Exponential growth one-liner function fails on one test but not others? - javascript

Can anyone debug this for me? I've been staring at it and testing things for hours but can't seem to get it working. I'm starting to wonder whether the coding challenge web app is wrong and I'm right!
The task is this:
Find the number of generations it would take for a population p0 to surpass a max population p given that the population increases by percent% plus aug every generation
My one-liner is as follows:
nbYear = (p0, percent, aug, p) => {
return Array(999).fill().filter((_,i)=>Array(i+1).fill().map((_,j)=>j==0?p0:0).reduce((y,_)=>Math.round(y*percent/100+y+aug))<=p).length;
}
The code I've written passes on 100 tests but fails on one in particular (they don't disclose the input paramters on which it failed). All it says is that the function gave the output: 51 when it should have been 50

I've concluded that the one test for which it failed must have been for a value over 999.

Related

Trying to write a basic script for a Google Sheets that will count total missed minutes by late students

I am (VERY) new to Apps Script and JS generally. I am trying to write a script that will automatically tally the difference between student entry time and start time of a course to deliver total minutes missed.
I have been able to get a function working that can do this for a single cell value, but am having trouble iterating it across a range. Doubtless this is due to a fundamental misunderstanding I have about the for loop I am using, but I am not sure where to look for more detailed information.
Any and all advice is appreciated. Please keep in mind my extreme "beginner status".
I have tried declaring a blank variable and adding multiple results of previously written single-cell functions to that total, but it is returning 0 regardless of given information.
I am including all three of the functions below, the idea is that each will do one part of the overall task.
function LATENESS (entry,start) {
return (entry-start)/60000
}
function MISSEDMINUTES(studenttime,starttime) {
const time = studenttime;
const begin = starttime;
if (time=="Present") {
return 0
} else if (time=="Absent") {
return 90
} else {
return LATENESS(time,begin)
}
}
function TOTALMISSED(range,begintime) {
var total = 0
for (let i = 0; i < range.length; i++) {
total = total + MISSEDMINUTES(i,begintime)
}
}```
If you slightly tweak your layout to have the 'missing minutes' column immediately adjacent to the column of names, you can have a single formula which will calculate the missing minutes for any number of students over any number of days:
Name
*
2/6
2/7
2/8
2/9
John Smith
-
Present
Present
Absent
10:06
Lucy Jenkins
-
Absent
Absent
Absent
Absent
Darren Polter
-
Present
Present
Present
10:01
With 'Name' present in A1, add the following to cell B1 (where I've marked an asterisk):
={"mins missed";
byrow(map(
C2:index(C2:ZZZ,counta(A2:A),counta(C1:1)),
lambda(x,switch(x,"Present",0,"Absent",90,,0,1440*(x-timevalue("10:00"))))),
lambda(row,sum(row)))}
We are MAPping a minute value onto each entry in the table (where 'Present'=0, 'Absent'=90 & a time entry = the number of minutes difference between then and 10am), then summing BYROW.
Updated
Based on the example, you could probably have a formula like the below one to conduct your summation:
=Sum(ARRAYFORMULA(if(B2:E2="Absent",90,if(isnumber(B2:E2),(B2:E2-$K$1)*60*24,0))))
Note that k1 has the start time of 10:00. Same sample sheet has working example.
Original Answer
I'm pretty sure you could do what you want with regular sheets formulas. Here'a sample sheet that shows how to get the difference in two times in minutes and seconds... Along with accounting for absent.
Here's the formula used that will update with new entries.
=Filter({if(B2:B="Absent",90*60,Round((C2:C-B2:B)*3600*24,0)),if(B2:B="Absent",90,Round((C2:C-B2:B)*3600*24/60,1))},(B2:B<>""))
This example might not solve all your issues, but from what I'm seeing, there's no need to be using an app script. If this doesn't cover it, post some sample data using Mark down table.

How to generically solve the problem of generating incremental integer IDs in JavaScript

I have been thinking about this for a few days trying to see if there is a generic way to write this function so that you don't ever need to worry about it breaking again. That is, it is as robust as it can be, and it can support using up all of the memory efficiently and effectively (in JavaScript).
So the question is about a basic thing. Often times when you create objects in JavaScript of a certain type, you might give them an ID. In the browser, for example with virtual DOM elements, you might just give them a globally unique ID (GUID) and set it to an incrementing integer.
GUID = 1
let a = createNode() // { id: 1 }
let b = createNode() // { id: 2 }
let c = createNode() // { id: 3 }
function createNode() {
return { id: GUID++ }
}
But what happens when you run out of integers? Number.MAX_SAFE_INTEGER == 2⁵³ - 1. That is obviously a very large number: 9,007,199,254,740,991 quadrillions perhaps. Many billions of billions. But if JS can reach 10 million ops per second lets say in a pick of the hat way, then that is about 900,719,925s to reach that number, or 10416 days, or about 30 years. So in this case if you left your computer running for 30 years, it would eventually run out of incrementing IDs. This would be a hard bug to find!!!
If you parallelized the generation of the IDs, then you could more realistically (more quickly) run out of the incremented integers. Assuming you don't want to use a GUID scheme.
Given the memory limits of computers, you can only create a certain number of objects. In JS you probably can't create more than a few billion.
But my question is, as a theoretical exercise, how can you solve this problem of generating the incremented integers such that if you got up to Number.MAX_SAFE_INTEGER, you would cycle back from the beginning, yet not use the potentially billions (or just millions) that you already have "live and bound". What sort of scheme would you have to use to make it so you could simply cycle through the integers and always know you have a free one available?
function getNextID() {
if (i++ > Number.MAX_SAFE_INTEGER) {
return i = 0
} else {
return i
}
}
Random notes:
The fastest overall was Chrome 11 (under 2 sec per billion iterations, or at most 4 CPU cycles per iteration); the slowest was IE8 (about 55 sec per billion iterations, or over 100 CPU cycles per iteration).
Basically, this question stems from the fact that our typical "practical" solutions will break in the super-edge case of running into Number.MAX_SAFE_INTEGER, which is very hard to test. I would like to know some ways where you could solve for that, without just erroring out in some way.
But what happens when you run out of integers?
You won't. Ever.
But if JS can reach 10 million ops per second [it'll take] about 30 years.
Not much to add. No computer will run for 30 years on the same program. Also in this very contrived example you only generate ids. In a realistic calculation you might spend 1/10000 of the time to generate ids, so the 30 years turn into 300000 years.
how can you solve this problem of generating the incremented integers such that if you got up to Number.MAX_SAFE_INTEGER, you would cycle back from the beginning,
If you "cycle back from the beginning", they won't be "incremental" anymore. One of your requirements cannot be fullfilled.
If you parallelized the generation of the IDs, then you could more realistically (more quickly) run out of the incremented integers.
No. For the ids to be strictly incremental, you have to share a counter between these parallelized agents. And access to shared memory is only possible through synchronization, so that won't be faster at all.
If you still really think that you'll run out of 52bit, use BigInts. Or Symbols, depending on your usecase.

I successfully compiled my program. Now how do I run it?

I want to solve Project Euler Problem 1:
If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.
Here's my code:
\documentclass[10pt,a4paper]{article}
\usepackage{hyperref}
\newcommand*\rfrac[2]{{}^{#1}\!/_{#2}}
\title{Solution to Project Euler Problem 1}
\author{Aadit M Shah}
\begin{document}
\maketitle
We want to find the sum of all the multiples of 3 or 5 below 1000. We can use the formula of the $n^{th}$ triangular number\footnote{\url{http://en.wikipedia.org/wiki/Triangular_number}} to calculate the sum of all the multiples of a number $m$ below 1000. The formula of the $n^{th}$ triangular number is:
\begin{equation}
T_n = \sum_{k = 1}^n k = 1 + 2 + 3 + \ldots + n = \frac{n (n + 1)}{2}
\end{equation}
If the last multiple of $m$ below 1000 is $x$ then $n = \rfrac{x}{m}$. The sum of all the multiples of $m$ below 1000 is therefore:
\begin{equation}
m \times T_{\frac{x}{m}} = m \times \sum_{k = 1}^{\frac{x}{m}} k = \frac{x (\frac{x}{m} + 1)}{2}
\end{equation}
Thus the sum of all the multiples of 3 or 5 below 1000 is equal to:
\begin{equation}
3 \times T_{\frac{999}{3}} + 5 \times T_{\frac{995}{5}} - 15 \times T_{\frac{990}{15}} = \frac{999 \times 334 + 995 \times 200 - 990 \times 67}{2}
\end{equation}
\end{document}
I compiled it successfully using pdflatex:
$ pdflatex Problem1.tex
This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2014/Arch Linux) (preloaded format=pdflatex)
.
.
.
Output written on Problem1.pdf (1 page, 106212 bytes).
Transcript written on Problem1.log.
It generated the following output PDF file along with a bunch of other files with scary extensions:
How do I run this PDF file so that it computes the solution? I know the solution to the problem but I want to know how to execute the PDF file to compute the solution.
The reason why I prefer LaTeX over other programming languages is because it supports literate programming, an approach to programming introduced by Donald Knuth, the creator of TeX and one of the greatest computer scientists of all time.
Edit: It would also be nice to be able to print the computed solution either on the screen or on paper. Computing the solution without printing it is useful for heating the room but it is so hot already with the onset of summer and global warming. In addition, printing the solution would teach me how to write a hello world program in LaTeX.
So, today seems to be a safe day to tackle this problem...
The OP does not seem to be quite so PDF-savvy.
However, he obviously is quite a literate LaTeX guy.
Which means, he also must be knowing TeX very well, given he is so much of a Donald Knuth admirer...
So much for the preliminaries.
Now for the real meat.
First, to quote the official PDF-1.7 specification document:
PDF is not a programming language, and a PDF file is not a program.
(p. 92, Section 7.10.1)
However, the pre-decessor of the PDF format, PostScript, IS a Turing-complete programming language... Turing-complete, just as TeX is, the creation of Donald Knuth, one of the greatest computer scientists of all time.
PostScript files, on the other hand, ARE programs, and can easily be executed by PostScript printers (though this execution time cannot reliably be determined in advance).
Hence, and second, the OP should be able to find a way to convert his hi-level LaTeX code to low-level TeX code.
That code needs to emit a PostScript program, which in turn can be executed by a PostScript printer.
Writing that TeX code should be trivial for somebody like the OP, once he is given the PostScript code that should be the result of his TeX code.
I myself am not so well-versed with the TeX aspect of that problem solving procedure.
However, I can help with the PostScript.
The PostScript which the OP's TeX code should produce goes like this (there are for sure more optimized versions possible -- this is only a first, quick'n'dirty shot at it):
%!PS
% define variables
/n1 999 def
/t1 334 def
/n2 995 def
/t2 200 def
/n3 990 def
/s1 67 def
/t3 2 def
% run the computational code
n1 t1 mul
n2 t2 mul
n3 s1 mul
sub
add
t3 div
% print result on printer, not on <stdout>
/Helvetica findfont
24 scalefont
setfont
30 500 moveto
(Result for 'Project Euler Problem No. 1' :) show
/Helvetica-Bold findfont
48 scalefont
setfont
80 400 moveto
( ) cvs show
showpage
Send this PostScript code to a PostScript printer, and it will compute and print the solution.
Update
To answer one of the comments: If you replace the last section of PostScript code starting with /Helvetica findfont with a simple print statement, it will not do what you might imagine.
print does not cause the printer to output paper. Instead it asks the PostScript interpreter to write the topmost item on the stack (which must be a (string)!) to the standard output channel. (If the topmost item on the stack is not of type (string), it will trigger a typecheck PostScript error.)
So sending a modified PostScript file (where print has replaced the last section of my PS code) to the printer will not work (unless that printer supports the interactive executive PostScript mode -- which is not a standard part of the PostScript language). It will work however if you feed that file to Ghostscript in a terminal or cmd.exe window.
You can't run pdf files. You need to use the latex command instead of pdflatex. e.g.
latex Problem1.tex
Here's some documentation

Speed up simplex algorithm

I am playing around with a great simplex algorithm I have found here: https://github.com/JWally/jsLPSolver/
I have created a jsfiddle where I have set up a model and I solve the problem using the algorithm above. http://jsfiddle.net/Guill84/qds73u0f/
The model is basically a long array of variables and constraints. You can think of it as trying to find the cheapest means of transportation of passengers between different hubs (countries), where each country has a minimum demand for passengers, a maximum supply of passengers, and each connection has a price. I don't care where passengers go, I just want to find the cheapest way to distribute them. To achieve this I use the following minimising objective:
model = {
"optimize": "cost",
"opType": "min",
"constraints": { \\etc...
I am happy with the model and the answer provided by the algorithm ... but the latter takes a very long time to run (>15 seconds...) Is there any possible way I can speed up the calculation?
Kind regards and thank you.
G.
It sounds as though you have a minimum-cost flow problem. There's a reasonable-looking TopCoder tutorial on min-cost flow by Zealint, who covers the cycle-canceling algorithm that would be my first recommendation (assuming that there's no quick optimization that can be done for your LP solver). If that's still too slow, there's a whole literature out there.
Since you're determined to solve this problem with an LP solver, my suggestion would be to write a simpler solver that is fast and greedy but suboptimal and use it as a starting point for the LP by expressing the LP in terms of difference from the starting point.
#Noobster, I'm glad that someone other than me is getting use out of my simplex library. I went through, looked at it, and was getting around the same runtime as you (10 - 20 seconds). There was a piece of the code that was needlessly transposing array to turn the RHS into a 1d array from a 2d array. With your problem, this killed performance eating up 60ms every time it happened (for your problem, 137 times).
I've corrected this in the repo and am seeing runtimes around 2 seconds. There are probably a ton of code clean up optimizations like this that need to happen but the problem set I built this (http://mathfood.com) for are so small that I never knew this was an issue. Thanks!
For what its worth, I took the simplex algo out of a college textbook and turned it into code; the MILP piece came from wikipedia.
Figured it out. The most expensive piece of the code was the pivoting operation; which it turns out was doing a lot of work to update the matrix by adding 0. Doing a little logic up front to prevent this dropped my run-time down on node from ~12 seconds to ~0.5.
for (i = 0; i < length; i++) {
if (i !== row) {
pivot_row = tbl[i][col];
for (j = 0; j < width; j++) {
// No point in doing math if you're just adding
// Zero to the thing
if (pivot_row !== 0 && tbl[row][j] !== 0) {
tbl[i][j] += -pivot_row * tbl[row][j];
}
}
}
}

Seed-based world generation using sin

I'm tried to make some world generation mechanism using Math.random() whenever I needed something random, but then decided that I wanted it seed-based, so, given a seed, I changed all of the Math.random() to Math.sin(seed++)/2+0.5, hoping it would do the same thing, but would be the same if the seed was the same seed.
Then someone made me notice that the sin wave hasn't got even distribution, and finally I saw why some of my code was working strangely.
I was wondering if there was a simple fix, or if there isn't, another very simple seed based randomizer like this
So, I looked at your method, t1wc, and I found that it isn't actually evenly distributed. It is significantly more likely to spit out numbers near 0 or near 1 than it is to spit out numbers near 0.5, for example. This is just a consequence of the way that the sine function works.
Instead, you might try using a method called Blum Blum Shub (named after the authors of the original paper, wonderfully). It is evenly distributed and quite fast. Given a seed, it works as follows:
Square the seed and put the result in a temporary variable (x).
Take the mod of x base M.
M is a product of two large primes.
The value of x is a new seed to be used for future calculations.
Return x/M as your pseudo-random number. It will be evenly distributed between 0 and 1.
Below is a simple implementation of a Blum Blum Shub:
var SeededRand = function(seed, mod1, mod2)
{
return function()
{
seed = (seed*seed) % (mod1*mod2);
return seed/(mod1*mod2);
};
};
If you want to make a new random number generator, you just call:
var rand = SeededRand(seed, mod1, mod2);
Where seed is some initial seed (1234567890 works well), and mod1 and mod2 are some large primes (7247 and 7823 work well). rand is just a variable that I've defined to hold the output.
Now, to start getting random values, you just call:
rand();
Which will spit out a different value each time you run it.
If you have any questions, please ask!
There is a very nice seed-based randomizing script already made. It can be found here.
ok guys, found out this is what I'm really looking for:
(((Math.sin(seed.value++)/2+0.5)*10000)%100)/100
It sends out even spreaded numbers, and I guess it's a lot simpler than any other number generator I've seen

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