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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

Digital information is stored using a series of ones and zeros. computers are digital machines because they can only read information as on or off –1 or 0. this method of computation is known as the system

Carlos, an algebra teacher, is creating a series of powerpoint presentations to use during class lectures. after writing, formatting, and stylizing the first presentation, he would like to begin writing the next presentation. he plans to insert all-new content, but he wants to have the same formatting and style as in the first one. what would be the most efficient way for carlos to begin creating the new presentation? going under the file tab and opening the first presentation, deleting all content from each page, and adding new content going under the file tab and clicking on new in the left pane, then choosing new from existing going under the design tab and clicking on themes, then selecting the theme that was used for the first template going under the design tab and opening the template that was created for the first presentation