D&amp;C Examples

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# D&C Examples - PowerPoint PPT Presentation

D&amp;C Examples. Notes:. There may be several ways to solve the same problem. Try to find a better one. To stick with the topic, try to think in the way of D&amp;C. In case you have a straight forward approach, try to compare the expected runtime with the D&amp;C result. D&amp;C: Tower of Hanoi.

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### D&C Examples

Notes:
• There may be several ways to solve the same problem. Try to find a better one.
• To stick with the topic, try to think in the way of D&C.
• In case you have a straight forward approach, try to compare the expected runtime with the D&C result.
D&C: Tower of Hanoi

You are given three pads (A,B,C). On pad A, you have n disks, arranged from the smallest on top and the largest at the bottom.

At any moment, a larger disk cannot be stacked on top of a smaller disk.

You can move the top disk of one pad to the other pad, provided that the constraint holds.

C

C

A

A

B

B

D&C: Tower of Hanoi

Find a way to move n disks from the pad A to pad C.

C

A

B

D&C: Tower of Hanoi

Restricted Tower of Hanoi

Modification:

Derive a way to move n disk from pad A to pad C.

D&C: Power

Derive a way to compute bp quickly.

You may ignore the possible overflow problem.

Modification:

Modulo power

Derive a way to compute bp mod n quickly.

D&C: Josephus Problem

Refer to task 1030 for the problem description.

Suppose you are to find the remainder only.

(The dying sequence is not important here)

Find a quick way to locate the survival position.

Modification:

General Josephus Problem

Suppose the killing sequence is skipping k people instead of 2. Is there any good method?