By Conti M., Terracini S., Verzini G.

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**Additional info for Neharis problem and competing species systems**

**Sample text**

Through library routines). Furthermore, the maximum depth of the function callstack should also be a constant, independent of the input. The standard algorithm for depth-first search of a graph is an example of an algorithm that does not perform any dynamic allocation, but uses the function call stack for implicit storage-its space complexity is not 0(1). A streaming algorithm is one in which the input is presented as a sequence of items and is examined in only a few passes (typically just one).

2. Roughly speaking, each pattern corresponds to a design methodology. An algorithm may use a combination of patterns. 2: Algorithm design patterns. Sorting Recursion Divide and conquer Dynamic program- ming The greedy method Incremental improvement Elimination Parallelism Caching Randomization Approximation State Uncover some structure by sorting the input. If the structure of the input is defined in a recursive manner, design a recursive algorithm that follows the input definition. Divide the problem into two or more smaller independent subproblems and solve the original problem using solutions to the subproblems.

This solution can be incrementally improved to make it optimum. This is especially true when a solution has to satisfy a set of constraints. As an example consider a department with n graduate students and n professors. Each student begins with a rank ordered preference list of the professors based on how keen he is to work with each of them. Each professor has a similar preference list of students. Suppose you were asked to devise an algorithm which takes as input the preference lists and outputs a one-to-one pairing of students and advisers in which there are no student-adviser pairs (sO,aO) and (51,a1) such that sOprefers a1 to aD and al prefers sOto sl.