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A General Method of Solving Divide-and-Conquer

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A General Method of Solving Divide-and-Conquer

## 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