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Some of your friends have gotten into the burgeoning field of time-series data mining, in which one looks for patterns in sequences of events that occur over time. purchases at stock exchanges--what’s being bought-- are one source of data with a natural ordering in time. given a long sequence s of such events, your friends want an efficient way to detect certain "patterns" in them--for example, they may want to know if the four events buy yahoo, buy ebay, buy yahoo, buy oracle occur in this sequence s, in order but not necessarily consecutively. they begin with a collection of possible events (e.g., the possible’ transactions) and a sequence s of n of these events. a given event may occur multiple times in s (e.g., yahoo stock may be bought many times in a single sequence s). we will say that a sequence s’ is a subsequence of s if there is a way to delete certain of the events from s so that the remaining events, in order, are equal to the sequence s’. so, for example, the sequence of four events above is a subsequence of the sequence buy amazon, buy yahoo, buy ebay, buy yahoo, buy yahoo, buy oracle their goal is to be able to dream up short sequences and quickly detect whether they are subsequences of s. so this is the problem they pose to you: give an algorithm that takes two sequences of even~s--s’ of length m and s of length n, each possibly containing an event more than once--and decides in time o(m n) whether s’ is a subsequence of s

Match the personality traits with their description

Petrică, tânăr licean în clasa a ix-a, a primit în dar de la părinţii săi un cont bancar pentru micile sale cheltuieli curente. el este pasionat de internet banking şi îşi verifică cu grijă toate tranzacţiile efectuate. pentru creşterea securităţii tranzacţiilor online, banca îi furnizează lui petrică un număr pe care el va trebui să îl modifice, obţinând un număr tan – număr de autentificare a tranzacţiei (transaction authentication number). regula de obţinere a numărului tan este următoarea: se formează cel mai mic număr par din toate cifrele numărului furnizat de bancă. cerinţă cunoscând numărul n furnizat de bancă, să se determine numărul tan obţinut de petrică. date de intrare fişierul tan.in conţine pe prima linie numărul natural n cu semnificaţia din enunţ. date de ieşire fişierul de ieşire tan.out va conţine o singură linie pe care va fi scris numărul tan cerut. restricţii • 0 < n < 18*1018 • n are cel puţin o cifră pară • numărul tan obţinut nu poate conţine zerouri nesemnificative