CS3230
Tutorial 6
1. Consider the greedy algorithm for coinchange problem.
Suppose the coin denominations are
d
1
> d
2
> . . . > d
n
= 1.
Suppose that
d
i
+1
is a factor of
d
i
, for 1
≤
i < n
.
Then, show that the greedy algorithm is optimal.
2. (a) Suppose we modify the greedy algorithm for fractional knapsack problem to con
sider the objects in order of “nonincreasing” value (rather than nonincreasing ratio of
value/weight as done in class).
Is the modified algorithm still optimal? If so, give an argument for its optimality. If not,
give a counterexample.
(b) Suppose we modify the greedy algorithm to consider the objects in order of “non
decreasing” weight (rather than nonincreasing ratio of value/weight as done in class).
Is the modified algorithm still optimal? If so, give an argument for its optimality. If not,
give a counterexample.
3. Using the algorithm done in class, give Huffman tree and code if the frequencies of the
letters are as follows:
freq
(
a
) = 25,
freq
(
b
) = 2,
freq
(
c
) = 5,
freq
(
d
) = 6,
freq
(
e
) = 6,
freq
(
f
) = 6
4. Suppose
T
is a Huffman coding tree for the frequencies
f
1
, f
2
, f
3
, . . . , f
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 Fall '10
 sanjay
 Algorithms, Dynamic Programming, Graph Theory, Greedy algorithm, WT

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