Problem 2: Cow Lineup [Brian Dean]
Farmer John has hired a professional photographer to take a picture of some
of his cows. Since FJ's cows represent a variety of different breeds, he
would like the photo to contain at least one cow from each distinct breed
present in his herd.
FJ's N cows are all standing at various positions along a line, each
described by an integer position (i.e., its x coordinate) as well as an
integer breed ID. FJ plans to take a photograph of a contiguous range of
cows along the line. The cost of this photograph is equal its size -- that
is, the difference between the maximum and minimum x coordinates of the
cows in the range of the photograph.
Please help FJ by computing the minimum cost of a photograph in which there
is at least one cow of each distinct breed appearing in FJ's herd.
PROBLEM NAME: lineup
INPUT FORMAT:
* Line 1: The number of cows, N (1 <= N <= 50,000).
* Lines 2..1+N: Each line contains two space-separated positive
integers specifying the x coordinate and breed ID of a single
cow. Both numbers are at most 1 billion.
SAMPLE INPUT (file lineup.in):
6
25 7
26 1
15 1
22 3
20 1
30 1
INPUT DETAILS:
There are 6 cows, at positions 25,26,15,22,20,30, with respective breed IDs
7,1,1,3,1,1.
OUTPUT FORMAT:
* Line 1: The smallest cost of a photograph containing each distinct
breed ID.
SAMPLE OUTPUT (file lineup.out):
4
OUTPUT DETAILS:
The range from x=22 up through x=26 (of total size 4) contains each of the
distinct breed IDs 1, 3, and 7 represented in FJ's herd.