Abstract
This chapter deals with mathematical topics that are recurrent in competitive programming. We will both discuss theoretical results and learn how to use them in practice in algorithms.
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- 1.
While the straightforward \(O(n^3)\) time algorithm is sufficient in competitive programming, there are theoretically more efficient algorithms. In 1969, Strassen [35] discovered the first such algorithm, now called Strassen’s algorithm, whose time complexity is \(O(n^{2.81})\). The best current algorithm, proposed by Le Gall [13] in 2014, works in \(O(n^{2.37})\) time.
- 2.
A deck of cards consists of 52 cards. Each card has a suit (spade \(\spadesuit \), diamond \(\diamondsuit \), club \(\clubsuit \), or heart \(\heartsuit \)) and a value (an integer between 1–13).
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Laaksonen, A. (2020). Mathematics. In: Guide to Competitive Programming. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-39357-1_11
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DOI: https://doi.org/10.1007/978-3-030-39357-1_11
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Online ISBN: 978-3-030-39357-1
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