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D&C Examples

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D&C Examples

- 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.

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

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

C

A

B

Restricted Tower of Hanoi

Modification:

You can move to and from adjacent pads (A<->B,B<->C)

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

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.

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?