We saw that bet t erchange is an incorrect algorithm for the...

Name: we saw that bet t erchange is an incorrect algorithm for the set of denominations 25 20 10 5 1 section 24 there are two possible denominations that can be added to this set such that bet t e 74477
Uploaded: 2022-12-05T14:00:22-08:00
Duration: 2 min 50 s
Channel: Madhur L
Description: we saw that bet t erchange is an incorrect algorithm for the set of denominations 25 20 10 5 1 section 24 there are two possible denominations that can be added to this set such that bet t e 74477

We saw that BET T ERCHANGE is an incorrect algorithm for the set of denominations (25, 20, 10, 5, 1) (section 2.4). There are two possible denominations that can be added to this set such that BET T ERCHANGE will return the correct change combination for any value of M. Provide these two denominations (4 marks) and explain your answers (6 marks).

3. In this problem, we are concerned with the number of ways to produce n cents using coins of denomination 1, 5, 10, and 25. (a) The obvious recurrence relation for this (using arguments instead of subscripts for reasons that will become clear in the next part) is: T(n) = T(n - 25) + T(n - 10) + T(n - 5) + T(n - 1) (with appropriate base cases), representing the possibilities of adding a quarter to n-25 cents, a dime to n-10 cents, and so on. Explain why this is incorrect. Recall that there are two ways of being wrong (double counting, excluding possibilities) and you should say how this recurrence violates one or both of these. (b) One general technique to avoid the error you identified above is to impose an ordering to reduce the problem to a different one. In this case, that is: T(n) = U25(n) + ... + U1(n) where Uk(n) is the number of ways to make n cents using a k-cent coin as the largest denomination. Write appropriate recurrence relations (for the Uk's).

Sri K.

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