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Assignment1 - CSIS0250A Design and Analysis of Algorithms...

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CSIS0250A Design and Analysis of Algorithms Assignment 1 Due Date: February 11, 2010, 11:59 pm Question 1. (10%) Solve the following recurrence relations (i.e., find out what is T ( n ), using big- O notation). You are required to show the results as well as the solving steps: 1. T ( n ) = 2 T ( n/ 3) + 1 2. T ( n ) = 5 T ( n/ 4) + n 3. T ( n ) = 7 T ( n/ 7) + n 4. T ( n ) = 9 T ( n/ 3) + n 2 5. T ( n ) = 8 T ( n/ 2) + n 3 6. T ( n ) = 49 T ( n/ 25) + n 3 / 2 7. T ( n ) = T ( n - 1) + 2 8. T ( n ) = 2 T ( n - 1) + 1 9. T ( n ) = T ( n ) + 1. 10. T ( n ) = 2 T ( n ) + 1 Note: The Master theorem may not be applicable in some cases. Question 2. (15%) Suppose you are choosing between the following three algo- rithms: Algorithm A solves problems by dividing them into five subproblems of half the size, recursively solving each subproblem, and then combining the solution in linear time. Algorithm B solves problems of size n by recursively solving two subprob- lems of size n - 1 and then combining the solutions in constant time. Algorithm C solves problems of size n by dividing them into nine subprob- lems of size n/
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