Algorithm Help

[aries0152]

Problem: I have coordinates of of two side of the rectangles-



Suppose I have coordinates of 5000 boxes. Like this-

         (    x1,    y1)    (    x2,    y2)     
         (0.0000,0.0000)    (0.3412,0.4175)     
         (0.7445,0.0000)    (1.0000,0.6553)     
         (0.7445,0.6553)    (1.0000,1.0000)     
         (0.0000,0.6553)    (0.7445,1.0000)     
         (0.3412,0.0000)    (0.7445,0.4175)     
         (0.3412,0.4175)    (0.7445,0.6553)     
         (0.0000,0.4175)    (0.3412,0.6553) ...etc

These coordinates subdivide an unit squre like this -



I want to calculate the number of nearest rectangles for each of the boxes using c++.

Example
For rectangle# 7 the nearest boxes are- 4,1,6 and 2
(If they share only corner they are not consider as nearest boxes, So rectangle 5 & 3 are not nearest of rectangle 7)

Can anyone help me how can I write the algorithm for this problem?

[oogabooga]

If two boxes are touching, they must be along the same vertical or horizontal line:

.        |-----
         |     |
         |  C  |
         |     |
     ----|-----
    | A  |
    |    |
     ----|
         |
         |----
         |    |
   ------| D  |
  |      |    |
  |   B  |    |
  |      |----
  |      |
   ------|
         |

A and D do not touch at all. A and C only touch at the corners. B and D touch at more than just corners. The kinds of comparisons you'd make to separate the cases are obvious.