An element of fewestCoins stores the fewest number of coins necessary for the amount of change corresponding to its index value.

For 29-cents using the set of coin types {1, 5, 10, 12, 25, 50}, determine the value of fewestCoins[29].

2. The binomial coefficient is the number of combinations/sets of picking k items form a bin containing n items. It is often written as:

=

a) What problems might arrive if we use the formula directly?

b) How might we write the binomial coefficient recursively?

(HINT: Split the sets into two groups as sets with a specific item and sets without the specific item.)

3. How can we write the dynamic programming algorithm for binomial coefficient?

3. For the 29-cent solution, what are the specific coins in the solution?

4. How much new information must we store to reconstruct the specific coins in a solution?