Project Euler Solution 9 Code Not Working - javascript

function getAnswer(){
var answer, c = 334;
while (c < 999){
var a = Math.round(((1000 - c) / 2) - 0.5), b = Math.round((1000 - c) / 2);
while (a > 0 && b < c){
if (Math.pow(a, 2) + Math.pow(b, 2) != Math.pow(c, 2)){
a -= 1;
b += 1;
}else{
answer = a * b * c;
}
}
c += 1;
}
document.getElementById("a").innerHTML = answer;
}
Hi! I am a beginner programmer in javascript, and I have been trying to solve problem 9 in Project Euler. That problem goes like this:
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
a^2 + b^2 = c^2
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
I don't know why no answer appears, and my script crashes/program stops running, whenever I run this script. Please explain and tell me what's wrong with my script.

When you have found the answer, you don't stop with the iteration. Even worse, you don't change the values of a and b any more, so they never reach the end of the iteration, and you're stuck in an infinite loop.
You'll need to break out of the loop when you've found the answer. Or even break out of both your nested loops, using a label:
function getAnswer() {
var answer,
c = 334;
find: while (c < 999) {
var a = Math.round(((1000 - c) / 2) - 0.5),
b = Math.round((1000 - c) / 2);
while (a > 0 && b < c) {
if (Math.pow(a, 2) + Math.pow(b, 2) == Math.pow(c, 2)) {
answer = a * b * c;
break find;
}
a -= 1;
b += 1;
}
c += 1;
}
document.getElementById("a").innerHTML = answer;
}
Notice that it would be easier if your function just returned the answer, instead of populating #a with it. You'd call it like
document.getElementById("a").innerHTML = getAnswer();
and can just return a * b * c; to break out of the whole function.

Related

Why does same javascript code give different result? [duplicate]

This question already has answers here:
How to add two strings as if they were numbers? [duplicate]
(20 answers)
Closed last year.
I am a beginner at javascript. I find following piece of code a bit difficult for me. I think both are same, and should have give the same result. But they are throwing different result.
var a = 5,
b = 6,
c = 7;
if (a + b > c || b + c > a || a + c > b) {
let s = (a + b + c) / 2;
let area = Math.sqrt(s * ((s - a) * (s - b) * (s - c)));
console.log(`The area of the triangle is: ${area}`);
} else {
console.log('Triangle does not exist');
}
It gives me a result. But when i try to take input from user and input the same value (5,6,7), find different result.
var a = prompt(),
b = prompt(),
c = prompt();
if (a + b > c || b + c > a || a + c > b) {
let s = (a + b + c) / 2;
let area = Math.sqrt(s * ((s - a) * (s - b) * (s - c)));
console.log(`The area of the triangle is: ${area}`);
} else {
console.log('Triangle does not exist');
}
Maybe I am wrong. But I just want know the reason.
Thanks.
My assumption is that this is related to prompt() returning a string and not an integer. Therefore the additions of the variables a, b and c would concatenate the strings and only after that - caused by the comparison > and after division / - convert it to a number. So in order to fix this, I think using parseInt() to parse the numbers returned from prompt() would fix the issue
The promt causes the variables to be defined as a string and as #Barmar pointed out in his comment, this changes the behavior of the '+' operation in your if-statement.
With numbers 1 +1 is returned as 2, with strings 11.
What you can do is change the following:
let s = (a + b + c) / 2;will give you 567/2 as you have strings.
let s = (parseInt(a) + parseInt(b) + parseInt(c) ) / 2; will give you the desired result as the method parseInt() returns a intger value.

How to convert this O(n^2) algorithm to O(n)?

https://www.codewars.com/kata/is-my-friend-cheating/train/javascript
My goal is to devise a function that finds number pairs (a, b) which satisfy the equation a * b == sum(1, 2, 3 ..., n-2, n-1, n) - a - b.
The following code finds all the pairs, but is too slow and times out. I have seen in the comments for this challenge that the algorithm needs to have O(n) complexity to pass. How is this done?
function removeNb (n) {
if(n===1) return null;
let sum = (n * (n+1))/2;
let retArr = [];
let a = n;
while( a !== 0){
let b = n;
while( b !== 0){
if(b != a && a*b == ((sum - b) - a) ){
retArr.push([a,b]);
}
b--;
}
a--;
}
retArr.sort( (a,b) => a[0] - b[0]);
return retArr;
}
Thanks to all for the assistance! Here is my final solution:
function removeNb (n) {
let retArr = [];
let a = 1;
let b = 0;
let sumN = (n * (n+1))/2;
while( a <= n){
b = parseInt((sumN - a) / (a + 1));
if( b < n && a*b == ((sumN - b) - a) )
retArr.push([a,b]);
a++;
}
return retArr;
}
I think my main issue was an (embarrassing) error with my algebra when I attempted to solve for b. Here are the proper steps for anyone wondering:
a*b = sum(1 to n) - a - b
ab + b = sumN - a
b(a + 1) = sumN - a
b = (sumN - a) / (a + 1)
You can solve for b and get: b = (sum - a)/(a + 1) (given a != -1)
Now iterate over a once -> O(n)
let n = 100;
let sumOfNum = n => {
return (n * (n + 1)) / 2;
};
let sum = sumOfNum(n);
let response = [];
for (let i = 1; i <= 26; i++) {
let s = (sum - i) / (i + 1);
if (s % 1 == 0 && s * i == sum - s - i && s <= n) {
response.push([s, i]);
}
}
// this is O(N) time complexity
Here's an implementation:
function removeNb(n){
var sum = (1 + n) * n / 2;
var candidates = [];
// O(n)
for(var y = n; y >= 1; y--){
x = (-y + sum) / (y + 1);
/*
* Since there are infinite real solutions,
* we only record the integer solutions that
* are 1 <= x <= n.
*/
if(x % 1 == 0 && 1 <= x && x <= n)
// Assuming .push is O(1)
candidates.push([x, y]);
}
// Output is guaranteed to be sorted because
// y is iterated from large to small.
return candidates;
}
console.log(removeNb(26));
console.log(removeNb(100));
https://jsfiddle.net/DerekL/anx2ox49/
From your question, it also states that
Within that sequence, he chooses two numbers, a and b.
However it does not mention that a and b are unique numbers, so a check is not included in the code.
As explained in other answers, it is possible to make a O(n) algorithm solving for b. Moreover, given the symmetry of solution -- if (a,b) is a solution, also (b,a) is -- it is also possible to save some iterations adding a couple of solutions at a time. To know how many iterations are required, let us note that b > a if and only if a < -1+sqrt(1+sum). To prove it:
(sum-a)/(a+1) > a ; sum-a > a^2+a ; sum > a^2+2a ; a^2+2a-sum < 0 ; a_1 < a < a_2
where a_1 and a_2 comes from 2-degree equation solution:
a_1 = -1-sqrt(1+sum) ; a_2 = -1+sqrt(1+sum)
Since a_1 < 0 and a > 0, finally we proved that b > a if and only if a < a_2.
Therefore we can avoid iterations after -1+sqrt(1+sum).
A working example:
function removeNb (n) {
if(n===1) return null;
let sum = (n * (n+1))/2;
let retArr = [];
for(let a=1;a<Math.round(Math.sqrt(1+sum));++a) {
if((sum-a)%(a+1)===0) {
let b=(sum-a)/(a+1);
if(a!==b && b<=n) retArr.push([a,b],[b,a]);
}
}
retArr.sort( (a,b) => a[0] - b[0]);
return retArr;
}
However, with this implementation we still need the final sort. To avoid it, we can note that b=(sum-a)/(a+1) is a decreasing function of a (derive it to prove). Therefore we can build retArr concatenating two arrays, one adding elements to the end (push), one adding elements at the beginning (unshift). A working example follows:
function removeNb (n) {
if(n===1) return null;
let sum = (n * (n+1))/2;
let retArr = [];
let retArr2 = [];
for(let a=1;a<Math.round(Math.sqrt(1+sum));++a) {
if((sum-a)%(a+1)===0) {
let b=(sum-a)/(a+1);
if(a!==b && b<=n) {
retArr.push([a,b]);
retArr2.unshift([b,a]); // b>a and b decreases with a
}
}
}
retArr=retArr.concat(retArr2); // the final array is ordered in the 1st component
return retArr;
}
As a non-native speaker, I would say that the phrase from the reference "all (a, b) which are the possible removed numbers in the sequence 1 to n" implies a!=b,
so I added this constraint.

Can't get BBP formula to work in nodejs

I've been trying to make a little program that can compute the n-th digit of pi.
After a few searches I've found that the most common formula is the BBP formula, wich is n-th digit = 16^-n[4/(8n + 1)-2/(8n + 4)-1/(8n + 5)-1/(8n + 6)].
The output is in base 16.
My code is the following:
function run(n) {
return Math.pow(16, -n) * (4 / (8 * n + 1) - 2 / (8 * n + 4) - 1 / (8 * n + 5) - 1 / (8 * n + 6));
}
function convertFromBaseToBase(str, fromBase, toBase) {
var num = parseInt(str, fromBase);
return num.toString(toBase);
}
for (var i = 0; i < 10; i++) {
var a = run(i);
console.log(convertFromBaseToBase(a, 16, 10));
}
So far, my output is the following:
1:3
2:0
3:0
4:0
5:1
6:7
7:3
8:1
9:7
10:3
Obviously, these are not the 10 first digits of PI.
My understanding is that values get rounded too often and that causes huge innacuracy in the final result.
However, I could be wrong, that's why I'm here to ask if I did anything wrong or if it's nodejs's fault. So I would loove if one of you guys have the answer to my problem!
Thanks!!
Unfortunately, 4/(8n + 1) - 2/(8n + 4) - 1/(8n + 5) - 1/(8n + 6) does not directly return the Nth hexadecimal digit of pi. I don't blame you, I made the same assumption at first. Although all the terms do indeed sum to pi, each individual term does not represent an individual hexadecimal digit. As seen here, the algorithm must be rewritten slightly in order to function correctly as a "digit spigot". Here is what your new run implementation ought to look like:
/**
Bailey-Borwein-Plouffe digit-extraction algorithm for pi
<https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula#BBP_digit-extraction_algorithm_for_.CF.80>
*/
function run(n) {
var partial = function(d, c) {
var sum = 0;
// Left sum
var k;
for (k = 0; k <= d - 1; k++) {
sum += (Math.pow(16, d - 1 - k) % (8 * k + c)) / (8 * k + c);
}
// Right sum. This converges fast...
var prev = undefined;
for(k = d; sum !== prev; k++) {
prev = sum;
sum += Math.pow(16, d - 1 - k) / (8 * k + c);
}
return sum;
};
/**
JavaScript's modulus operator gives the wrong
result for negative numbers. E.g. `-2.9 % 1`
returns -0.9, the correct result is 0.1.
*/
var mod1 = function(x) {
return x < 0 ? 1 - (-x % 1) : x % 1;
};
var s = 0;
s += 4 * partial(n, 1);
s += -2 * partial(n, 4);
s += -1 * partial(n, 5);
s += -1 * partial(n, 6);
s = mod1(s);
return Math.floor(s * 16);
}
// Pi in hex is 3.243f6a8885a308d313198a2e037073...
console.log(run(0) === 3); // 0th hexadecimal digit of pi is the leading 3
console.log(run(1) === 2);
console.log(run(2) === 4);
console.log(run(3) === 3);
console.log(run(4) === 15); // i.e. "F"
Additionally, your convertFromBaseToBase function is more complicated than it needs to be. You have written it to accept a string in a specific base, but it is already being passed a number (which has no specific base). All you should really need is:
for (var i = 0; i < 10; i++) {
var a = run(i);
console.log(a.toString(16));
}
Output:
3
2
4
3
f
6
a
8
8
8
I have tested this code for the first 30 hexadecimal digits of pi, but it might start to return inaccurate results once Math.pow(16, d - 1 - k) grows beyond Number.MAX_SAFE_INTEGER, or maybe earlier for other reasons. At that point you may need to implement the modular exponentiation technique suggested in the Wikipedia article.

algorithm connect four javascript

Hy,
I am trying to implement an Connect Four Game in javascript / jQuery. First off this is no homework or any other duty. I'm just trying to push my abilities.
My "playground" is a simple html table which has 7 rows and 6 columns.
But now I have reached my ken. I'm stuck with the main functionality of checking whether there are 4 same td's around. I am adding a class to determine which color it should represent in the game.
First I thought I could handle this with .nextAll() and .prevAll() but this does not work for me because there is no detection between.
Because I was searching for siblings, when adding a new Item and just looked up the length of siblings which were found and if they matched 4 in the end I supposed this was right, but no its not :D Is there maybe any kind of directNext() which provides all next with a css selector until something different comes up ?
I will put all of my code into this jsfiddle: http://jsfiddle.net/LcUVf/5/
Maybe somebody has ever tried the same or someone comes up with a good idea I'm not asking anybody to do or finish my code. I just want to get hints for implementing such an algorithm or examples how it could be solved !
Thanks in anyway !
DOM traversal is not particularly efficient so, when you can avoid it, I'd recommend doing so. It'd make sense for you to build this as a 2D array to store and update the state of the game. The table would only be a visual representation of the array.
I know that, normally, you would build the array with rows as the first dimension and columns as the second dimension but, for the purposes of being able to add pieces to each column's "stack," I would make the first dimension the columns and the second dimension the rows.
To do the check, take a look at this fiddle I made:
http://jsfiddle.net/Koviko/4dTyw/
There are 4 directions to check: North-South, East-West, Northeast-Southwest, and Southeast-Northwest. This can be represented as objects with the delta defined for X and Y:
directions = [
{ x: 0, y: 1 }, // North-South
{ x: 1, y: 0 }, // East-West
{ x: 1, y: 1 }, // Northeast-Southwest
{ x: 1, y: -1 } // Southeast-Northwest
];
Then, loop through that object and loop through your "table" starting at the farthest bounds that this piece can possibly contribute to a win. So, since you need 4 pieces in a row, the currently placed piece can contribute in a win for up to 3 pieces in any direction.
minX = Math.min(Math.max(placedX - (3 * directions[i].x), 0), pieces.length - 1);
minY = Math.min(Math.max(placedY - (3 * directions[i].y), 0), pieces[0].length - 1);
maxX = Math.max(Math.min(placedX + (3 * directions[i].x), pieces.length - 1), 0);
maxY = Math.max(Math.min(placedY + (3 * directions[i].y), pieces[0].length - 1), 0);
To avoid any issues with less-than and greater-than (which I ran into), calculate the number of steps before looping through your pieces instead of using the calculated bounds as your conditions.
steps = Math.max(Math.abs(maxX - minX), Math.abs(maxY - minY));
Finally, loop through the items keeping a count of consecutive pieces that match the piece that was placed last.
function isVictory(pieces, placedX, placedY) {
var i, j, x, y, maxX, maxY, steps, count = 0,
directions = [
{ x: 0, y: 1 }, // North-South
{ x: 1, y: 0 }, // East-West
{ x: 1, y: 1 }, // Northeast-Southwest
{ x: 1, y: -1 } // Southeast-Northwest
];
// Check all directions
outerloop:
for (i = 0; i < directions.length; i++, count = 0) {
// Set up bounds to go 3 pieces forward and backward
x = Math.min(Math.max(placedX - (3 * directions[i].x), 0), pieces.length - 1);
y = Math.min(Math.max(placedY - (3 * directions[i].y), 0), pieces[0].length - 1);
maxX = Math.max(Math.min(placedX + (3 * directions[i].x), pieces.length - 1), 0);
maxY = Math.max(Math.min(placedY + (3 * directions[i].y), pieces[0].length - 1), 0);
steps = Math.max(Math.abs(maxX - x), Math.abs(maxY - y));
for (j = 0; j < steps; j++, x += directions[i].x, y += directions[i].y) {
if (pieces[x][y] == pieces[placedX][placedY]) {
// Increase count
if (++count >= 4) {
break outerloop;
}
} else {
// Reset count
count = 0;
}
}
}
return count >= 4;
}
I released a fully working version of the game on Github.
It implements an optimised variation on the algorythm Sirko mentioned.
To avoid any unnecessary redunancy, the algorythm directly checks the DOM rather than a JS table. As that algorythm requires a minimum amount of checks, the performance overhead for accessing the DOM is neglectable.
The current player and a flag for keeping track of whether the game has ended are basicly the only statuses stored in the JS itself.
I even used the DOM to store strings. It has no external dependencies and is supported by all versions of IE from IE6 upwards as well as modern browsers.
Code is optimised for filesize and performance. The latest version also includes animation, even though the total JS code of the game is still only 1.216 bytes after minification.
The Code :
Here's the full, un-minified JS code :
(function (doc, win, onclick, gid, classname, content, showMessage) {
var
a, b, c, colorLabel, cid, players, current, finished, newgameLabel, wonLabel, laststart = 1,
cellAt = function (i, j) {
return doc[gid](cid + i + j);
},
isCurrentColor = function (i, j) {
return cellAt(i, j)[classname] === players[current];
},
start = function () {
current = laststart = (laststart + 1) % 2;
finished = 0;
colorLabel[content] = colorLabel[classname] = players[current = (current + 1) % 2];
for (a = 1; a < 7; a++)
for (b = 1; b < 8; b++)
cellAt(a, b)[classname] = '';
},
makeMove = function (i, j, s) {
s > 0 && (cellAt(s, j)[classname] = '');
cellAt(s + 1, j)[classname] = players[current];
s === i - 1 ? function (i, j) {
return function (i, j) {
for (a = j - 1; 0 < a && isCurrentColor(i, a); a--) {
}
for (b = j + 1; 8 > b && isCurrentColor(i, b); b++) {
}
return 4 < b - a;
}(i, j) || function (i, j) {
for (c = i + 1; 7 > c && isCurrentColor(c, j); c++) {
}
return 3 < c - i;
}(i, j) || function (i, j) {
for (a = i - 1, b = j - 1; 0 < a && !(1 > b) && isCurrentColor(a, b); a--)
b--;
for (c = i + 1, b = j + 1; 7 > c && !(7 < b) && isCurrentColor(c, b); c++)
b++;
return 4 < c - a
}(i, j) || function (i, j) {
for (a = i - 1, b = j + 1; 0 < a && !(7 < b) && isCurrentColor(a, b); a--)
b++;
for (c = i + 1, b = j - 1; 7 > c && !(1 > b) && isCurrentColor(c, b); c++)
b--;
return 4 < c - a;
}(i, j);
}(i, j)
? finished = 1 && win[showMessage](doc[gid](wonLabel)[content].replace("%s", players[current].toLowerCase())) && start()
: colorLabel[content] = colorLabel[classname] = players[current = (current + 1) % 2]
: setTimeout(function () {
makeMove(i, j, s + 1)
}, 20);
};
return function (n, w, c, h, p1, p2) {
cid = c;
newgameLabel = n;
wonLabel = w;
colorLabel = doc[gid](c);
players = [doc[gid](p1)[content], doc[gid](p2)[content]];
for (a = 1; a < 7; a++)
for (b = 1; b < 8; b++)
cellAt(a, b)[onclick] = function (b, a) {
return function () {
if (!finished)
for (a = 6; a > 0; a--)
if (!cellAt(a, b)[classname]) {
makeMove(a, b, 0);
break;
}
};
}(b);
;
doc[gid](h)[onclick] = function () {
win[showMessage](doc[gid](newgameLabel)[content]) && start()
};
start();
};
})(document, window, "onclick", "getElementById", "className", "innerHTML", "confirm")("newgame", "won", "color", "restart", "p1", "p2");
A screenshot :
In general a 2dimensional array would be better suited for checking for a line of 4. You could then do something like the following:
function check( lastPiece, playground, player ) {
// check length in each direction
var l = 1,
i = 1;
// top to bottom
while( (playground[ lastPiece.x ][ lastPiece.y - i ] === player) && ((lastPiece.y - i) >= 0) ) { l += 1; i += 1; };
i = 1;
while( (playground[ lastPiece.x ][ lastPiece.y + i ] === player) && ((lastPiece.y + i) <= MAX_Y) ) { l += 1; i += 1; };
if ( l >= 4 ) { return true; }
// left to right
l = 1;
while( (playground[ lastPiece.x - i][ lastPiece.y ] === player) && ((lastPiece.x - i) >= 0) ) { l += 1; i += 1; };
i = 1;
while( (playground[ lastPiece.x + i][ lastPiece.y ] === player) && ((lastPiece.x + i) <= MAX_X) ) { l += 1; i += 1; };
if ( l >= 4 ) { return true; }
// same for top left to bottom right and bottom left to top right
// . . .
// if we got no hit until here, there is no row of 4
return false;
}
EDIT: added checks for borders of the playground

Strange off-by-one issue with snippet to generate gradients

I use my own library for a lot of stuff, and recently I decided to add gradient functionality, but I've encountered a problem that I seem to remember having a while ago also, and this is the matter of my gradient being slightly off near the end. First, the code in question:
gradient = function(l, g)
{
var r = [], s = [], f = g.length - 1;
for (var x = 0; x < g.length; x++)
g[x] = (typeof(g[x]) == 'string' ? g[x] : g[x].join(','))._replace(['#', ' ', 'rgb(', ')'], ''),
g[x] = (g[x].indexOf(',') != -1
? g[x].split(',')
: g[x].chunk(2).map(function(_)
{
return _.fromBase('hex');
}));
for (var x = 0; x < f; x++)
s[x] = [(g[x][0] - g[x + 1][0]) / (l - 1) * f, (g[x][1] - g[x + 1][2]) / (l - 1) * f, (g[x][2] - g[x + 1][2]) / (l - 1) * f];
for (var x = 0; x < l; x++)
r[x] = '', ([0, 1, 2]).map(function(_)
{
var c = Math.floor(x / (l / (g.length - 1)));
r[x] += (g[c][_] - s[c][_] * (x - (l / (g.length - 1)) * c)).toBase('hex').pad('0', 2);
});
return r;
};
And, of course, my library: http://wimg.co.uk/HJ0X8B.js
Have fun in there! : ) If you think you might be able to help in any way at all, the custom functions I use in the gradient snippet are _replace(), chunk(), map(), and toBase() and fromBase()... as you'll be able to see at this demo page, everything pretty much works (at least in Opera and Firefox) save for the gradient being ever so slightly off at the end (hover to be shown the hex value). For example, calling gradient(50, ['ffffff', 'ffff00', '00ff00']) does indeed create an array of length fifty that contains hexadecimal color values gradually shifting from red to yellow and then to lime, however the last color isn't exactly lime (in this case, it comes out 05ff00); this means that there's something slightly off in the mathematics and not the methodology.
So... anybody willing to wade through the jungle that is the code I find so strangely beautiful to help me arrive at a solution? All assistance is greatly appreciated.
gradient = function(l, g)
{
var r = [], s = [], f = g.length - 1;
for (var x = 0; x < g.length; x++)
g[x] = (typeof(g[x]) == 'string' ? g[x] : g[x].join(','))._replace(['#', ' ', 'rgb(', ')'], ''),
g[x] = (g[x].indexOf(',') != -1
? g[x].split(',')
: g[x].chunk(2).map(function(_)
{
return _.fromBase('hex');
}));
for (var x = 0; x < f; x++)
s[x] = [(g[x][0] - g[x + 1][0]) / (l - 1) * f, (g[x][1] - g[x + 1][1]) / (l - 1) * f, (g[x][2] - g[x + 1][2]) / (l - 1) * f];
for (var x = 0; x < l; x++)
r[x] = '', ([0, 1, 2]).map(function(_)
{
var c = Math.floor(x / (l / (g.length - 1)));
r[x] += (g[c][_] - s[c][_] * (x - ((l-1) / (g.length - 1)) * c)).toBase('hex').pad('0', 2);
});
return r;
};
Use (l-1) instead of l on the last calculation line since you have prepared the s array for l-1 steps not l.
BTW your code is really hard to understand, try to write more understandable and standart code. And do write for loops instead of [0, 1, 2].map(sth).

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