Problem B: Saskatchewan
The province of Saskatchewan is surveyed in sections.
A section is a square mile of land. Grid roads delimit sections; there is
one north-south and one east-west road exactly every mile. (Complications
arise because of the curvature of the earth but you can disregard these
and assume that the province is a plane.) The provincial border is
a polygon whose vertices correspond to the intersections of grid roads.
However, the edges do not necessarily follow grid roads; some sections are cut by the border. Your
job is to compute how many sections are completely within a province like
Saskatchewan.
Standard input contains a series of no more than 100 coordinate pairs,
one pair per line. These coordinates give the vertices of the perimeter of the
province; the border is formed by connecting them in order. All coordinates
are in the first quadrant; they range from 0 to 100,000.
Your output should be a single integer: the number of sections
(i.e. unit squares with corners at integer coordinates)
fully contained within the
province.
Sample Input
0 0
0 100000
99999 100000
100000 0
Output for Sample Input
9999900000