To calculate the distance, rotate the square and the point so that the diagonal (if it is not a zero vector) becomes parallel to (1,1). In this case sides of the square are parallel to axes and the distance is trivial to calculate.

The problem can be solved without floating point operations: the square of the distance is a rational number. But note that to compare (an/ad < bn/bd) you cannot use (an*bd < bn*ad) since the products can overflow 64-bit integers. Instead first compare the integer parts, and in case they are equal to the same number, subtract this number from both parts and compare the results using multiplication (denominators are 32-bit integers).

Nice solution !

Edited by author 11.02.2011 15:53