I can generate grid in stylus:
generate-grid(mod)
total = 0
for n, x in 0..11
total = round(8.3333333% * (x + 1))
.{mod}-{x + 1}
flex 0 0 total
.offset-{mod}-{x + 1}
margin-left total
But if I do this in sass then I'll get a bunch of mistakes. How to do it correctly?
#function generate-grid() {
#for $i from 1 through 12 {
.col-{$i} {
width: 8.3333333% * $i;
}
.offset-{$i} {
margin-right: 8.3333333% * $i;
}
}
}
interpolation is different than stylus in sass, it use #{}:
http://sass-lang.com/documentation/file.SASS_REFERENCE.html#Interpolation_____
I have a 2d array of Labels, each label contains a String version of an int. I'm attempting to traverse my array and check to see if each element contains the same int. Am I going about this the wrong way?
public boolean isPattern(Label[][] matirx) {
boolean pattern = false;
for (int rPos = 0; rPos < rows; rPos++) {
for (int cPos = 0; cPos < columns - 3; cPos++) {
if (matrix[cPos][rPos].equals(matrix[cPos + 1][rPos])
&& matrix[cPos][rPos].equals(matrix[cPos + 2][rPos])
&& matrix[cPos][rPos].equals(matrix[cPos + 3][rPos])) {
pattern = true;
}
}
}
When I print my boolean to the output window, I get false no matter what. So I guess my real question is. Am I comparing the contents of each Label or the value at each index, thus causing the variable never to be true?
So I ended up using this solution:
for (int rPos = 0; rPos < rows - 3; rPos++) {
for (int cPos = 0; cPos < columns; cPos++) {
if (matrix[cPos][rPos].getText().equals(matrix[cPos][rPos + 1].getText())
&& matrix[cPos][rPos].getText().equals(matrix[cPos][rPos + 2].getText())
&& matrix[cPos][rPos].getText().equals(matrix[cPos][rPos + 3].getText())) {
pattern = true;
Works as needed. If anyone comes across this and knows a better way, please do share.
Based on How to determine if a list of polygon points are in clockwise order?
I've come up with the following code:
bool PointsClockwise(const std::vector<MyPoint>& points)
{
double sum = 0.0;
for(size_t i = 0; i < points.size() - 1; ++i)
sum += (points[i+1].x()-points[i].x()) * (points[i+1].y()+points[i].y());
return sum > 0.0;
}
However, this seems to have wrong result in certain cases. Take for example the following ring:
LINESTRING(0 119,0 60,694 70,704 72,712 77,719 83,723 92,725 102,723 111,719 120,712 126,703 130)
It is in counter-clockwise order, but the function returns true.
Thanks!
You missed one of the line segments from your summation - namely the one connecting the last point with the first.
Try that:
bool PointsClockwise(const std::vector<MyPoint>& points)
{
double sum = 0.0;
for(size_t i = 0; i < points.size() - 1; ++i)
sum += (points[i+1].x()-points[i].x()) * (points[i+1].y()+points[i].y());
sum += (points[0].x()-points[points.size()-1].x()) * (points[0].y()+points[points.size()-1].y());
return sum > 0.0;
}
You need to include the case i == points.size() - 1, but to do that, you need to do some modular arithmetic in the loop, or else separate out the last iteration. Actually, just initialize sum to the last iteration:
double sum = (points[0].x() - points[points.size() - 1].x())
* (points[0].y() + points[points.size() - 1].y());
and end the iteration at i < points.size() - 1
Ok, my math is a bit rusty and I feel like this should be an easy problem, but yet I am here.
For SimpleAudioEngine in Cocos2d, there is a pitch argument. It is defined as follows:
1.0 is original pitch
0.5 is one octave (12 half steps) lower
2.0 is one octave (12 half steps) higher
So if I need:
input: 0 output: 1
input:-12 output: 0.5
input:12 output: 2
The equation has to be something like:
f(x) = f(x-1) * 2
But I don't remember how to solve equations like that. Thanks!
A look-up table would be faster but here's an equation (in C#):
public double NormalizeScaleStep(int Input)
{
double Note = 1.0;
if (Input == 0)
return Note;
if (Input > 0)
{
for (int Index = 0; Index < Input; Index++)
{
Note = Note * 1.059463094;
}
}
else
{
for (int Index = Input; Index < 0; Index++)
{
Note = Note / 1.059463094;
}
}
return Note;
}
Project Euler problem 14:
The following iterative sequence is
defined for the set of positive
integers:
n → n/2 (n is even) n → 3n + 1 (n is
odd)
Using the rule above and starting with
13, we generate the following
sequence: 13 → 40 → 20 → 10 → 5 → 16 →
8 → 4 → 2 → 1
It can be seen that this sequence
(starting at 13 and finishing at 1)
contains 10 terms. Although it has not
been proved yet (Collatz Problem), it
is thought that all starting numbers
finish at 1.
Which starting number, under one
million, produces the longest chain?
My first instinct is to create a function to calculate the chains, and run it with every number between 1 and 1 million. Obviously, that takes a long time. Way longer than solving this should take, according to Project Euler's "About" page. I've found several problems on Project Euler that involve large groups of numbers that a program running for hours didn't finish. Clearly, I'm doing something wrong.
How can I handle large groups of numbers quickly?
What am I missing here?
Have a read about memoization. The key insight is that if you've got a sequence starting A that has length 1001, and then you get a sequence B that produces an A, you don't to repeat all that work again.
This is the code in Mathematica, using memoization and recursion. Just four lines :)
f[x_] := f[x] = If[x == 1, 1, 1 + f[If[EvenQ[x], x/2, (3 x + 1)]]];
Block[{$RecursionLimit = 1000, a = 0, j},
Do[If[a < f[i], a = f[i]; j = i], {i, Reverse#Range#10^6}];
Print#a; Print[j];
]
Output .... chain length´525´ and the number is ... ohhhh ... font too small ! :)
BTW, here you can see a plot of the frequency for each chain length
Starting with 1,000,000, generate the chain. Keep track of each number that was generated in the chain, as you know for sure that their chain is smaller than the chain for the starting number. Once you reach 1, store the starting number along with its chain length. Take the next biggest number that has not being generated before, and repeat the process.
This will give you the list of numbers and chain length. Take the greatest chain length, and that's your answer.
I'll make some code to clarify.
public static long nextInChain(long n) {
if (n==1) return 1;
if (n%2==0) {
return n/2;
} else {
return (3 * n) + 1;
}
}
public static void main(String[] args) {
long iniTime=System.currentTimeMillis();
HashSet<Long> numbers=new HashSet<Long>();
HashMap<Long,Long> lenghts=new HashMap<Long, Long>();
long currentTry=1000000l;
int i=0;
do {
doTry(currentTry,numbers, lenghts);
currentTry=findNext(currentTry,numbers);
i++;
} while (currentTry!=0);
Set<Long> longs = lenghts.keySet();
long max=0;
long key=0;
for (Long aLong : longs) {
if (max < lenghts.get(aLong)) {
key = aLong;
max = lenghts.get(aLong);
}
}
System.out.println("number = " + key);
System.out.println("chain lenght = " + max);
System.out.println("Elapsed = " + ((System.currentTimeMillis()-iniTime)/1000));
}
private static long findNext(long currentTry, HashSet<Long> numbers) {
for(currentTry=currentTry-1;currentTry>=0;currentTry--) {
if (!numbers.contains(currentTry)) return currentTry;
}
return 0;
}
private static void doTry(Long tryNumber,HashSet<Long> numbers, HashMap<Long, Long> lenghts) {
long i=1;
long n=tryNumber;
do {
numbers.add(n);
n=nextInChain(n);
i++;
} while (n!=1);
lenghts.put(tryNumber,i);
}
Suppose you have a function CalcDistance(i) that calculates the "distance" to 1. For instance, CalcDistance(1) == 0 and CalcDistance(13) == 9. Here is a naive recursive implementation of this function (in C#):
public static int CalcDistance(long i)
{
if (i == 1)
return 0;
return (i % 2 == 0) ? CalcDistance(i / 2) + 1 : CalcDistance(3 * i + 1) + 1;
}
The problem is that this function has to calculate the distance of many numbers over and over again. You can make it a little bit smarter (and a lot faster) by giving it a memory. For instance, lets create a static array that can store the distance for the first million numbers:
static int[] list = new int[1000000];
We prefill each value in the list with -1 to indicate that the value for that position is not yet calculated. After this, we can optimize the CalcDistance() function:
public static int CalcDistance(long i)
{
if (i == 1)
return 0;
if (i >= 1000000)
return (i % 2 == 0) ? CalcDistance(i / 2) + 1 : CalcDistance(3 * i + 1) + 1;
if (list[i] == -1)
list[i] = (i % 2 == 0) ? CalcDistance(i / 2) + 1: CalcDistance(3 * i + 1) + 1;
return list[i];
}
If i >= 1000000, then we cannot use our list, so we must always calculate it. If i < 1000000, then we check if the value is in the list. If not, we calculate it first and store it in the list. Otherwise we just return the value from the list. With this code, it took about ~120ms to process all million numbers.
This is a very simple example of memoization. I use a simple list to store intermediate values in this example. You can use more advanced data structures like hashtables, vectors or graphs when appropriate.
Minimize how many levels deep your loops are, and use an efficient data structure such as IList or IDictionary, that can auto-resize itself when it needs to expand. If you use plain arrays they need to be copied to larger arrays as they expand - not nearly as efficient.
This variant doesn't use an HashMap but tries only to not repeat the first 1000000 numbers. I don't use an hashmap because the biggest number found is around 56 billions, and an hash map could crash.
I have already done some premature optimization. Instead of / I use >>, instead of % I use &. Instead of * I use some +.
void Main()
{
var elements = new bool[1000000];
int longestStart = -1;
int longestRun = -1;
long biggest = 0;
for (int i = elements.Length - 1; i >= 1; i--) {
if (elements[i]) {
continue;
}
elements[i] = true;
int currentStart = i;
int currentRun = 1;
long current = i;
while (current != 1) {
if (current > biggest) {
biggest = current;
}
if ((current & 1) == 0) {
current = current >> 1;
} else {
current = current + current + current + 1;
}
currentRun++;
if (current < elements.Length) {
elements[current] = true;
}
}
if (currentRun > longestRun) {
longestStart = i;
longestRun = currentRun;
}
}
Console.WriteLine("Longest Start: {0}, Run {1}", longestStart, longestRun);
Console.WriteLine("Biggest number: {0}", biggest);
}