Could anyone suggest some problems which utilize Dilworth's theorem? Thanks in advance :)
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MDOLLS on SPOJ uses Dilworth's theorem.
Appreciated :D
The classical O(N lg N) algorithm for longest increasing subsequence (LIS) can be seen as an application of Dilworth's Theorem. See here: http://www.geeksforgeeks.org/longest-monotonically-increasing-subsequence-size-n-log-n/
A problem from the third round of 2015 Facebook Hacker Cup
https://www.facebook.com/hackercup/problem/847639175277938/
Solution: https://www.facebook.com/notes/1056536891028878
Another good problem (Dilworth's on longest increasing subsequence) is Cow Jog from USACO December 2014.