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CPSC 320 Intermediate Algorithm Design And Analysis Assignment Sample UBC Canada
CPSC 320 Intermediate Algorithm Design and Analysis Assignment Answers that cover important topics in designing and analyzing algorithms. CPSC 320 Assessment Samples begins with a review of elementary data structures, such as arrays, linked lists, stacks, queues, and trees. It then moves on to more advanced data structures, such as heaps, disjoint sets, sorting networks, and shortest path algorithms. After discussing data structures, CPSC 320 Assignment Answers turns to algorithm design techniques, such as divide-and-conquer algorithms, greedy algorithms, dynamic programming algorithms, and amortized analysis. Finally, CPSC 320 Assignment Sample covers several important topics in algorithm analysis, including running time analysis, average-case analysis, and worst-case analysis.
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Assignment Activity 1: Come up with clear problem formulations, given poorly specified computational tasks.
Problem formulations are important in all areas of computer science, but they are especially important in the study of algorithms. In this assignment, you will be asked to come up with clear problem formulations for a number of computational tasks.
For each task, first come up with a brief description of the task, and then state the problem that needs to be solved in order to complete the task. Be as specific as possible in your problem formulation.
Assignment Activity 2: Recognize which algorithm design technique, such as brute force, divide and conquer, greedy, or dynamic programming is used in a given algorithm.
There are many algorithm design techniques out there, but the most common one is brute force, divide and conquer. This technique involves splitting a problem into smaller subproblems, solving those subproblems, and then combining the solutions to get the solution to the original problem. Other popular techniques include greedy algorithms and dynamic programming.
- Brute force: A brute force algorithm is one that simply tries every possible solution until it finds the correct one.
- Divide and conquer: A divide and conquer algorithm is one that divides the problem into smaller subproblems, solves each subproblem, and then combines the solutions to the subproblems to solve the original problem.
- Greedy: A greedy algorithm is one that makes the locally optimal choice at each step in the hope of finding the global optimum.
- Dynamic programming: A dynamic programming algorithm is one that breaks the problem down into smaller subproblems, solves each subproblem, and then remembers the solutions to the subproblems so that they can be reused when solving the original problem.
Assignment Activity 3: Evaluate which design technique and/or data structures can be used to solve a given problem efficiently.
There are a variety of design techniques and data structures that can be used to solve a given problem efficiently. The best approach depends on the specific details of the problem at hand. However, some general tips that can be useful include:
- Identifying the most important inputs and outputs for the problem.
- Determining what operations need to be performed on the data.
- Select an appropriate data structure that can efficiently store and manipulate the data.
- designing algorithms that can operate on the data in the chosen data structure(s).
One common way to solve a problem efficiently is to use a data structure that is specifically designed for the type of data involved. For example, if the data is a list of numbers, then using a sorted array or linked list can be more efficient than using an unsorted array. Another approach is to use an algorithm that is designed to work with the chosen data structure. For example, if a problem can be solved by traversing a graph, then using a depth-first search or breadth-first search algorithm can be more efficient than using a brute force algorithm.
Assignment Activity 4: Implement a solution to a problem using a specified algorithm design technique
When implementing a solution to a problem, it is often helpful to use an algorithm design technique. This technique can be used to improve the efficiency of the algorithms or to reduce the amount of memory required. For example, when using a sorting algorithm, one might implement a quicksort instead of a selection sort. This would require less memory and would run faster on average.
When implementing a solution to a problem, it is also important to use the correct data structures. For example, if the problem involves sorting a list of numbers, then using a sorted array or linked list can be more efficient than using an unsorted array.
Finally, when implementing a solution to a problem, it is important to choose an algorithm that is appropriate for the problem at hand. For example, if the problem can be solved by traversing a graph, then using a depth-first search or breadth-first search algorithm can be more efficient than using a brute force algorithm.
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Assignment Activity 4: Select and apply mathematical techniques, such as asymptotic notation or recurrence relations, to obtain good upper and lower bounds on the running time of algorithms
There are a variety of mathematical techniques that can be used to obtain upper and lower bounds on the running time of algorithms. One common technique is asymptotic notation, which can be used to express the running time of an algorithm as a function of the input size. For example, if an algorithm has a running time of O(n), then this means that the running time is proportional to the square of the input size.
Another common technique is recurrence relations, which can be used to express the running time of an algorithm as a function of the number of times the algorithm has been called. For example, if an algorithm has a running time of T(n), then this means that the running time is proportional to T(n) multiplied by the input size.
Using these mathematical techniques can be helpful in order to get a better understanding of the running time of an algorithm, and can be used to compare different algorithms.
Assignment Activity 5: Recognize similarities between a new problem and problems that you have already encountered, and judge whether or not these similarities can be leveraged to design an algorithm for the new problem.
When considering a new problem, it is often helpful to see if there are any similarities between the new problem and problems that have already been solved. If there are similarities, then this can be leveraged to design an algorithm for the new problem. For example, if the new problem is similar to a sorting problem, then one might use a sorting algorithm to solve the new problem.
Another way to look at this is by considering the data structures and algorithms that are available for solving a problem. If there is a data structure or algorithm that is suitable for solving a particular problem, then this can be leveraged to design a solution for the new problem. For example, if the new problem can be solved by traversing a graph, then one might use a depth-first search or breadth-first search algorithm to solve the new problem.
Assignment Activity 6: Apply the theory of NP-completeness to provide evidence that certain problems may not have algorithms that are efficient on all inputs.
The theory of NP-completeness can be used to provide evidence that certain problems may not have algorithms that are efficient on all inputs. This is because the theory of NP-completeness proves that there are some problems that are intractable, meaning that they cannot be solved in polynomial time.
One example of a problem that is intractable is the problem of deciding whether a graph is connected. This problem cannot be solved in polynomial time, meaning that there is no algorithm that can solve this problem on all graphs in polynomial time. This is because the problem of deciding whether a graph is connected is NP-complete, which means that it can be reduced to any other NP-complete problem.
This theory can be helpful in order to determine whether a problem is tractable or not, and can help to guide the search for algorithms for solving certain problems. It is important to note, however, that the theory of NP-completeness does not prove that a problem is unsolvable, but rather that it is intractable. Therefore, it is still possible to design algorithms for solving NP-complete problems, but these algorithms may not be efficient on all inputs.
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