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CSE 830: Design and Theory of Algorithms
Homework #3
Due Monday, Feb. 18
th
2008, 3pm
Each problem should be solved on a separate sheet of paper to facilitate grading. Limit the
solution of each problem to one sheet of paper. Please don't wait until the last minute to look at
the problems.
1.
The natural greedy algorithm for making change of n units using the smallest number of coins
is as follows. Give the customer one unit of the highest denomination coin of at most
n
units, say
d
units. Now repeat to make change of the remaining
n

d
units.
For each of the following nation’s coinage, establish whether or not this greedy algorithm always
minimizes the number of coins returned in change. If so, prove it, if not give a counter example.
•
English coinage before the decimalization, which consisted of halfcrowns (30 pence),
florins(24 pence), shillings (12 pence), sixpence (6 pence), threepence (3 pence), pennies
(1 pence), half pennies (1/2 pence), and farthings (1/4 pence).
•
Portuguese coinage, which includes coins for 1, 2.5, 5, 10, 20, 25 and 50 escudos. You
need only consider change for an integer number of escudos.
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 Spring '08
 OFRIA
 Algorithms

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