[1] ==> 0 + undefined = NaN
So that's why your logic does not work when n < 2
To correct it, you need to avoid the loop if n < 2
//if n=1 or n=2, it won't trigger the loop due to `i < n-2`
for (var i = 0; i < n-2; i++) {
fArray.push(fArray[i] + fArray[i + 1]);
}

The idea to have i start with 0 instead of 2, and to adjust the body of the loop accordingly, is fine, but there is one thing that the first version didn't adjust: the stop condition of the loop.
By setting i=0, the first version loops 2 times more than the second version. You should also alter the end condition in the same way: instead of i < n, it should have i < n - 2, so to ensure the number of iterations is the same as in the second version.
Not related to your question, but the console.log should better be placed outside of the function. The job of the function should be to return the array, not to print it. So also, when n > 0 is false, it should return an empty array.
function fibonacciGenerator(n) {
var fArray = [];
if (n > 0) {
fArray.push(0);
if (n >= 2) {
fArray.push(1);
}
for (var i = 0; i < n - 2; i++) {
fArray.push(fArray[i] + fArray[i + 1]);
}
}
return fArray;
}
console.log(fibonacciGenerator(1));
console.log(fibonacciGenerator(2));

First you have to identify the pattern.
Fibonacci series -> 0 1 1 2 3 5 8 13 21
Term -> 0 1 2 3 4 5 6 7 8
0th term =0, 1st term =1
From the second term,
2nd = 1st term + 0th term = 1+0 = 1
3rd = 2nd term + 1st term = 1+1 = 2
4th = 3rd term + 2nd term = 2+1 = 3
5th = 4th term + 3rd term = 3+2 = 5
nth = (n-1) + (n-2)
since the first 2 terms are fixed, you have to start for loop from i= 2.
Also, according to the above shown pattern, you have to use following code inside the for loop.
fArray.push(fArray[i - 1] + fArray[i-2]);

creating a function that only returns odd numbers [duplicate]

This question already has answers here:
How do I extract even elements of an Array?
(8 answers)
How to do a script for odd and even numbers from 1 to 1000 in Javascript?
(8 answers)
Closed 2 years ago.
I've spent an embarrassing amount of time on this question only to realize my function is only right 50% of the time. So the goal here is to return only the odd numbers of all the numbers in between the two arguments. (for instance if the arguments are 1 and 5 i'd need to return 2 & 3) the function I wrote is completely dependent on the first argument. if it's even my function will return odds, but if the first number is odd it'll return evens. does anyone know how i can fix this?
function oddNumbers(l, r) {
const arr = [];
const theEvens = [];
for (let i= l; i<r; i++) {
arr.push(i)
}
console.log(arr)
for (let i= 0; i < arr.length; i+= 2 ) {
const evens = arr[0] + i;
theEvens.push(evens);
}
theEvens.forEach(item => arr.splice(arr.indexOf(item), 1));
console.log(arr)
}
oddNumbers(2, 20);

I modified the code a bit to return only odd numbers
We use the % operator that behaves like the remainder operator in math:
so when we say i % 2 if the number is even the result of the operation will be 0
but when the "i" is an odd number the result will be 1
so now we can filter the even from the odd numbers using this operation
function oddNumbers(l, r) {
const arr = [];
for (let i= l; i<r; i++) {
if(i % 2 !== 0) arr.push(i);
}
console.log(arr);
}
oddNumbers(2, 20);

You can loop from initial to end parameters and get odd numbers using modulo, try this:
let result = [];
let returnOdd = (n1, n2) => {
for(i = n1; i < n2; i++){
if(i % 2 != 0){
result.push(i)
}
}
return result;
}
console.log(returnOdd(2, 20));

You could use the filter method.
This method creates a new array based on the condition it has. In this case it will to go through all the numbers in the array, and check if the number is odd (though the remainder operator).
For example:
1 % 2 = 1 ( true, keep in the new array )
2 % 2 = 0 ( false ignore in the new array )
function OddNumbers(start, end) {
// Create an array from the given range
const nums = Array(end - start + 1).fill().map((_, idx) => start + idx);
// Use filter to return the odd numbers via the % operator
return nums.filter(num => num % 2);
}
console.log(OddNumbers(2,20))

If statement involving modulo behaving erratically [duplicate]

This question already has answers here:
Looping through array and removing items, without breaking for loop
(17 answers)
Closed 2 years ago.
I'm making a function to create a list of prime numbers from 0 to num. I start off with a list of integers from 2 to num, and iterate over each one that goes from 2 to i < num; if at any point item % i === 0, the item is removed from the list. This works fine:
function getPrimes(num) {
// get list of ints from 2 to num
let primes = [...Array(num + 1).keys()];
primes = primes.splice(2);
let lastNumber = primes[primes.length - 1];
// make iterable, run its loop
// for each number in primes
for (let number of primes) {
// use iterable to remove if not prime
for (let i = 2; i < num; i++) {
if (number % i === 0) {
primes.splice(primes.indexOf(number), 1);
}
}
}
// add back two
primes.unshift(2);
return primes;
But when I try and make the iterable for each number only to up to Math.floor(num / 2) for the sake of efficiency, it breaks the code somehow:
function getPrimes(num) {
// get list of ints from 2 to num
let primes = [...Array(num + 1).keys()];
primes = primes.splice(2);
let lastNumber = primes[primes.length - 1];
// make iterable, run its loop
// for each number in primes
for (let number of primes) {
// use iterable to remove if not prime
for (let i = 2; i < Math.floor(num / 2); i++) {
if (number % i === 0) {
primes.splice(primes.indexOf(number), 1);
}
}
}
// add back two
primes.unshift(2);
return primes;
When I tried it out, getPrimes(10) gives me [ 2, 3, 5 ]. So seven is missing from the list of prime numbers from 0 to 10. Why is that? I checked and 7 modulo 2, 3, and 4 returns 1, 1, and 3, respectively. So why is the code in the loop running that removes 7 from primes? It's the only place in the code where I put that I wanted to remove a number from the array.

The first issue is that you are looping while removing items, which causes some items to be skipped. Loop backwards instead, so that only items that have already been checked are shifted. Second, num / 2 should be changed to Math.sqrt(number), as that is the maximum factor that needs to be checked before we can be sure that a number is prime. With this method, there is no need to add 2 back to the array.
function getPrimes(num) {
// get list of ints from 2 to num
let primes = [...Array(num + 1).keys()];
primes = primes.splice(2);
let lastNumber = primes[primes.length - 1];
// make iterable, run its loop
// for each number in primes
for(let i = primes.length - 1; i >= 0; i--){
let number = primes[i];
// use iterable to remove if not prime
for (let j = 2; j * j <= number; j++) {
if (number % j === 0) {
primes.splice(i, 1);
break;
}
}
}
return primes;
}
console.log(...getPrimes(10));

Permutations without recursive function call

Requirement: Algorithm to generate all possible combinations of a set , without duplicates , or recursively calling function to return results.
The majority , if not all of the Answers provided at Permutations in JavaScript? recursively call a function from within a loop or other function to return results.
Example of recursive function call within loop
function p(a, b, res) {
var b = b || [], res = res || [], len = a.length;
if (!len)
res.push(b)
else
for (var i = 0; i < len
// recursive call to `p` here
; p(a.slice(0, i).concat(a.slice(i + 1, len)), b.concat(a[i]), res)
, i++
);
return res
}
p(["a", "b", "c"]);
The current Question attempts to create the given permutation in a linear process , relying on the previous permutation.
For example , given an array
var arr = ["a", "b", "c"];
to determine the total number of possible permutations
for (var len = 1, i = k = arr.length; len < i ; k *= len++);
k should return 6 , or total number of possible permutations of arr ["a", "b", "c"]
With the total number of individual permutations determined for a set , the resulting array which would contain all six permutations could be created and filled using Array.prototype.slice() , Array.prototype.concat() and Array.prototype.reverse()
var res = new Array(new Array(k));
res[0] = arr;
res[1] = res[0].slice(0,1).concat(res[0].slice(-2).reverse());
res[2] = res[1].slice(-1).concat(res[1].slice(0,2));
res[3] = res[2].slice(0,1).concat(res[2].slice(-2).reverse());
res[4] = res[3].slice(-2).concat(res[3].slice(0,1));
res[5] = res[4].slice(0,1).concat(res[4].slice(-2).reverse());
Attempted to reproduce results based on the pattern displayed at the graph for An Ordered Lexicographic Permutation Algorithm based on one published in Practical Algorithms in C++ at Calculating Permutations and Job Interview Questions .
There appears to be a pattern that could be extended if the input set was , for example
["a", "b", "c", "d", "e"]
where 120 permutations would be expected.
An example of an attempt at filling array relying only on previous permutation
// returns duplicate entries at `j`
var arr = ["a", "b", "c", "d", "e"], j = [];
var i = k = arr.length;
arr.forEach(function(a, b, array) {
if (b > 1) {
k *= b;
if (b === i -1) {
for (var q = 0;j.length < k;q++) {
if (q === 0) {
j[q] = array;
} else {
j[q] = !(q % i)
? array.slice(q % i).reverse().concat(array.slice(0, q % i))
: array.slice(q % i).concat(array.slice(0, q % i));
}
}
}
}
})
however have not yet been able to make the necessary adjustments at parameters for .slice() , .concat() , .reverse() at above js to step from one permutation to the next ; while only using the previous array entry within res to determine current permutation , without using recursive.
Noticed even , odd balance of calls and tried to use modulus % operator and input array .length to either call .reverse() or not at ["a", "b", "c", "d", "e"] array , though did not produce results without duplicate entries.
The expected result is that the above pattern could be reduced to two lines called in succession for the duration of the process until all permutations completed, res filled ; one each for call to .reverse() , call without .reverse() ; e.g., after res[0] filled
// odd , how to adjust `.slice()` , `.concat()` parameters
// for array of unknown `n` `.length` ?
res[i] = res[i - 1].slice(0,1).concat(res[i - 1].slice(-2).reverse());
// even
res[i] = res[1 - 1].slice(-1).concat(res[i - 1].slice(0,2));
Question: What adjustments to above pattern are necessary , in particular parameters , or index , passed .slice() , .concat() to produce all possible permutations of a given set without using a recursive call to the currently processing function ?
var arr = ["a", "b", "c"];
for (var len = 1, i = k = arr.length; len < i; k *= len++);
var res = new Array(new Array(k));
res[0] = arr;
res[1] = res[0].slice(0, 1).concat(res[0].slice(-2).reverse());
res[2] = res[1].slice(-1).concat(res[1].slice(0, 2));
res[3] = res[2].slice(0, 1).concat(res[2].slice(-2).reverse());
res[4] = res[3].slice(-2).concat(res[3].slice(0, 1));
res[5] = res[4].slice(0, 1).concat(res[4].slice(-2).reverse());
console.log(res);
Edit, Update
Have found a process to utilize pattern described above to return permutations in lexicographic order for an input up to .length 4 , using a single for loop. Expected results are not returned for array with .length of 5.
The pattern is based on the second chart at "Calculating Permutations and Job Interview Questions"[0].
Would prefer not to use .splice() or .sort() to return results, though used here while attempting to adhere to last "rotate" requirement at each column. The variable r should reference the index of the first element of the next permutation, which it does.
The use of .splice() , .sort() could be included if their usage followed the pattern at the chart ; though at js below, they actually do not.
Not entirely certain that the issue with js below is only the statement following if (i % (total / len) === reset) , though that portion required the most investment of time; yet still does not return expected results.
Specifically, now referring to the chart, at rotating , for example 2 to index 0, 1 to index 2. Attempted to achieve this by using r , which is a negative index, to traverses from right to left to retrieve next item that should be positioned at index 0 of adjacent "column".
At next column, 2 would be placed at index 2 , 3 would be placed at index 0. This is portion, as far as have been able to grasp or debug, so far, is the area where error is occurring.
Again, returns expected results for [1,2,3,4], though not for [1,2,3,4,5]
var arr = [1, 2, 3, 4];
for (var l = 1, j = total = arr.length; l < j ; total *= l++);
for (var i = 1
, reset = 0
, idx = 0
, r = 0
, len = arr.length
, res = [arr]
; i < total; i++) {
// previous permutation
var prev = res[i - 1];
// if we are at permutation `6` here, or, completion of all
// permutations beginning with `1`;
// setting next "column", place `2` at `index` 0;
// following all permutations beginning with `2`, place `3` at
// `index` `0`; with same process for `3` to `4`
if (i % (total / len) === reset) {
r = --r % -(len);
var next = prev.slice(r);
if (r === -1) {
// first implementation used for setting item at index `-1`
// to `index` 0
// would prefer to use single process for all "rotations",
// instead of splitting into `if` , `else`, though not there, yet
res[i] = [next[0]].concat(prev.slice(0, 1), prev.slice(1, len - 1)
.reverse());
} else {
// workaround for "rotation" at from `index` `r` to `index` `0`
// the chart does not actually use the previous permutation here,
// but rather, the first permutation of that particular "column";
// here, using `r` `,i`, `len`, would be
// `res[i - (i - 1) % (total / len)]`
var curr = prev.slice();
// this may be useful, to retrieve `r`,
// `prev` without item at `r` `index`
curr.splice(prev.indexOf(next[0]), 1);
// this is not optiomal
curr.sort(function(a, b) {
return arr.indexOf(a) > arr.indexOf(b)
});
// place `next[0]` at `index` `0`
// place remainder of sorted array at `index` `1` - n
curr.splice(0, 0, next[0])
res[i] = curr
}
idx = reset;
} else {
if (i % 2) {
// odd
res[i] = prev.slice(0, len - 2).concat(prev.slice(-2)
.reverse())
} else {
// even
--idx
res[i] = prev.slice(0, len - (len - 1))
.concat(prev.slice(idx), prev.slice(1, len + (idx)))
}
}
}
// try with `arr` : `[1,2,3,4,5]` to return `res` that is not correct;
// how can above `js` be adjusted to return correct results for `[1,2,3,4,5]` ?
console.log(res, res.length)
Resources:
Generating Permutation with Javascript
(Countdown) QuickPerm Head Lexicography:
(Formally Example_03 ~ Palindromes)
Generating all Permutations [non-recursive]
(Attempt to port to from C++ to javascript jsfiddle http://jsfiddle.net/tvvvjf3p/)
Calculating Permutation without Recursion - Part 2
permutations of a string using iteration
iterative-permutation
Permutations by swapping
Evaluation of permutation algorithms
Permutation algorithm without recursion? Java
Non-recursive algorithm for full permutation with repetitive elements?
String permutations in Java (non-recursive)
Generating permutations lazily
How to generate all permutations of a list in Python
Can all permutations of a set or string be generated in O(n log n) time?
Finding the nth lexicographic permutation of ‘0123456789’
Combinations and Permutations

Here is a simple solution to compute the nth permutation of a string:
function string_nth_permutation(str, n) {
var len = str.length, i, f, res;
for (f = i = 1; i <= len; i++)
f *= i;
if (n >= 0 && n < f) {
for (res = ""; len > 0; len--) {
f /= len;
i = Math.floor(n / f);
n %= f;
res += str.charAt(i);
str = str.substring(0, i) + str.substring(i + 1);
}
}
return res;
}
The algorithm follows these simple steps:
first compute f = len!, there are factorial(len) total permutations of a set of len different elements.
as the first element, divide the permutation number by (len-1)! and chose the element at the resulting offset. There are (len-1)! different permutations that have any given element as their first element.
remove the chosen element from the set and use the remainder of the division as the permutation number to keep going.
perform these steps with the rest of the set, whose length is reduced by one.
This algorithm is very simple and has interesting properties:
It computes the n-th permutation directly.
If the set is ordered, the permutations are generated in lexicographical order.
It works even if set elements cannot be compared to one another, such as objects, arrays, functions...
Permutation number 0 is the set in the order given.
Permutation number factorial(a.length)-1 is the last one: the set a in reverse order.
Permutations outside this range are returned as undefined.
It can easily be converted to handle a set stored as an array:
function array_nth_permutation(a, n) {
var b = a.slice(); // copy of the set
var len = a.length; // length of the set
var res; // return value, undefined
var i, f;
// compute f = factorial(len)
for (f = i = 1; i <= len; i++)
f *= i;
// if the permutation number is within range
if (n >= 0 && n < f) {
// start with the empty set, loop for len elements
for (res = []; len > 0; len--) {
// determine the next element:
// there are f/len subsets for each possible element,
f /= len;
// a simple division gives the leading element index
i = Math.floor(n / f);
// alternately: i = (n - n % f) / f;
res.push(b.splice(i, 1)[0]);
// reduce n for the remaining subset:
// compute the remainder of the above division
n %= f;
// extract the i-th element from b and push it at the end of res
}
}
// return the permutated set or undefined if n is out of range
return res;
}
clarification:
f is first computed as factorial(len).
For each step, f is divided by len, giving exacty the previous factorial.
n divided by this new value of f gives the slot number among the len slots that have the same initial element. Javascript does not have integral division, we could use (n / f) ... 0) to convert the result of the division to its integral part but it introduces a limitation to sets of 12 elements. Math.floor(n / f) allows for sets of up to 18 elements. We could also use (n - n % f) / f, probably more efficient too.
n must be reduced to the permutation number within this slot, that is the remainder of the division n / f.
We could use i differently in the second loop, storing the division remainder, avoiding Math.floor() and the extra % operator. Here is an alternative for this loop that may be even less readable:
// start with the empty set, loop for len elements
for (res = []; len > 0; len--) {
i = n % (f /= len);
res.push(b.splice((n - i) / f, 1)[0]);
n = i;
}

I think this post should help you. The algorithm should be easily translatable to JavaScript (I think it is more than 70% already JavaScript-compatible).
slice and reverse are bad calls to use if you are after efficiency. The algorithm described in the post is following the most efficient implementation of the next_permutation function, that is even integrated in some programming languages (like C++ e.g.)
EDIT
As I iterated over the algorithm once again I think you can just remove the types of the variables and you should be good to go in JavaScript.
EDIT
JavaScript version:
function nextPermutation(array) {
// Find non-increasing suffix
var i = array.length - 1;
while (i > 0 && array[i - 1] >= array[i])
i--;
if (i <= 0)
return false;
// Find successor to pivot
var j = array.length - 1;
while (array[j] <= array[i - 1])
j--;
var temp = array[i - 1];
array[i - 1] = array[j];
array[j] = temp;
// Reverse suffix
j = array.length - 1;
while (i < j) {
temp = array[i];
array[i] = array[j];
array[j] = temp;
i++;
j--;
}
return true;
}

One method to create permutations is by adding each element in all of the spaces between elements in all of the results so far. This can be done without recursion using loops and a queue.
JavaScript code:
function ps(a){
var res = [[]];
for (var i=0; i<a.length; i++){
while(res[res.length-1].length == i){
var l = res.pop();
for (var j=0; j<=l.length; j++){
var copy = l.slice();
copy.splice(j,0,a[i]);
res.unshift(copy);
}
}
}
return res;
}
console.log(JSON.stringify(ps(['a','b','c','d'])));

Here could be another solution, inspired from the Steinhaus-Johnson-Trotter algorithm:
function p(input) {
var i, j, k, temp, base, current, outputs = [[input[0]]];
for (i = 1; i < input.length; i++) {
current = [];
for (j = 0; j < outputs.length; j++) {
base = outputs[j];
for (k = 0; k <= base.length; k++) {
temp = base.slice();
temp.splice(k, 0, input[i]);
current.push(temp);
}
}
outputs = current;
}
return outputs;
}
// call
var outputs = p(["a", "b", "c", "d"]);
for (var i = 0; i < outputs.length; i++) {
document.write(JSON.stringify(outputs[i]) + "<br />");
}

Here's a snippet for an approach that I came up with on my own, but naturally was also able to find it described elsewhere:
generatePermutations = function(arr) {
if (arr.length < 2) {
return arr.slice();
}
var factorial = [1];
for (var i = 1; i <= arr.length; i++) {
factorial.push(factorial[factorial.length - 1] * i);
}
var allPerms = [];
for (var permNumber = 0; permNumber < factorial[factorial.length - 1]; permNumber++) {
var unused = arr.slice();
var nextPerm = [];
while (unused.length) {
var nextIndex = Math.floor((permNumber % factorial[unused.length]) / factorial[unused.length - 1]);
nextPerm.push(unused[nextIndex]);
unused.splice(nextIndex, 1);
}
allPerms.push(nextPerm);
}
return allPerms;
};
Enter comma-separated string (e.g. a,b,c):
<br/>
<input id="arrInput" type="text" />
<br/>
<button onclick="perms.innerHTML = generatePermutations(arrInput.value.split(',')).join('<br/>')">
Generate permutations
</button>
<br/>
<div id="perms"></div>
Explanation
Since there are factorial(arr.length) permutations for a given array arr, each number between 0 and factorial(arr.length)-1 encodes a particular permutation. To unencode a permutation number, repeatedly remove elements from arr until there are no elements left. The exact index of which element to remove is given by the formula (permNumber % factorial(arr.length)) / factorial(arr.length-1). Other formulas could be used to determine the index to remove, as long as it preserves the one-to-one mapping between number and permutation.
Example
The following is how all permutations would be generated for the array (a,b,c,d):
# Perm 1st El 2nd El 3rd El 4th El
0 abcd (a,b,c,d)[0] (b,c,d)[0] (c,d)[0] (d)[0]
1 abdc (a,b,c,d)[0] (b,c,d)[0] (c,d)[1] (c)[0]
2 acbd (a,b,c,d)[0] (b,c,d)[1] (b,d)[0] (d)[0]
3 acdb (a,b,c,d)[0] (b,c,d)[1] (b,d)[1] (b)[0]
4 adbc (a,b,c,d)[0] (b,c,d)[2] (b,c)[0] (c)[0]
5 adcb (a,b,c,d)[0] (b,c,d)[2] (b,c)[1] (b)[0]
6 bacd (a,b,c,d)[1] (a,c,d)[0] (c,d)[0] (d)[0]
7 badc (a,b,c,d)[1] (a,c,d)[0] (c,d)[1] (c)[0]
8 bcad (a,b,c,d)[1] (a,c,d)[1] (a,d)[0] (d)[0]
9 bcda (a,b,c,d)[1] (a,c,d)[1] (a,d)[1] (a)[0]
10 bdac (a,b,c,d)[1] (a,c,d)[2] (a,c)[0] (c)[0]
11 bdca (a,b,c,d)[1] (a,c,d)[2] (a,c)[1] (a)[0]
12 cabd (a,b,c,d)[2] (a,b,d)[0] (b,d)[0] (d)[0]
13 cadb (a,b,c,d)[2] (a,b,d)[0] (b,d)[1] (b)[0]
14 cbad (a,b,c,d)[2] (a,b,d)[1] (a,d)[0] (d)[0]
15 cbda (a,b,c,d)[2] (a,b,d)[1] (a,d)[1] (a)[0]
16 cdab (a,b,c,d)[2] (a,b,d)[2] (a,b)[0] (b)[0]
17 cdba (a,b,c,d)[2] (a,b,d)[2] (a,b)[1] (a)[0]
18 dabc (a,b,c,d)[3] (a,b,c)[0] (b,c)[0] (c)[0]
19 dacb (a,b,c,d)[3] (a,b,c)[0] (b,c)[1] (b)[0]
20 dbac (a,b,c,d)[3] (a,b,c)[1] (a,c)[0] (c)[0]
21 dbca (a,b,c,d)[3] (a,b,c)[1] (a,c)[1] (a)[0]
22 dcab (a,b,c,d)[3] (a,b,c)[2] (a,b)[0] (b)[0]
23 dcba (a,b,c,d)[3] (a,b,c)[2] (a,b)[1] (a)[0]
Note that each permutation # is of the form:
(firstElIndex * 3!) + (secondElIndex * 2!) + (thirdElIndex * 1!) + (fourthElIndex * 0!)
which is basically the reverse process of the formula given in the explanation.

I dare to add another answer, aiming at answering you question regarding slice, concat, reverse.
The answer is it is possible (almost), but it would not be quite effective. What you are doing in your algorithm is the following:
Find the first inversion in the permutation array, right-to-left (inversion in this case defined as i and j where i < j and perm[i] > perm[j], indices given left-to-right)
place the bigger number of the inversion
concatenate the processed numbers in reversed order, which will be the same as sorted order, as no inversions were observed.
concatenate the second number of the inversion (still sorted in accordsnce with the previos number, as no inversions were observed)
This is mainly, what my first answer does, but in a bit more optimal manner.
Example
Consider the permutation 9,10, 11, 8, 7, 6, 5, 4 ,3,2,1
The first inversion right-to-left is 10, 11.
And really the next permutation is:
9,11,1,2,3,4,5,6,7,8,9,10=9concat(11)concat(rev(8,7,6,5,4,3,2,1))concat(10)
Source code
Here I include the source code as I envision it:
var nextPermutation = function(arr) {
for (var i = arr.length - 2; i >= 0; i--) {
if (arr[i] < arr[i + 1]) {
return arr.slice(0, i).concat([arr[i + 1]]).concat(arr.slice(i + 2).reverse()).concat([arr[i]]);
}
}
// return again the first permutation if calling next permutation on last.
return arr.reverse();
}
console.log(nextPermutation([9, 10, 11, 8, 7, 6, 5, 4, 3, 2, 1]));
console.log(nextPermutation([6, 5, 4, 3, 2, 1]));
console.log(nextPermutation([1, 2, 3, 4, 5, 6]));
The code is avaiable for jsfiddle here.

A fairly simple C++ code without recursion.
#include <vector>
#include <algorithm>
#include <iterator>
#include <iostream>
#include <string>
// Integer data
void print_all_permutations(std::vector<int> &data) {
std::stable_sort(std::begin(data), std::end(data));
do {
std::copy(data.begin(), data.end(), std::ostream_iterator<int>(std::cout, " ")), std::cout << '\n';
} while (std::next_permutation(std::begin(data), std::end(data)));
}
// Character data (string)
void print_all_permutations(std::string &data) {
std::stable_sort(std::begin(data), std::end(data));
do {
std::copy(data.begin(), data.end(), std::ostream_iterator<char>(std::cout, " ")), std::cout << '\n';
} while (std::next_permutation(std::begin(data), std::end(data)));
}
int main()
{
std::vector<int> v({1,2,3,4});
print_all_permutations(v);
std::string s("abcd");
print_all_permutations(s);
return 0;
}
We can find next permutation of a sequence in linear time.

Here is an answer from #le_m. It might be of help.
The following very efficient algorithm uses Heap's method to generate all permutations of N elements with runtime complexity in O(N!):
function permute(permutation) {
var length = permutation.length,
result = [permutation.slice()],
c = new Array(length).fill(0),
i = 1, k, p;
while (i < length) {
if (c[i] < i) {
k = i % 2 && c[i];
p = permutation[i];
permutation[i] = permutation[k];
permutation[k] = p;
++c[i];
i = 1;
result.push(permutation.slice());
} else {
c[i] = 0;
++i;
}
}
return result;
}
console.log(JSON.stringify(permute([1, 2, 3, 4])));

You can use a stack to go through permutations.
This approach is ideal when dealing with trees or other problems while not leaning on recursion.
You will need to make adjustments to not have any duplicate values.
type permutation = [string, string[]]
function p(str: string): string[]{
const res: string[] = []
const stack: permutation[] = [["", str.split('')]]
while(stack.length){
const [head, tail] = stack.pop()
if(!tail.length){
res.push(head)
continue
}
for(let i = 0; i < tail.length; i++){
let newTail = tail.slice()
newTail.splice(i, 1)
stack.push([head + tail[i], newTail])
}
}
return res
}

Coderbyte Array Addition Solution -- For Loop with a For Loop

I'm trying to understand the logic in a solution to the Array Addition CoderByte problem. Here is the question prompt -- "Using the JavaScript language, have the function ArrayAdditionI(arr) take the array of numbers stored in arr and return the string true if any combination of numbers in the array can be added up to equal the largest number in the array, otherwise return the string false. For example: if arr contains [4, 6, 23, 10, 1, 3] the output should return true because 4 + 6 + 10 + 3 = 23. The array will not be empty, will not contain all the same elements, and may contain negative numbers."
This is a solution that works, but I get lost with the for loop within the for loop. Why isn't it always the case that i = j since the for loops both start with their counters at 0. So wouldn't it always be 0 = 0?
function ArrayAdditionI(arr) {
arr.sort(function(a,b){return a - b})
var largest = arr.pop();
var sum = 0;
for (var i = 0; i < arr.length; i++){
sum += arr[i];
for (var j = 0; j < arr.length; j++){
if (i != j) {
sum += arr[j];
if (sum == largest) {
return true;
}
}
}
for (var k = 0; k < arr.length; k++) {
if (i != k) {
sum -= arr[k];
if (sum == largest) {
return true;
}
}
}
sum = 0;
}
// code goes here
return false;
}
Thanks!

i_made_that & user3085131:
To further explain the k loop, it is used to work back through and subtract array values in the order that they were initially added, to yield new results not otherwise obtainable.
Without the k loop you can't solve many potential arrays (although it will actually pass the coderbyte test cases due to lack of appropriate test).
Consider [1,2,3,98,100]...this should pass since 2+98 = 100. However it won't without the k loop. If you log the results of sum without the k, you would see:
3 (1 + 2)
6 (3 + 3)
104 (6 + 98)
3 (2 + 1)
6 (3 + 3)
104 (6 + 98)
4 (3 + 1)
6 (4 + 2)
104 (6 + 98)
99 (98 + 1)
101 (99 + 2)
104 (101 + 3)
With the k loop however, on the second iteration of i it will pass as it will subtract 1 from 104, and then 3 from 103 to reach 100.

The thing is, is that you have 2 for loops inside the for loop with the "i" variable.
variable "i" is always going to be 0 until you finish iterating thru the 2 for loops that are inside.
for(var i=0){
for(var j=0){}
for(var k=0){}
}