Transcript D&C: Tower of Hanoi

D&C Examples
Notes:
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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.
D&C: Tower of Hanoi
A
B
C
A
B
C
Find a way to move n disks from the pad A to pad C.
D&C: Tower of Hanoi
Restricted Tower of Hanoi
Modification:
You can move to and from adjacent pads (A<->B,B<->C)
A
B
C
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?