How do I implement BFS using recursion, given the linked list representation?
I know DFS can be implemented using recursion, but not with BFS. Please suggest a possible method?
Note that [] represents a list.
f(graph, past_nodes, current_nodes, mark):
new_nodes = all neighbors of current_nodes which are not in past_nodes
if new_nodes == []:
return
else
for each n in new_nodes:
mark(n)
f(graph, past_nodes union current_nodes, new_nodes, mark)
Begin by calling f(graph, [], [start_node], m) where m is the function you want to run for each node in BFS order.
void bfs(int vertex)
{
int p;
void mark(int);
m=g[vertex];
if(m->v==1)
return;
m->v=1;
printf("%c ",m->a);
while(m->link!=NULL)
{
m=m->link;
if(m->v==0)
{
m->v=1;
p=int(m->a)-65;
mark(p);
}
}
m=g[vertex];
while(m->link!=NULL)
{
m=m->link;
bfs(p);
}
}
i get stuck here.
Related
Is there a fast (native) method to search for a sequence in a Uint8List?
///
/// Return index of first occurrence of seq in list
///
int indexOfSeq(Uint8List list, Uint8List seq) {
...
}
EDIT: Changed List<int> into Uint8List
No. There is no built-in way to search for a sequence of elements in a list.
I am also not aware of any dart:ffi based implementations.
The simplest approach would be:
extension IndexOfElements<T> on List<T> {
int indexOfElements(List<T> elements, [int start = 0]) {
if (elements.isEmpty) return start;
var end = length - elements.length;
if (start > end) return -1;
var first = elements.first;
var pos = start;
while (true) {
pos = indexOf(first, pos);
if (pos < 0 || pos > end) return -1;
for (var i = 1; i < elements.length; i++) {
if (this[pos + i] != elements[i]) {
pos++;
continue;
}
}
return pos;
}
}
}
This has worst-case time complexity O(length*elements.length). There are several more algorithms with better worst-case complexity, but they also have larger constant factors and more expensive pre-computations (KMP, BMH). Unless you search for the same long list several times, or do so in a very, very long list, they're unlikely to be faster in practice (and they'd probably have an API where you compile the pattern first, then search with it.)
You could use dart:ffi to bind to memmem from string.h as you suggested.
We do the same with binding to malloc from stdlib.h in package:ffi (source).
final DynamicLibrary stdlib = Platform.isWindows
? DynamicLibrary.open('kernel32.dll')
: DynamicLibrary.process();
final PosixMalloc posixMalloc =
stdlib.lookupFunction<Pointer Function(IntPtr), Pointer Function(int)>('malloc');
Edit: as lrn pointed out, we cannot expose the inner data pointer of a Uint8List at the moment, because the GC might relocate it.
One could use dart_api.h and use the FFI to pass TypedData through the FFI trampoline as Dart_Handle and use Dart_TypedDataAcquireData from the dart_api.h to access the inner data pointer.
(If you want to use this in Flutter, we would need to expose Dart_TypedDataAcquireData and Dart_TypedDataReleaseData in dart_api_dl.h https://github.com/dart-lang/sdk/issues/40607 I've filed https://github.com/dart-lang/sdk/issues/44442 to track this.)
Alternatively, could address https://github.com/dart-lang/sdk/issues/36707 so that we could just expose the inner data pointer of a Uint8List directly in the FFI trampoline.
I'm giving Kotlin a go; coding contently, I have an ArrayList of chars which i want to classify depending on how brackets are matched:
(abcde) // ok characters other than brackets can go anywhere
)abcde( // ok matching the brackets 'invertedly' are ok
(({()})) // ok
)()()([] // ok
([)] // bad can't have different overlapping bracket pairs
((((( // bad all brackets need to have a match
My solution comes out(recursive):
//charList is a property
//Recursion starter'upper
private fun classifyListOfCharacters() : Boolean{
var j = 0
while (j < charList.size ) {
if (charList[j].isBracket()){
j = checkMatchingBrackets(j+1, charList[j])
}
j++
}
return j == commandList.size
}
private fun checkMatchingBrackets(i: Int, firstBracket :Char) : Int{
var j = i
while (j < charList.size ) {
if (charList[j].isBracket()){
if (charList[j].matchesBracket(firstBracket)){
return j //Matched bracket normal/inverted
}
j = checkMatchingBrackets(j+1, charList[j])
}
j++
}
return j
}
This works, but is this how you do it in Kotlin? It feels like I've coded java in Kotlin syntax
Found this Functional languages better at recursion, I've tried thinking in terms of manipulating functions and sending them down the recursion but to no avail. I'd be glad to be pointed in the right direction, code, or some pseudo-code of a possible refactoring.
(Omitted some extension methods regarding brackets, I think it's clear what they do)
Another, possibly a simpler approach to this problem is maintaining a stack of brackets while you iterate over the characters.
When you encounter another bracket:
If it matches the top of the stack, you pop the top of the stack;
If it does not match the top of the stack (or the stack is empty), you push it onto the stack.
If any brackets remain on the stack at the end, it means they are unmatched, and the answer is false. If the stack ends up empty, the answer is true.
This is correct, because a bracket at position i in a sequence can match another one at position j, only if there's no unmatched bracket of a different kind between them (at position k, i < k < j). The stack algorithm simulates exactly this logic of matching.
Basically, this algorithm could be implemented in a single for-loop:
val stack = Stack<Char>()
for (c in charList) {
if (!c.isBracket())
continue
if (stack.isNotEmpty() && c.matchesBracket(stack.peek())) {
stack.pop()
} else {
stack.push(c)
}
}
return stack.isEmpty()
I've reused your extensions c.isBracket(...) and c.matchesBracket(...). The Stack<T> is a JDK class.
This algorithm hides the recursion and the brackets nesting inside the abstraction of the brackets stack. Compare: your current approach implicitly uses the function call stack instead of the brackets stack, but the purpose is the same: it either finds a match for the top character or makes a deeper recursive call with another character on top.
Hotkey's answer (using a for loop) is great. However, you asked for an optimized recursion solution. Here is an optimized tail recursive function (Note the tailrec modifier before the function):
tailrec fun isBalanced(input: List<Char>, stack: Stack<Char>): Boolean = when {
input.isEmpty() -> stack.isEmpty()
else -> {
val c = input.first()
if (c.isBracket()) {
if (stack.isNotEmpty() && c.matchesBracket(stack.peek())) {
stack.pop()
} else {
stack.push(c)
}
}
isBalanced(input.subList(1, input.size), stack)
}
}
fun main(args: Array<String>) {
println("check: ${isBalanced("(abcde)".toList(), Stack())}")
}
This function calls itself until the input becomes empty and returns true if the stack is empty when the input becomes empty.
If we look at the decompiled Java equivalent of the generated bytecode, this recursion has been optimized to an efficient while loop by the compiler so we won't get StackOverflowException (removed Intrinsics null checks):
public static final boolean isBalanced(#NotNull String input, #NotNull Stack stack) {
while(true) {
CharSequence c = (CharSequence)input;
if(c.length() == 0) {
return stack.isEmpty();
}
char c1 = StringsKt.first((CharSequence)input);
if(isBracket(c1)) {
Collection var3 = (Collection)stack;
if(!var3.isEmpty() && matchesBracket(c1, ((Character)stack.peek()).charValue())) {
stack.pop();
} else {
stack.push(Character.valueOf(c1));
}
}
input = StringsKt.drop(input, 1);
}
}
I'm trying to write what I would think of as an extremely simple piece of code in Rascal: Testing if list A contains list B.
Starting out with some very basic code to create a list of strings
public list[str] makeStringList(int Start, int End)
{
return [ "some string with number <i>" | i <- [Start..End]];
}
public list[str] toTest = makeStringList(0, 200000);
My first try was 'inspired' by the sorting example in the tutor:
public void findClone(list[str] In, str S1, str S2, str S3, str S4, str S5, str S6)
{
switch(In)
{
case [*str head, str i1, str i2, str i3, str i4, str i5, str i6, *str tail]:
{
if(S1 == i1 && S2 == i2 && S3 == i3 && S4 == i4 && S5 == i5 && S6 == i6)
{
println("found duplicate\n\t<i1>\n\t<i2>\n\t<i3>\n\t<i4>\n\t<i5>\n\t<i6>");
}
fail;
}
default:
return;
}
}
Not very pretty, but I expected it to work. Unfortunately, the code runs for about 30 seconds before crashing with an "out of memory" error.
I then tried a better looking alternative:
public void findClone2(list[str] In, list[str] whatWeSearchFor)
{
for ([*str head, *str mid, *str end] := In)
if (mid == whatWeSearchFor)
println("gotcha");
}
with approximately the same result (seems to run a little longer before running out of memory)
Finally, I tried a 'good old' C-style approach with a for-loop
public void findClone3(list[str] In, list[str] whatWeSearchFor)
{
cloneLength = size(whatWeSearchFor);
inputLength = size(In);
if(inputLength < cloneLength) return [];
loopLength = inputLength - cloneLength + 1;
for(int i <- [0..loopLength])
{
isAClone = true;
for(int j <- [0..cloneLength])
{
if(In[i+j] != whatWeSearchFor[j])
isAClone = false;
}
if(isAClone) println("Found clone <whatWeSearchFor> on lines <i> through <i+cloneLength-1>");
}
}
To my surprise, this one works like a charm. No out of memory, and results in seconds.
I get that my first two attempts probably create a lot of temporary string objects that all have to be garbage collected, but I can't believe that the only solution that worked really is the best solution.
Any pointers would be greatly appreciated.
My relevant eclipse.ini settings are
-XX:MaxPermSize=512m
-Xms512m
-Xss64m
-Xmx1G
We'll need to look to see why this is happening. Note that, if you want to use pattern matching, this is maybe a better way to write it:
public void findClone(list[str] In, str S1, str S2, str S3, str S4, str S5, str S6) {
switch(In) {
case [*str head, S1, S2, S3, S4, S5, S6, *str tail]: {
println("found duplicate\n\t<S1>\n\t<S2>\n\t<S3>\n\t<S4>\n\t<S5>\n\t<S6>");
}
default:
return;
}
}
If you do this, you are taking advantage of Rascal's matcher to actually find the matching strings directly, versus your first example in which any string would match but then you needed to use a number of separate comparisons to see if the match represented the combination you were looking for. If I run this on 110145 through 110150 it takes a while but works and it doesn't seem to grow beyond the heap space you allocated to it.
Also, is there a reason you are using fail? Is this to continue searching?
It's an algorithmic issue like Mark Hills said. In Rascal some short code can still entail a lot of nested loops, almost implicitly. Basically every * splice operator on a fresh variable that you use on the pattern side in a list generates one level of loop nesting, except for the last one which is just the rest of the list.
In your code of findClone2 you are first generating all combinations of sublists and then filtering them using the if construct. So that's a correct algorithm, but probably slow. This is your code:
void findClone2(list[str] In, list[str] whatWeSearchFor)
{
for ([*str head, *str mid, *str end] := In)
if (mid == whatWeSearchFor)
println("gotcha");
}
You see how it has a nested loop over In, because it has two effective * operators in the pattern. The code runs therefore in O(n^2), where n is the length of In. I.e. it has quadratic runtime behaviour for the size of the In list. In is a big list so this matters.
In the following new code, we filter first while generating answers, using fewer lines of code:
public void findCloneLinear(list[str] In, list[str] whatWeSearchFor)
{
for ([*str head, *whatWeSearchFor, *str end] := In)
println("gotcha");
}
The second * operator does not generate a new loop because it is not fresh. It just "pastes" the given list values into the pattern. So now there is actually only one effective * which generates a loop which is the first on head. This one makes the algorithm loop over the list. The second * tests if the elements of whatWeSearchFor are all right there in the list after head (this is linear in the size of whatWeSearchFor and then the last *_ just completes the list allowing for more stuff to follow.
It's also nice to know where the clone is sometimes:
public void findCloneLinear(list[str] In, list[str] whatWeSearchFor)
{
for ([*head, *whatWeSearchFor, *_] := In)
println("gotcha at <size(head)>");
}
Rascal does not have an optimising compiler (yet) which might possibly internally transform your algorithms to equivalent optimised ones. So as a Rascal programmer you are still asked to know the effect of loops on your algorithms complexity and know that * is a very short notation for a loop.
I cannot understand the effectiveness of an algorithm in the Dart SDK.
Here is the algorithm (List factory in dart:core, file list.dart)
factory List.from(Iterable other, { bool growable: true }) {
List<E> list = new List<E>();
for (E e in other) {
list.add(e);
}
if (growable) return list;
int length = list.length;
List<E> fixedList = new List<E>(length);
for (int i = 0; i < length; i ) {
fixedList[i] = list[i];
}
return fixedList;
}
If growable is false then both lists will be created.
List<E> list = new List<E>();
List<E> fixedList = new List<E>(length);
But the creation of list #1 in this case is redundant because it's a duplicate of Iterable other. It just wastes CPU time and memory.
In this case this algorithm will be more efficient because it wont create an unnecessary list # 1 (growable is false).
factory List.from(Iterable other, { bool growable: true }) {
if(growable) {
List<E> list = new List<E>();
for (E e in other) {
list.add(e);
}
return list;
}
List<E> fixedList = new List<E>(other.length);
var i = 0;
for (E e in other) {
fixedList[i++] = e;
}
return fixedList;
}
Or am I wrong and missed some subtleties of programming?
We usually avoid invoking the length getter on iterables since it can have linear performance and side-effects. For Example:
List list = [1, 2, 3];
Iterable iterable1 = list.map((x) {
print(x);
return x + 1;
});
Iterable iterable2 = iterable1.where((x) => x > 2);
var fixedList = new List.from(iterable2, growable: false);
If List.from invoked the length getter it would run over all elements twice (where does not cache its result). It would furthermore execute the side-effect (printing 1, 2, 3) twice. For more information on Iterables look here.
Eventually we want to change the List.from code so that we avoid the second allocation and the copying. To do this we need (internal) functionality that transforms a growable list into a fixed-length list. Tracking bug: http://dartbug.com/9459
It looks like it was just an incremental update to the existing function.
See this commit and this diff
The function started just with
List<E> list = new List<E>();
for (E e in other) {
list.add(e);
}
and had some more bits added as part of a fairly major refactoring of numerous libraries.
I would say that the best thing to do is to raise a bug report on dartbug.com, and either add a patch, or commit a CL - see instructions here: https://code.google.com/p/dart/wiki/Contributing (Note, you do need to jump through some hoops first, but once you're set up, it's all good).
It might also be worth dropping a note to one of the committers or reviewers from the original commit to let them know your plans.
Does a pugixml node object have a number-of-child-nodes method? I cannot find it in the documentation and had to use an iterator as follows:
int n = 0;
for (pugi::xml_node ch_node = xMainNode.child("name"); ch_node; ch_node = ch_node.next_sibling("name")) n++;
There is no built-in function to compute that directly; one other approach is to use std::distance:
size_t n = std::distance(xMainNode.children("name").begin(), xMainNode.children("name").end());
Of course, this is linear in the number of child nodes; note that computing the number of all child nodes, std::distance(xMainNode.begin(), xMainNode.end()), is also linear - there is no constant-time access to child node count.
You could use an expression based on an xpath search (no efficiency guarantees, though):
xMainNode.select_nodes( "name" ).size()
int children_count(pugi::xml_node node)
{
int n = 0;
for (pugi::xml_node child : node.children()) n++;
return n;
}