Compute every possible combination of numbers [duplicate] - objective-c

Question

This question already has answers here:
combinations of a set with given number elements
(2 answers)
Closed 9 years ago.
I have 9 tiles labeled 1-9 with corresponding values. Tile 1=1, tile 6=6, etc. A user can press down tiles that equal the sum of the die. When they press confirm move, those tales can not be used anymore.
I need to compute every possible combination of numbers to check whether or not the user can go again. Currently I am computing it like this, but I'm sure there has to be a better way.
allTiles contains the tiles that are still available to be computed.
What would be the best way to check for all combinations?
- (void) getCombinations {
NSMutableArray *combinations = [[NSMutableArray alloc] init];
for (int i = 0; i < [allTiles count]; i++) {
for (int j = i + 1; j < [allTiles count]; j++) {
for (int k = i+2; k < [allTiles count]; k++) {
TileView *first = [allTiles objectAtIndex:i];
TileView *second = [allTiles objectAtIndex:j];
TileView *third = [allTiles objectAtIndex:k];
NSNumber *total = [NSNumber numberWithInt:first.getTileValue + second.getTileValue];
NSNumber *total2 = [NSNumber numberWithInt:
first.getTileValue +
second.getTileValue +
third.getTileValue];
[combinations addObject:[NSNumber numberWithInt:first.getTileValue]];
[combinations addObject:[NSNumber numberWithInt:second.getTileValue]];
[combinations addObject:[NSNumber numberWithInt:third.getTileValue]];
[combinations addObject:total];
[combinations addObject:total2];
}
}
}
if ([combinations containsObject:[NSNumber numberWithInt:[self diceTotal]]]) {
NSLog(#"STILL COMBINATION AVAILABLE");
}
else {
NSString *message = [NSString stringWithFormat:#"Your score: %i", player1Score];
UIAlertView *alert = [[UIAlertView alloc]
initWithTitle:#"No more combinations left."
message: message
delegate:self
cancelButtonTitle:#"Go to player2"
otherButtonTitles: nil];
[alert show];
[alert release];
}
}
Here is a a screenshot of one of scenarios where my method doesn't work.

Answer 1

In your example, there are four tiles available to the player. Whether or not to include a tile is a binary choice (YES or NO), and there are 4 such choices in this example, so there are 2×2×2×2 = 24 possible combinations of tiles. In general, there are 2n combinations where there are n tiles available.
The simplest way to check for a combination that sums to your target is simply to enumerate the integers from 0 through 2n. For each integer i, write i in binary and add up the tile values of the tiles corresponding to the 1's of the binary representation.
We'll cache the tile values in a local array to avoid sending the tileValue message over and over.
static int selectedNumbersSum(unsigned int selector, int const *numbers) {
int sum = 0;
for (int i = 0; selector != 0; i += 1, selector >>= 1) {
if (selector & 1) {
sum += numbers[i];
}
}
return sum;
}
static BOOL tilesCanMakeTarget(NSArray *tiles, int target) {
NSUInteger count = tiles.count;
int numbers[count];
for (int i = 0; i < count; ++i) {
numbers[i] = [tiles[i] tileValue];
}
for (unsigned int step = 0, maxStep = 1 << count; step < maxStep; ++step) {
if (selectedNumbersSum(step, numbers) == target)
return YES;
}
return NO;
}
- (void)checkForEndOfPlayer1Turn {
if (tilesCanMakeTarget(allTiles, self.diceTotal)) {
NSLog(#"STILL COMBINATION AVAILABLE");
} else {
NSString *message = [NSString stringWithFormat:#"Your score: %i",
player1Score];
UIAlertView *alert = [[UIAlertView alloc]
initWithTitle:#"No more combinations left."
message:message delegate:self cancelButtonTitle:#"Go to player 2"
otherButtonTitles:nil];
[alert show];
[alert release];
}
}
Incidentally, we don't usually start our getter method names with get. Your getCombinations method should probably be called checkCombinations (or something like that) since it's not even a getter. And your getTileValue method should just be called tileValue.