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# master - n 4 lg n Problem 1-12 T n = T n 2 T n 4 n 2...

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Massachusetts Institute of Technology Handout 9 6.046J/18.410J: Introduction to Algorithms February 15, 2002 Professors Michel Goemans and Piotr Indyk Master Theorem Worksheet This is a worksheet to help you master solving recurrence relations using the Master Theorem. For each recurrence, either give the asympotic solution using the Master Theorem (state which case), or else state that the Master Theorem doesn’t apply. You should be able to go through these 25 recurrences in 10 minutes. Problem 1-1. T ( n ) = 3 T ( n/ 2) + n 2 Problem 1-2. T ( n ) = 7 T ( n/ 2) + n 2 Problem 1-3. T ( n ) = 4 T ( n/ 2) + n 2 Problem 1-4. T ( n ) = 3 T ( n/ 4) + n lg n Problem 1-5. T ( n ) = 4 T ( n/ 2) + lg n Problem 1-6. T ( n ) = T ( n - 1) + n

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2 Handout 9: Master Theorem Worksheet Problem 1-7. T ( n ) = 4 T ( n/ 2) + n 2 lg n Problem 1-8. T ( n ) = 5 T ( n/ 2) + n 2 lg n Problem 1-9. T ( n ) = 3 T ( n/ 3) + n/ lg n Problem 1-10. T ( n ) = 2 T ( n/ 4) + c Problem 1-11. T ( n ) = T (

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Unformatted text preview: n/ 4) + lg n Problem 1-12. T ( n ) = T ( n/ 2) + T ( n/ 4) + n 2 Problem 1-13. T ( n ) = 2 T ( n/ 4) + lg n Problem 1-14. T ( n ) = 3 T ( n/ 3) + n lg n Handout 9: Master Theorem Worksheet 3 Problem 1-15. T ( n ) = 8 T (( n-√ n ) / 4) + n 2 Problem 1-16. T ( n ) = 2 T ( n/ 4) + √ n Problem 1-17. T ( n ) = 2 T ( n/ 4) + n . 51 Problem 1-18. T ( n ) = 16 T ( n/ 4) + n ! Problem 1-19. T ( n ) = 3 T ( n/ 2) + n Problem 1-20. T ( n ) = 4 T ( n/ 2) + cn Problem 1-21. T ( n ) = 3 T ( n/ 3) + n/ 2 Problem 1-22. T ( n ) = 4 T ( n/ 2) + n/ lg n 4 Handout 9: Master Theorem Worksheet Problem 1-23. T ( n ) = 7 T ( n/ 3) + n 2 Problem 1-24. T ( n ) = 8 T ( n/ 3) + 2 n Problem 1-25. T ( n ) = 16 T ( n/ 4) + n...
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master - n 4 lg n Problem 1-12 T n = T n 2 T n 4 n 2...

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