USACO 2011 November Contest, Silver Division 2- Cow Lineup > 문제은행 : 정보올림피아드&알고리즘

3738 : Cow Lineup

1000 ms   
128 MB   
0 회   
0 회   


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.​


* 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.​


* Line 1: The smallest cost of a photograph containing each distinct breed ID.​

입력 예

25 7
26 1
15 1
22 3
20 1
30 1

출력 예




There are 6 cows, at positions 25,26,15,22,20,30, with respective breed IDs 7,1,1,3,1,1.​





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.​

경기도 안양시 동안구 평촌대로 109 협성골드프라자 601호

TEL : 031-360-4144 FAX : 031-388-0996 E-mail :,

Copyrightⓒ 2010 jungol. All right reserved.