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1 of 51 Interaction public int countCookiesEaten(Bowl bowl) { if (bowl.isEmpty()) { return 0; } else { this.eatCookie(bowl); return this.countCookiesEaten(bowl) + 1; }

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2 of 51 Big-O and Sorting Lecture 15

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3 of 51 Importance of Algorithm Analysis 1/2 Performance of an algorithm often refers to how quickly it executes and/or how much memory it needs o performance matters when the data grows in size! o can observe and/or analyze, then tune or revise algorithm Algorithm analysis is so important that every Brown CS student is required to take at least one course covering it

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4 of 51 Importance of Algorithm Analysis 2/2 Many important factors that make performance important o computing resources o implementation (like machine, language) o size of data, denoted N number of elements to be sorted number of elements in ArrayList to iterate through ex: much faster to search through CS15 course-list than the Social Security Database This lecture: a brief introduction to Algorithm Analysis! Goal: learning how to maximize efficiency of an algorithm and conserve resources

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5 of 51 Runtime The runtime of an algorithm varies with the input and typically grows with the input size In most of computer science we focus on the worst case running time. o easier to analyze and important for unforeseen inputs Average case is what will happen most often. Best case requires the least amount of work and is the best situation you could have. o average case is also important, best case is interesting but not insightful How to determine runtime? o by inspecting pseudocode, can determine the number of statements executed by an algorithm as a function of input size o allows us to evaluate approximate speed of an algorithm independent of the hardware or software environment o memory use may be even more important for small and embedded devices

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6 of 51 Elementary Operations Algorithmic time is measured in elementary operations o math (+, -, *, /, max, min, log, sin, cos, abs,...) o comparisons ( ==, >,