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D.2.5  Chapter 10: Greedy Algorithms

On analysing the problem one finds that:

1. There is no exact change for all odd values.
2. The C value can be represented as sum of 1s.
3. A possible algorithm is:

Algorithm D.26 | Coinchange(N)

 1 [Makes change for N units using coins from A] 2 const A ← the coinage set; 3 L ← Ø; 4 [L is the list holding the solution] 5 s ← 0; 6 [s is the sum of items in L] 7 while s < N do 8 x ← largest item in A such that s + x ≤ N; 9 L ← L,x; 10 s ← s + x; 11 end 12 return L;

Let C = 30. Then the greedy solution is L = {25, 1, 1, 1, 1, 1}, while the optimal solution is: Opt = {10, 10, 10}, and |Opt| = 3 < 6 = |L|.

4. We define L to be promising if it can be extended (by adding a list of coins) ...

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