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A General Method of Solving Divide-and-Conquer

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  1. A General Method of Solving Divide-and-Conquer 計算方法設計 Chapter05重要補充 唐傳義老師

  2. given rewrite it into template given , Deduction-1

  3. (1) (1) Example1-(1) • Example 1 : Solution:

  4. iteration and cancellation 又 log n terms , Deduction-2 • 而

  5. Deduction-3 • Ο:upper bound ex: • Ω:lower bound ex: • Θ:exactly ex: • ο:exactly,even constant ex: 不同的 g(n)對應不同的

  6. Example1-(2) • Example 1 : Solution: From (1)

  7. , Example2 • Example 2 : Solution:

  8. given , , 仍然是 只差 的constant If g(n) is monotone General Representation • In general

  9. Example3-- Pan’s Matrix • Example 3 : Solution:

  10. More General Representation • More general given ,

  11. Example4 • Example 4 : Solution: ,

  12. Reference • Bentley, Haken & Saxe “A General Method of Solving Divide-and-Conquer Recurrences”, SIGACT News Fall 1980,page36-44