Algorithm Design and Analysis - Assignment2: Greedy Algorithms - Subdivide a plot of land
Algorithm Design and AnalysisGreedy AlgorithmsBrute-force ApproachApproximate Greedy ApproachExact ApproachUniversity at BuffaloCSE 431CSE431CSE531CSE 531JavaC++Python
Algorithm Design and Analysis
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Assignment Two Due 14 October 2022
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Suppose the values of different sizes of rectangular pieces of land are known (presumed rounded to the nearest metre), and held in a two-dimensional array, with the price for an m×n sized piece the same as for an n×m piece of land. Also suppose a given rectangular piece of land can be subdivided into two (equal or unequal sized) rectangular pieces by splitting parallel to one side at a cost proportional to the length of the split.
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The following diagram illustrates subdivisions of an M × N piece of land via four splits to give five smaller pieces of land.
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The purpose of this assignment is to develop software that can determine the best way to progressively subdivide a plot of land of a given size to maximize the overall value of the subdivision.
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The assignment should include the following components:
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Brute-force Approach which is a program that implements a brute-force approach to solving the subdivision problem that simply finds all valid sub- divisions (eg finding them by using recursion) and calculates the overall price. (12 marks)
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Approximate Greedy Approach which is a program that demonstrates a approximate approach to solving the subdivision problem, and which im- proves on the performance of the brute-force approach. Please include comments in your program that clearly explain the approach you have taken and good test cases. (12 marks)
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Exact Approach which is a program that demonstrates an approach that correctly and efficiently solves the subdivision problem. Please include comments in your program that clearly explain the approach you have taken, particularly why it works, and include good test cases that illustrate its correctness. (12 marks)
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Graphical Illustration which is a user interface that graphically displays a rectangular plot of land with its subdivision and overall value. (9 marks)
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Demonstration video with clear explanation of the algorithms and programs. (5 marks)
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