Inputs: vector q below and c = 0.8

Here is how the vectors r, X, and Y are computed, resulting in 4 maximal regions of q that each have density at least 0.8 of 1's:

      0    1    1    1    0    1    1    1    1    1    0    1    1    0    1    1    1    0    1    1    0    1   q
     -.8   .2   .2   .2  -.8   .2   .2   .2   .2   .2  -.8   .2   .2  -.8   .2   .2   .2  -.8   .2   .2  -.8   .2  q-.8
0.0  -.8  -.6  -.4  -.2 -1.0  -.8  -.6  -.4  -.2  0.0  -.8  -.6  -.4 -1.2 -1.0  -.8  -.6 -1.4 -1.2 -1.0 -1.8 -1.6  r
0.0  -.8  -.8  -.8  -.8 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.2 -1.2 -1.2 -1.2 -1.4 -1.4 -1.4 -1.8 -1.8  X
0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  -.4  -.4  -.4  -.6  -.6  -.6  -.6 -1.0 -1.0 -1.0 -1.6 -1.6  Y
     ________________________________________________
                       8/10 = 0.8
          ______________________________________________________________________________
                                          13/16 = 0.8125
                              _________________________________________________________________________
                                                               12/15 = 0.8
                                                                                                              ___
                                                                                                              1.0