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# Discrete Mathematics and its Applications : Greedy Algorithms

Greedy Algorithms

procedure change (c1, c2, ...., cr: values of denominations of coins, where c1 > c2 > ... > cr; n: a positive integer)
for i : = 1 to r
while n &#8805; ci
begin
add a coin with value ci to the change
n :=n - ci
end

2. Use the greedy algorithm to make change using quarters, dimes, nickels, and pennies for:
a) 87 cents.
b) 49 cents.
c) 99 cents.
d) 33 cents.

Please see the attached file for the fully formatted problems.

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Greedy Algorithms

c1=25 c2=10 c3=5 c4=1

87 cents:

Initial Amount87
=============================
Step: 1 (i= 1)
Coin Denomination: 25
Number of coins of this denomination: 1
Current Change Left: 62
------------------------------------
Step: 2 (i= 1)
Coin Denomination: 25
Number of coins of this denomination: 2
Current Change Left: 37
------------------------------------
Step: 3 (i= 1)
Coin Denomination: 25
Number of coins of this denomination: 3
Current Change Left: 12
------------------------------------
Step: 4 (i= 2)
Coin Denomination: 10
Number of coins of this denomination: 1
Current Change Left: 2
------------------------------------
Step: 5 (i= 4)
Coin Denomination: 1
Number of coins of this denomination: 1
Current Change Left: 1
------------------------------------
Step: 6 (i= 4)
Coin Denomination: 1
Number of coins of this denomination: 2
Current Change Left: 0
------------------------------------
Final Distribution of Coins
25: 3 10: 1 5: 0 1: 2

Initial Change Amount: 49
=============================
Step: 1 (i= 1)
Coin Denomination: 25
Number of coins of this denomination: 1
Change left: ...

#### Solution Summary

Greedy Algorithms are investigated. The solution is detailed and well presented.

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