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Estimating the running time of programs using the big-oh notation. Using recurrence relations to evaluate the running time of recursive programs.
An algorithm for a particular task can be de ned as \a nite sequence of instructions, each of which has a clear meaning and can be performed with a nite amount of e ort in a nite length of time". As such, an algorithm must be precise enough to be understood by human beings.
We can understand an algorithm’s cost by nding its complexity class: { If T(N) = k, where k is some constant, then we can say T(N) is a constant time algorithm. This is a O(1) algorithm. { If T(N) = kN, where k is some constant, then we can say T(N) is a linear time algorithm. This is a O(N) algorithm.
For simplicity, we compute the running time of an algorithm as a function of the length of the string that represents the input. In worst-case analysis, we consider the longest running time of all inputs of a particular length (that is all we care about in this class)
Analysis of Algorithm 4. Limitations of Experiments. It is necessary to implement the algorithm, which may be difficult. Results may not be indicative of the running time on other inputs not included in the experiment. In order to compare two algorithms, the same hardware and software environments must be used.
We would like to be able to characterize the time it takes to run an algorithm. At first glance it is not obvious how to do so, since there are several different questions one might ask. • What operations are involved in each instruction? For example, in the instruction. x = myVar.myMethod( 2.3*y + a[i], myOtherArg);
Designing better algorithms. Analyzing the asymptotic running time of algorithms is a useful way of thinking about algorithms that often leads to nonobvious improvements. Understanding. An analysis can tell us what parts of an algorithm are crucial for what kinds of inputs, and why.
