Question

I have an NSMutable array of N elements. Each element is also an NSMutable array of k NSNumbers. In other words a table with variable length columns.

I need to generate a new array containing all the possible ways of selecting one element per column.

Example:

1 1 1 1 1 1
2         2

Result:

1 1 1 1 1 1
2 1 1 1 1 1
1 1 1 1 1 2
2 1 1 1 1 2

Answer 1

The following method will iterate through the possible column indices that you want to take, beginning with [0,0,...,0]:

-(NSMutableArray *)nextIndex:(NSMutableArray *)prevIndex {
    NSMutableArray newIndex = [NSMutableArray arrayWithArray:prevIndex];
    int numCols = [bigArray count];
    for (int i=numCols-1; i>=0; --i) {
        if ([[prevIndex objectAtIndex:i] intValue] < [[bigArray objectAtIndex:i] count]-1) {
            [newIndex replaceObjectAtIndex:i withObject:[NSNumber numberWithInt:[[prevIndex objectAtIndex:i] intValue]+1]];
            for (int j=i+1; j<numCols; ++j) {
                [newIndex replaceObjectAtIndex:j withObject:[NSNumber numberWithInt:0]];
            }
            return newIndex;
        }
    }
    return nil;
}

To use it, do something along these lines:

-(NSMutableArray*)matrixArray {
    NSMutableArray *matrix = [[NSMutableArray alloc] init];
    NSMutableArray *index = [[NSMutableArray alloc] init];
    NSMutableArray *values = [[NSMutableArray alloc] init];
    int numCols = [bigArray count];
    for (int i=0; i<numCols; ++i) {
        [index addObject:[NSNumber numberWithInt:0]];
    }
    while (index != nil) {
        [values removeAllObjects];
        for (int i=0; i<numCols; ++i) {
            [values addObject:[bigArray objectAtIndex:[index objectAtIndex:i]]];
        }
        [matrix addObject:values];
        index = [self nextIndex];
    }
    return [matrix autorelease];
}

Note that I did not test or debug this code, it’s just to give you an idea of what to do.