Take a recursive function, say:
public static long rekurs(long n) {
if (n == 0) {
return 1;
} else if (n == 1) {
return 1;
} else {
return rekurs(n - 1)*(rekurs(n - 2)+4;
}
}
When n=20, the function has to find all the values S(n) for n=2,...,19 first.
When I let n go from 20 to 21, it does the same thing again (plus finding S(20)).
Now I want to create an array, in which the found values S(n) for n=2,...,19 are filled into, so that the function for n=21 does not have to do the same thing again, but how do I get those elements?
This is the solution I figured out, it's a little bit different from the lecture example.
The keyword that helped me is "dynamic programming".
import java.util.Arrays;
public class Bsp13 {
public static final int N = 0;
public static final int Ende = 20;
public static long[] schroe = new long[N + Ende + 1];
public static void main(String[] args) {
schroe[0] = 1;
schroe[1] = 1;
for (int n = 2; n <= Ende + N; n++) {
schroe[n] = ((6 * n - 3) * (schroe[n-1]) - (n - 2) * (schroe[n-2])) / (n + 1);
}
System.out.println(schroe[N]);
System.out.println(Arrays.toString(schroe));
System.out.println(schroe[N+Ende]);
}
}
What you are trying to do is called dynamic programming. Basically it is bookkeeping in order to not compute subsolutions more than once.
So basically, you need a mapping of n values to solution values. I would suggest you use a dictionary-like-datastructure for this task.
When a value for n needs to be computed, you first check whether the solution is in the dictionary, if yes you return the result. If not, you compute the result and put it into the dictionary.
Think about how you would initialize this dictionary and how you would pass it down to the recursive function calls.
Here's a lecture video on dynamic programming where the computation of Fibonnaci-numbers using dynamic programming is explained, which is very similar to what you are trying to do:
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/lecture-videos/lecture-19-dynamic-programming-i-fibonacci-shortest-paths/
Related
i am trying to learn how to use LSTM with deeplearning4j lib.
I created a dummy scenario where i want to get an output (3 classes) based on data that i collected.
I got the data from here (http://www.osservatoriodioropa.it/meteoropa/NOAAMO.TXT) if someone is curious :)
Back to the scenario.
I created 2 matrix, one with features, other with classes that i want to output, just as a test.
When i try the classifier i got
Exception in thread "main" java.lang.IllegalStateException: 3D input expected to RNN layer expected, got 2
i think because the RnnOutputLayer expect a 3d matrix, but i am not able to understand how to populate it. How can i convert a 2d matrix into a 3d matrix correlating the previous event with the new one? The data are a time serie, and i want to relate the classification of the new day based on previous days as well. (I know that probably the data won't fit this scenario and that there are better way to do that, but that's just to learning how to use LSTM, not how to classify this specific dataset)
this is the code so far
public class Test {
public static void main(String args[]) {
int events = 5;
int features = 6;
int classes = 3;
double[][] featureMatrix = new double[events][features];
double[][] labelMatrix = new double[events][classes];
for (int i = 0; i < events; i++) {
for (int f = 0; f < features; f++) {
featureMatrix[i][f] = getFeature(i, f);
}
for (int c = 0; c < classes; c++) {
labelMatrix[i][c] = getResult(i, c);
}
}
INDArray trainingIn = Nd4j.create(featureMatrix);
INDArray trainingOut = Nd4j.create(labelMatrix);
DataSet myData = new DataSet(trainingIn, trainingOut);
MultiLayerNetwork multiLayerNetwork = createModel(features,classes);
multiLayerNetwork.init();
multiLayerNetwork.fit(myData);
}
private static double getFeature(int i, int f) {
//dummy
return 1.;
}
private static double getResult(int i, int c) {
//dummy
return 1.;
}
public static MultiLayerNetwork createModel(int inputNum, int outputNum) {
MultiLayerConfiguration conf = new NeuralNetConfiguration.Builder()
.trainingWorkspaceMode(ENABLED).inferenceWorkspaceMode(ENABLED)
.seed(123456)
.optimizationAlgo(OptimizationAlgorithm.STOCHASTIC_GRADIENT_DESCENT)
.updater(new RmsProp.Builder().learningRate(0.05).rmsDecay(0.002).build())
.l2(0.0005)
.weightInit(WeightInit.XAVIER)
.activation(Activation.TANH)
.list()
.layer(new LSTM.Builder().name("1").nIn(inputNum).nOut(inputNum).build())
.layer(new LSTM.Builder().name("2").nIn(inputNum).nOut(inputNum).build())
.layer(new RnnOutputLayer.Builder().name("output").nIn(inputNum).nOut(outputNum)
.activation(Activation.IDENTITY).lossFunction(LossFunctions.LossFunction.MSE).build())
.build();
MultiLayerNetwork net = new MultiLayerNetwork(conf);
net.init();
return net;
}
}
I would like to express something like this in Critcl:
void setter(int* grid, int value, int x, int y) {
grid[xy2addr(x,y)] = value;
}
I'm in particular stuck on how to deal with int* grid in Critcl. object? bytes? Custom type maybe?
Related to this question.
This case doesn't map very well onto Tcl's value model. The issue is that grid is (a pointer to) an updateable value collection. There are two ways of modelling this in Tcl in general:
As an opaque object.
As a variable containing a Tcl list (since in model terms, while Tcl values are thought of as immutable, Tcl variables are mutable).
I'll describe how to do both below, but I'm guessing that you're going to be thinking of these zOrder things as a distinct mutable type and that the additional modest one-time overhead of making the custom type will suit you far better.
Opaque (Mutable) Objects
When working with opaque objects, you pass handles to them (basically just a name) around and then you unpack them as a custom Critcl type. The trick is to create some helper functions in C to do the mapping (this can be in a critcl::ccode command) that does the mapping between names and pointers. This is slightly messy to do, but is just about building a couple of hash tables.
critcl::ccode {
static Tcl_HashTable *zOrderMap = NULL, *zOrderRevMap = NULL;
static Tcl_Obj *
MakeZOrderObj(int *zOrder) {
/* Initialize the two maps, if needed */
if (zOrderMap == NULL) {
zOrderMap = (Tcl_HashTable *) Tcl_Alloc(sizeof(Tcl_HashTable));
Tcl_InitObjHashTable(zOrderMap);
zOrderRevMap = (Tcl_HashTable *) Tcl_Alloc(sizeof(Tcl_HashTable));
Tcl_InitHashTable(zOrderRevMap, TCL_ONE_WORD_KEYS);
}
int isNew;
Tcl_HashEntry *hPtr = Tcl_FindHashEntry(zOrderRevMap, (char*) zOrder, &isNew);
if (!isNew) {
return Tcl_GetHashValue(hPtr);
}
/* make a handle! */
Tcl_Obj *handle = Tcl_ObjPrintf("zOrder%ld", (long) zOrder);
Tcl_SetHashValue(hPtr, handle);
Tcl_IncrRefCount(handle);
hPtr = Tcl_CreateHashEntry(zOrderMap, (char*) handle, &isNew);
Tcl_SetHashValue(hPtr, zOrder);
return handle;
}
static int
GetZOrderFromObj(Tcl_Interp *interp, Tcl_Obj *objPtr, int **zOrderPtr) {
Tcl_HashTable *hPtr;
if (!zOrderMap || (hPtr = Tcl_FindHashEntry(zOrderMap, (char *) objPtr)) == NULL) {
Tcl_SetObjResult(interp, Tcl_ObjPrintf("no such zOrder \"%s\"",
Tcl_GetString(objPtr)));
return TCL_ERROR;
}
*zOrderPtr = (int *) Tcl_GetHashValue(hPtr);
return TCL_OK;
}
}
With that helper code in place, you can then define a custom Critcl type like this:
critcl::argtype zOrder {
if (GetZOrderFromObj(interp, ##, #A) != TCL_OK) {
return TCL_ERROR;
}
} int*
critcl::resulttype zOrder {
if (rv == NULL) {
return TCL_ERROR;
}
Tcl_SetObjResult(interp, MakeZOrderObj(rv));
return TCL_OK;
} int*
That then lets you write your real code as something like this. Note that grid is defined as being of (custom) type zOrder, and that those can only be manufactured by some code that returns a zOrder as its result.
critcl::cproc setter {zOrder grid int value int x int y} void {
grid[xy2addr(x,y)] = value;
}
(The deletion function that removes the entries from the hash tables and deletes the C array is left as an exercise.)
Tcl List Variable
The other way of doing this is to make zOrder values be held in Tcl variables as lists of integers. This can be nice because it lets you look inside easily, but it can also be not so nice in other ways, as the code is not constrained to work with proper values and you expose your cprocs to more details of what's happening in Tcl.
critcl::cproc setter {Tcl_Interp* interp object varName int value int x int y} ok {
/* Unpack the list of ints from the variable */
Tcl_Obj *listObj = Tcl_ObjGetVar2(interp, varName, NULL, TCL_LEAVE_ERR_MSG);
if (listObj == NULL)
return TCL_ERROR;
Tcl_Obj **listv; int listc;
if (Tcl_ListObjGetElements(interp, listObj, &listc, &listv) != TCL_OK)
return TCL_ERROR;
int *grid = alloca(sizeof(int) * listc);
for (int i=0; i<listc; i++)
if (Tcl_GetIntFromObj(interp, listv[i], &grid[i]) != TCL_OK)
return TCL_ERROR;
/* The core of the functionality */
grid[xy2addr(x,y)] = value;
/* Repack the list of ints from the variable; this code could be optimized in this case! */
for (int i=0; i<listc; i++)
listv[i] = Tcl_NewIntObj(grid[i]);
listObj = Tcl_NewListObj(listc, listv);
Tcl_ObjSetVar2(interp, varName, NULL, listObj, 0);
return TCL_OK;
}
How can I find the permutations of k in a given length?
For example:
The word cat has 3 letters: How can I find all the permutations of 2 in the word cat.
Result should be: ac, at, ca, ac, etc...
This is not a homework problem.
Any language could be used but more preferable: C/C++ or C#.
I know how to create the recursion for size LENGTH but not for a custom size.
Here is one in C#, which should work even with repeated characters. For example on "banana" for permutations of length 2 it gives:
ba bn ab aa an nb na nn
The basic idea is to fix the first character, then form all permutations of length k-1, then prepend the character to those k-1 length permutations. To deal with duplicate characters, we keep track of the count left (i.e the ones which can be used for sub-permutations).
Not exemplary code, but should give you the idea. (If you find bugs, let me know and I can edit).
static List<string> Permutations(Dictionary<char, int> input, int length) {
List<string> permutations = new List<string>();
List<char> chars = new List<char>(input.Keys);
// Base case.
if (length == 0) {
permutations.Add(string.Empty);
return permutations;
}
foreach (char c in chars) {
// There are instances of this character left to use.
if (input[c] > 0) {
// Use one instance up.
input[c]--;
// Find sub-permutations of length length -1.
List<string> subpermutations = Permutations(input, length - 1);
// Give back the instance.
input[c]++;
foreach (string s in subpermutations) {
// Prepend the character to be the first character.
permutations.Add(s.Insert(0,new string(c,1)));
}
}
}
return permutations;
}
And here is the full program I have, to use it:
using System;
using System.Collections.Generic;
namespace StackOverflow {
class Program {
static void Main(string[] args) {
List<string> p = Permutations("abracadabra", 3);
foreach (string s in p) {
Console.WriteLine(s);
}
}
static List<string> Permutations(string s, int length) {
Dictionary<char, int> input = new Dictionary<char, int>();
foreach (char c in s) {
if (input.ContainsKey(c)) {
input[c]++;
} else {
input[c] = 1;
}
}
return Permutations(input, length);
}
static List<string> Permutations(Dictionary<char, int> input,
int length) {
List<string> permutations = new List<string>();
List<char> chars = new List<char>(input.Keys);
if (length == 0) {
permutations.Add(string.Empty);
return permutations;
}
foreach (char c in chars) {
if (input[c] > 0) {
input[c]--;
List<string> subpermutations = Permutations(input,
length - 1);
input[c]++;
foreach (string s in subpermutations) {
permutations.Add(s.Insert(0,new string(c,1)));
}
}
}
return permutations;
}
}
}
What's wrong with the recursive solution and passing an extra parameter (depth) so that the recursive function returns immediately for depth > n.
Not the most efficient, but it works:
public class permutation
{
public static List<string> getPermutations(int n, string word)
{
List<string> tmpPermutation = new List<string>();
if (string.IsNullOrEmpty(word) || n <= 0)
{
tmpPermutation.Add("");
}
else
{
for (int i = 0; i < word.Length; i++)
{
string tmpWord = word.Remove(i, 1);
foreach (var item in getPermutations(n - 1, tmpWord))
{
tmpPermutation.Add(word[i] + item);
}
}
}
return tmpPermutation;
}
}
void Prem (char *str, int k, int length) {
if (k == length-1){
printf("%s\n",str);
return;
} else {
for (int i = k ; i < length; ++i) {
char t = str[k];
str[k] = str[i];
str[i] = t;
Prem(str,k+1,length);
t = str[k];
str[k] = str[i];
str[i] = t;
}
}
}
If I'm not mistaken, this problem can be solved by combinadics too, as on http://en.wikipedia.org/wiki/Combinadic/, there are reference implementations there too.
I have used the Java solution (http://docs.google.com/Doc?id=ddd8c4hm_5fkdr3b/) myself for generating all possible triples from a sequence of numbers, this should be no different.
I lack the wherewithal to explain the math behind it, but as I understand this is the least complex way to iterate over all possible nCr (i.e. 3C2 for your cat example) choices within a collection.
First find the possible subsets of your array. You can do this in
a recursive way it was discussed in Iterating over subsets of any size
Second calculate the permutations of every subset with the STL-Algorithm
next_permutation
I haven't implemented it but i think it should work.
so, i have a method: I'm counting a number in a sequence with holes, this number should be the first hole or max()
public static int GetRegisterNumber<T>(this IQueryable<T> enumerable, Func<T, bool> whereFunc, Func<T, int?> selectFunc)
{
var regNums = enumerable.OrderBy(selectFunc).Where(whereFunc).ToArray();
if (regNums.Count() == 0)
{
return 1;
}
for (int i = 0; i < regNums.Count(); i++)
{
if (i + 1 != regNums[i])
{
return regNums[i].Value + 1;
}
}
return regNums.Last().Value + 1;
}
i use it like:
var db = new SomeDataContext();
db.Goals.GetRegisterNumber(g => g.idBudget == 123, g => g.RegisterNumber);
So, i expect from linq some query like:
SELECT [t0].[id], [t0].[tstamp], [t0].[idBudget], [t0].[RegisterNumber], FROM [ref].[GoalHierarchy] AS [t0] WHERE [t0].[idBudget] = 123 ORDER BY [t0].[RegisterNumber]
instead i'm getting:
SELECT [t0].[id], [t0].[tstamp], [t0].[idBudget], [t0].[RegisterNumber], FROM [ref].[GoalHierarchy] AS [t0]
So linq gets ALL the table data and then filters it, but that behavior is not acceptable, because the table contains much data. Is there any solution?
Change your method signature to look like this:
public static int GetRegisterNumber<T>(this IQueryable<T> enumerable, Expression<Func<T, bool>> whereFunc, Expression<Func<T, int?>> selectFunc)
This way it will call the appropriate extension methods for IQueryable<T>. If you only have a Func<TSource, bool>, it will call the extension method for IEnumerable<T>.
I have have a class that I wrote, and it seems bigger than it should be. It doesn't extend anything, and has very little going on - or so I thought - but each one is taking up just under 100k100 bytes ( thanks back2dos ). I guess that I don't have a very good understanding of what really affects how much memory an object takes up in AS3.
If anyone can point me to some reading on the subject that might be helpful, or perhaps explain some insight into how to think about this, that would be awesome.
I would like to keep a LOT of these objects in memory - and I thought I could until now, but at this size I'm going to have to create them or use an object pooling technique of some kind.
Thanks for the assistance.
Edit: Although I've got this in order, I'm keeping the code I posted here for completeness. The class has been heavily modified from the original version. Values that were referencing other files have been made static as to allow the code to run for someone else ( in theory hehehe... ).
Although my situation is sorted out, I'll give the answer to a good reference for information on classes and memory.
In this case the class has 15 variables. I'm only using a single String and a bunch of ints, Numbers, and Booleans with some references to more of the same in globally available XML data. It also imports Point for the constructor, though no points are stored. In testing, even without the global XML references or Point class it's still around a ~84k each. There are getters for 7 of the variables and a couple methods in addition to the constructor. All of which are less than 20 lines ( and I have a very sparse coding style ).
The class mentioned for reference, but feel free to generalize:
package
{
public class AObject
{
private var _counter:int;
private var _frames:int;
private var _speed:int;
private var _currentState:String;
private var _currentFrame:int;
private var _offset:int;
private var _endFrame:int;
private var _type:int;
private var _object:int;
private var _state:int;
private var _x:Number;
private var _y:Number;
private var _w:int;
private var _h:int;
private var _update:Boolean;
public function AObject( targetX : int, targetY : int, state : int, object : int, type : int )
{
_x = targetX;
_y = targetY;
_type = type;
_object = object;
_state = state;
_counter = 0;
_w = 32;
_h = 32
_update = true;
setState( state );
}
public function setState( state:int ) : void
{
_currentState = "bob";
var frameCounter : int = 0;
var stateCounter : int = state - 1;
while ( state > 0 )
{
frameCounter += 4;
--stateCounter;
}
_offset = frameCounter;
_currentFrame = _offset;
_speed = 10;
_frames = 4;
_endFrame = _offset + _frames - 1;
}
public function get state() : int
{
return _state;
}
public function animate() : Boolean
{
if ( count() )
{
if( _currentFrame < _endFrame )
{
++_currentFrame;
}
else
{
_currentFrame = _offset;
}
_speed = 10;
return true;
}
else
{
return false;
}
}
private var adder: Number = 0;
private function count():Boolean
{
_counter++;
if ( _counter == _speed )
{
_counter = 0;
return true;
}
else
{
return false;
}
}
public function get x():int
{
return _x;
}
public function get y():int
{
return _y;
}
public function get type():int
{
return _type;
}
public function get object():int
{
return _object;
}
public function get currentFrame():int
{
return _currentFrame;
}
public function get w():int
{
return _w;
}
public function get h():int
{
return _h;
}
}
}
i am amazed, this compiles at all ... when i try to compile it with the flex SDK, it creates an enormous collision with the built-in class Object, which is the base class of any class, making my trace output overflow ...
other than that, this is an infinite loop if you pass a value for state bigger than 0
while ( state > 0 )
{
frameCounter += 4;
--stateCounter;
}
but it seems really strange these objects are so big ... after renaming and taking care not to pass in 0 for the state, i ran a test:
package {
import flash.display.Sprite;
import flash.sampler.getSize;
import flash.system.System;
public class Main extends Sprite {
public function Main():void {
const count:int = 100000;
var start:uint = System.totalMemory;
var a:Array = [];
for (var i:int = 0; i < count; i++) {
a.push(new MyObject(1, 2, 0, 4, 5));
}
var mem:uint = System.totalMemory - start - getSize(a);
trace("total of "+mem+" B for "+count+" objects, aprox. avg. size per object: "+(mem/count));
}
}
}
it yields:
total of 10982744 B for 100000 objects, aprox. avg. size per object: 109.82744
so that's quite ok ... i think the actual size should be 4 (for the bool) + 4 * 11 (for the ints) + 4 (for the reference to the string) + 8 * 3 (for the three floats (you have the adder somewhere over the count) + 8 for an empty class (reference to the traits objects + something else), giving you a total of 88 bytes ... which is, what you get, if you getSize the object ... please note however, that getSize will only give you the size of the object itself (as calculated here) ignoring the size of what strings or other objects your object references ...
so yeah, apart from that name you definitely should change, the problem must be somewhere else ...
greetz
back2dos
If you really want to save on space, you can fake shorts by using unsigned integers, and using upper/lower bits for one thing or another.
ints are 4 bytes by nature, you can reuse that int on anything less than 2^8.
width height
0xFFFF + 0xFFFF
offset endframe
0xFFFF + 0xFFFF
This though gets ugly when you want to write anything or read anything, as to write width or height you'd have to:
writing:
size = (width & 0x0000FFFF) << 16 | (height & 0x0000FFFF);
reading:
get width():uint { return (size & 0xFFFF0000) >> 16 };
That's ugly. Since you're using getters anyways, and assuming computation speed is not an issue, you could use internal byte arrays which could give you even more granularity for how you want to store your information. Assuming your strings are more than 4 bytes, makes more sense to use a number rather than a string.
Also, I believe you will actually get some memory increase by declaring the class as final, as I believe final functions get placed into the traits object, rather than