I'm trying to generate a sudoku board, and although I can generate a solution, I now need to remove squares that a user can then fill in. In order to do this, I'd like to use backtracking to check each time that I remove a square, the board is
1. still solvable and 2. has only one solution.
The Problem
When I test my backtracking algorithm on this board (where the zeroes are empty squares), it returns this solution. Obviously I would prefer not to end up with several 9s in the first row, for example.
My Code
- (BOOL) solveArray: (NSArray*) numArray {
NSMutableArray* board = [numArray mutableCopy];
for (int i=0; i<9; i++) { //make all of the arrays mutable as well (since it's 2D)
[board replaceObjectAtIndex:i withObject:[board[i] mutableCopy]];
}
//if everything is filled in, it's done
if (![self findUnassignedLocation:board]) {
NSLog(#"\n%#", [SudokuBoard sudokuBoardWithArray:board]);
return TRUE;
}
NSArray* poss = [[SudokuBoard sudokuBoardWithArray:board] possibleNumbersForRow:self.arow Col:self.acol];
//if there are no options for a location, this didn't work.
if ([poss count] == 0) {
return FALSE;
}
//otherwise, continue recursively until we find a solution
else {
for (int i=0; i<[poss count]; i++) {
//make a tentative assignment
board[self.arow][self.acol] = poss[i];
//return, if successful, done
if ([self solveArray:board]) {
return TRUE;
}
//if that didn't work, unmake it and retry with other options
board[self.arow][self.acol] = [NSNumber numberWithInt:0];
}
}
return FALSE;
}
Any thoughts on where I might be going wrong?
Each level of recursion needs its own row and column variables. That is, row and column should be inputs to solveArray and outputs of findUnassignedLocation instead of being member variables. As it is, when there is backtracking the row and column of the failed level get reused by the caller.
Given that some assigned locations are being overwritten, maybe findUnassignedLocation also contains an error.
Given that the result is invalid, maybe possibleNumbersForRow also contains an error.
Related
I have an array in an old objective-C app that I am using to learn more "complicated" coding. It is back from the old days of OS X and was very much broken. I have gotten it to work (mostly)! However, the app has an NSMutableArray of images, 7 in total. I use a random number generator to insert the images on the screen, some code to allow them to fall, and then, using screen bounds, when they reach "0" on the Y axis they are removed from the array.
I initially just had:
if( currentFrame.origin.y+currentFrame.size.height <= 0 )
{
[flakesArray removeObject:myItem];
I have read when removing objects from an array it is best practice to iterate in reverse...so I have this bit of code:
for (NSInteger i = myArray.count - 1; i >= 0; i--)
{ //added for for statement
if( currentFrame.origin.y+currentFrame.size.height <= 0 )
{
[myArray removeObjectAtIndex:i];
}
Sadly both methods result in the same mutated while enumerated error. Am I missing something obvious?
If I add an NSLog statement I can get, I think, the index of the item that needs to be removed:
NSLog (#"Shazam! %ld", (long)i);
2017-01-07 14:39:42.086667 MyApp[45995:7500033] Shazam! 2
I have looked through a lot and tried several different methods including this one, which looks to be the most popular with the same error.
Thank you in advance! I will happily provide any additional information!
Adding more:
Sorry guys I am not explicitly calling NSFastEnumeration but I have this:
- (void) drawRectCocoa:(NSRect)rect
{
NSEnumerator* flakesEnum = [flakesArray objectEnumerator];
then
for( i = 0; i < numberToCreate; i++ )
{
[self newObject:self];
}
while( oneFlake = [flakesEnum nextObject] )
It is here where:
if( currentFrame.origin.y+currentFrame.size.height <= 0 )
{
NSLog (#"Shazam! %i", oneFlake);
[flakesArray removeObject:oneFlake];
}
Thank you all. I am learning a lot from this discussion!
There are two ways to go: (1) collect the objects to remove then remove them with removeObjectsInArray:.
NSMutableArray *removeThese = [NSMutableArray array];
for (id item in myArray) {
if (/* item satisfies some condition for removal */) {
[removeThese addObject:item];
}
}
// the following (and any other method that mutates the array) must be done
// *outside of* the loop that enumerates the array
[myArray removeObjectsInArray:removeThese];
Alternatively, reverseObjectEnumeration is tolerant of removes during iteration...
for (id item in [myArray reverseObjectEnumerator]) {
if (/* item satisfies some condition for removal */) {
[myArray removeObject: item];
}
}
As per the error, you may not mutate any NSMutableArray (or any NSMutable... collection) while it is being enumerated as part of any fast enumeration loop (for (... in ...) { ... }).
#danh's answer works as well, but involves allocating a new array of elements. There are two simpler and more efficient ways to filter an array:
[array filterUsingPredicate:[NSPredicate predicateWithBlock:^(id element, NSDictionary<NSString *,id> *bindings) {
// if element should stay, return YES; if it should be removed, return NO
}];
or
NSMutableIndexSet *indicesToRemove = [NSMutableIndexSet new];
for (NSUInteger i = 0; i < array.count; i += 1) {
if (/* array[i] should be removed */) {
[indicesToRemove addIndex:i];
}
}
[array removeObjectsAtIndexes:indicesToRemove];
filterUsingPredicate: will likely be slightly faster (since it uses fast enumeration itself), but depending on the specific application, removeObjectsAtIndexes: may be more flexible.
No matter what, if you're using your array inside a fast enumeration loop, you will have to perform the modification outside of the loop. You can use filterUsingPredicate: to replace the loop altogether, or you can keep the loop and keep track of the indices of the elements you want to remove for later.
Here is my Objective-C implementation of a disjoint set.
- Positive number point to parent.
- Negative number indicate root & children count. (So they each start disjointed at -1.)
- The index acts as the data I am grouping.
Seems to work ok... just had a couple questions.
find: How can I compress the path? Because I am not doing it recursively, do I have to store the path and loop it again to set after find root?
join: I am basing join on children count instead of depth!? I guess that is not right. Do I need to do something special during join if depths equal?
Thanks.
DisjointSet.h
#interface DisjointSet : NSObject
{
NSMutableArray *_array;
}
- (id)initWithSize:(NSInteger)size;
- (NSInteger)find:(NSInteger)item;
- (void)join:(NSInteger)root1 root2:(NSInteger)root2;
#end
DisjointSet.m
#import "DisjointSet.h"
#implementation DisjointSet
- (id)initWithSize:(NSInteger)size
{
self = [super init];
if (self)
{
_array = [NSMutableArray arrayWithCapacity:size];
for (NSInteger i = 0; i < size; i++)
{
[_array addObject:[NSNumber numberWithInteger:-1]];
}
}
return self;
}
- (NSInteger)find:(NSInteger)item
{
while ([[_array objectAtIndex:item] integerValue] >= 0)
{
item = [[_array objectAtIndex:item] integerValue];
}
return item;
}
- (void)join:(NSInteger)root1 root2:(NSInteger)root2
{
if (root1 == root2) return;
NSInteger data1 = [[_array objectAtIndex:root1] integerValue];
NSInteger data2 = [[_array objectAtIndex:root2] integerValue];
if (data2 < data1)
{
[_array setObject:[NSNumber numberWithInteger:data2 + data1] atIndexedSubscript:root2];
[_array setObject:[NSNumber numberWithInteger:root2] atIndexedSubscript:root1];
}
else
{
[_array setObject:[NSNumber numberWithInteger:data1 + data2] atIndexedSubscript:root1];
[_array setObject:[NSNumber numberWithInteger:root1] atIndexedSubscript:root2];
}
}
#end
For the find operation, there is no need to store the path (separately from your _array) or to use recursion. Either of those approaches requires O(P) storage (P = path length). Instead, you can just traverse the path twice. The first time, you find the root. The second time, you set all of the children to point to the root. This takes O(P) time and O(1) storage.
- (NSInteger)findItem:(NSInteger)item {
NSInteger root;
NSNumber *rootObject = nil;
for (NSInteger i = item; !rootObject; ) {
NSInteger parent = [_array[i] integerValue];
if (parent < 0) {
root = i;
rootObject = #(i);
}
i = parent;
}
for (NSInteger i = item; i != root; ) {
NSInteger parent = [_array[i] integerValue];
_array[i] = rootObject;
i = parent;
}
return root;
}
For the merge operation, you want to store each root's rank (which is an upper bound on its depth), not each root's descendant count. Storing each root's rank allows you to merge the shorter tree into the taller tree, which guarantees O(log N) time for find operations. The rank only increases when the trees to be merged have equal rank.
- (void)joinItem:(NSInteger)a item:(NSInteger)b {
NSInteger aRank = -[_array[a] integerValue];
NSInteger bRank = -[_array[b] integerValue];
if (aRank < bRank) {
NSInteger t = a;
a = b;
b = t;
} else if (aRank == bRank) {
_array[a] = #(-aRank - 1);
}
_array[b] = #(a);
}
You definitely should implement path compression using recursion. I would not even think about trying to do it non-recursively.
Implementing the disjoin-set datastructure should be very easy, and can be done in few lines. Its very, very easy to translate it from the pseudocode to any programming language. You can find the pseudocode on Wikipedia. (Unfortunately, I can't read Objective-C, so I cannot really judge wether your code is correct or not).
Yes. To implement highest ancestor compression without recursion you need to maintain your own list. Make one pass up the chain to get pointers to the sets that need their parent pointers changed and also to learn the root. Then make a second pass to update the necessary parent pointers.
The recursive method is doing the same thing. The first pass is the "winding up" of the recursion, which stores the sets needing parent pointer updates on the program stack. The second pass is in reverse as the recursion unwinds.
I differ with those who say the recursive method is always best. In a reasonable number systems (especially embedded ones), the program stack is of limited size. There are cases where many unions are performed in a row before a find. In such cases, the parent chain can be O(n) in size for n elements. Here collapsing by recursion can blow out the stack. Since you are working in Objective C, this may be iOS. I do not know the default stack size there, but if you use recursion it's worth looking at. It might be smaller than you think. This article implies 512K for secondary threads and 1Mb for the main thread.
Iterative, constant space alternative
Actually the main reason I'm writing is to point out that you still get O(log^* n) for n ammortized operations -- just a shade less efficient than collapsing, and still effectively O(1) -- if you only do factor-of-two compression: in the find operation, change parent pointers so that they point to the grandparents instead instead of the root. This can be done with iteration in constant storage. This lecture at Princeton talks about this algorithm and implements it in a loop with 5 lines of C. See slide 29.
Annoying newbie problem here. This variable isPlayerTouchingAnotherPlayer is being set to true as soon as I touch the piece. I'm almost positive I know why but I can't find a way to display this in log to confirm. I could probably do it by setting different flag numbers for each of the objects but I was hoping there is another way.
The problem is that piece is an object that is also located in p1Array so as soon as I touch it it hits itself and isPlayerTouchingAnotherPlayer is evaluated to true.
Is there a way I could print out the view or image name of the objects touching somehow to confirm this? And furthermore, is there a way to somehow avoid this annoying conflict.
for (int i = 0; i <[p1Array count]; i++) {
UIImageView *tempP1;
tempP1 =[p1Array objectAtIndex:i];
if (CGRectIntersectsRect(piece.frame, tempP1.frame)) {
NSLog(#"selected piece: %#, touched piece: %# ", piece, tempP1);
isPlayerTouchingAnotherPlayer = TRUE;
}
}
why not use fast enumeration and skip the image view you are not interested in checking.
for (UIImageView *imageView in p1Array) {
if (imageView == piece)
continue;
if (CGRectIntersectsRect(imageView.frame, piece.frame)) {
// do whatever
}
}
it seems like you are already printing out the names of the objects touching in the code sample you have provided. if you want to print out specific properties of the objects you can do that to.
as soon as i touch it it hits itself and isPlayerTouchingAnotherPlayer
is evaluated to true.
Then you should get a log message that shows the same object for the selected piece and the touched piece. If that's what's happening, then just add a condition to your if to prevent it:
if (piece != tempP1 && CGRectIntersectsRect(piece.frame, tempP1.frame)) {
Simply
NSLog(#"%# %#", piece, tempP1);
or
NSLog(#"%ld %ld", (NSInteger) piece, (NSInteger) tempP1);
The first will show you the description of the object, the second the address in memory, if it's same address, it's the same object.
You can simply check if it's the same object (pointer) with a simple equal check to exclude the same object :
if (piece != tempP1) {
if (CGRectIntersectsRect(piece.frame, tempP1.frame)) {
...
}
Furthermore, you would like to write this:
for ( int i = 0;
( ( i < [p1Array count] )
&& ( ! isPlayerTouchingAnotherPlayer )
);
i++
) {
...
}
What is the best way to "slice" an NSArray from the end, rather than the beginning, of the array (for example, finding the subarray containing the last few elements of a NSArray of unknown length)? In Python, you can use negative indices to accomplish this, e.g.:
new_list = old_list[-5:-3]
What's the most natural way to do this in Objective-C?
There's nothing to match Python's nice syntax for this, but you could do:
NSUInteger count = [myArray count];
NSArray * slice = [myArray subarrayWithRange:(NSRange){count-n, n}];
You could also write up a category for NSArray, something like:
#interface NSArray (jrdioko_slice)
- (NSArray *) jrdioko_sliceFrom:(NSInteger)start to:(NSInteger)stop;
#end
If you want to go this route, the Python source will certainly repay study. A list object creates a slice object when a slice operation is performed. The relevant method on a slice object is PySlice_GetIndicesEx. You'll just have to be careful turning those indexes into an NSRange. As the comment in that function warns "this is harder to get right than you might think". (I'll try to take a crack at this later.)
UPDATE: Here we have a slice category on NSArray. The index calculation logic is pretty much straight out of the Python code that I linked to above.* It's actually a lot easier than I thought at first if you don't have to worry about the stride part of a Python slice. I've run this through a few tests and it seems to work the same as the Python version.
#interface NSArray (WSS_Slice)
- (NSArray *)WSS_arrayBySlicingFrom:(NSInteger)start to:(NSInteger)stop;
#end
// Python allows skipping any of the indexes of a slice and supplies default
// values. Skipping an argument to a method is not possible, so (ab)use
// NSNotFound as "not specified" index value. The other way to do this would
// be with varargs, which might be even handier if one decided to implement
// the stride functionality.
enum {
WSS_SliceNoIndex = NSNotFound
};
#implementation NSArray (WSS_Slice)
- (NSArray *)WSS_arrayBySlicingFrom:(NSInteger)start to:(NSInteger)stop {
// There's an important caveat here: specifying the parameters as
// NSInteger allows negative indexes, but limits the method's
// (theoretical) use: the maximum size of an NSArray is NSUIntegerMax,
// which is quite a bit larger than NSIntegerMax.
NSUInteger count = [self count];
// Due to this caveat, bail if the array is too big.
if( count >= NSIntegerMax ) return nil;
// Define default start and stop
NSInteger defaultStart = 0;
NSInteger defaultStop = count;
// Set start to default if not specified
if( start == WSS_SliceNoIndex ){
start = defaultStart;
}
else {
// If start is negative, change it to the correct positive index.
if( start < 0 ) start += count;
// Correct for out-of-bounds index:
// If it's _still_ negative, set it to 0
if( start < 0 ) start = 0;
// If it's past the end, set it to just include the last item
if( start > count ) start = count;
}
// Perform all the same calculations on stop
if( stop == WSS_SliceNoIndex ){
stop = defaultStop;
}
else {
if( stop < 0 ) stop += count;
if( stop < 0 ) stop = 0;
if( stop > count ) stop = count;
}
// Calculate slice length with corrected indexes
NSInteger sliceLength = stop - start;
// If no slice, return a new empty array
if( sliceLength <= 0 ){
return [NSArray array];
}
else {
return [self subarrayWithRange:(NSRange){start, sliceLength}];
}
}
#end
*Therefore I think I need to include a link to the Python License and also note that this may still be “Copyright © 2001-2010 Python Software Foundation; All Rights Reserved”, because although this looks to me like a separately-copyrightable derivative work, I ain't a lawyer.
I am interfacing with a hardware device that streams data to my app over Wifi. The data is streaming in just fine. The data contains a character header (DATA:) that indicates a new record has begun. The issues is that the data I receive doesn't necessarily fall on the header boundary, so I have to capture the data until what I've captured contains the header. Then, everything that precedes the header goes into the previous record and everything that comes after it goes into a new record. I have this working, but wondered if anyone has done this before and has a good computer-sciencey way to solve the problem.
Here's what I do:
Convert the NSData of the current read to an NSString
Append the NSString to a placeholder string
Check placeholder string for the header (DATA:). If the header is not there, just wait for the next read.
If the header exists, append whatever precedes it to a previous record placeholder and hand that placeholder off to an array as a complete record that I can further parse into fields.
Take whatever shows up after the header and place it in the record placeholder so that it can be appended to in the next read. Repeat steps 3 - 5.
Let me know if you see any flaws with this or have a suggestion for a better way.
Seems there should be some design pattern for this, but I can't think of one.
Thanks.
UPDATE: Here is a little bit of code:
uint8_t buf[1024];
unsigned int len = 0;
len = [(NSInputStream *)stream read:buf maxLength:1024];
if(len) {
[data appendBytes:(const void *)buf length:len];
int bytesRead;
bytesRead += len;
} else {
NSLog(#"No data.");
}
How would this code be changed then to implement a finite state machine?
That seems pretty much how I'd do it. The only thing I might do differently is write an NSData category that does the linear search of DATA: for me, just to save the overhead of converting it to a string. It wouldn't be that hard to do, either. Something like:
#interface NSData (Search)
- (NSRange) rangeOfData:(NSData *)aData;
#end
#implementation NSData (Search)
- (NSRange) rangeOfData:(NSData *)aData {
const void * bytes = [self bytes];
NSUInteger length = [self length];
const void * searchBytes = [aData bytes];
NSUInteger searchLength = [aData length];
NSUInteger searchIndex = 0;
NSRange foundRange = {NSNotFound, searchLength};
for (NSUInteger index = 0; index < length; index++) {
if (bytes[index] == searchBytes[searchIndex]) {
//the current character matches
if (foundRange.location == NSNotFound) {
foundRange.location = index;
}
searchIndex++;
if (searchIndex >= searchLength) { return foundRange; }
} else {
searchIndex = 0;
foundRange.location = NSNotFound;
}
}
return foundRange;
}
#end
Then you can just use:
NSData * searchData = [#"DATA:" dataUsingEncoding:NSUTF8StringEncoding];
while(receivingData) {
if ([receivedData rangeOfData:searchData].location != NSNotFound) {
//WOOO!
}
}
(warning: typed in a browser)
This is a classic finite state machine problem. A lot of data protocols that are stream based can be described with a finite state machine.
Basically you have a state, and transition. Boost has a finite state machine library, but it could be overkill. You can implement it as a switch.
while(stream.hasData) {
char nextInput = stream.get();
switch(currentState) {
case D: {
if(nextInput == A)
currentState = A;
else
currentState = D; //die
} case A: {
//Same for A
}
}
}
Requested elaboration:
Basically look at the diagram below...it's a finite state machine. At any given time the machine is in exactly one state. Every time a character is input into the state machine a transition is taken, and the current state moves. (possibly back into the same state). So all you have to do is model your networked data as a finite state machine then implement that machine. There are libraries that lay it out for you, then all you have to do is implement exactly what happens on each transition. For you that you probably mean interpreting or saving the byte of data. The interpretation depends on what transition. The transition depends on the current state and the current input. Here is an example FSM.
alt text http://www.freeimagehosting.net/uploads/b1706f2a8d.png
Note that if the characters DATA: are entered the state moves to the last circle. Any other sequence will keep the state in one of first 5 states. (top row) You can also have splits. So the FSM can make decisions, so if you get a sequence like DATA2: then you can branch off of that machine into the data2: part and interpret differently in a totally different part of the machine.