The greedy strategy works as follows:
To find an optimal solution, we construct the solution
by making decisions to choose each item to add to
the solution optimally, and never reversing decisions
already made.A greedy algorithm for the problem runs like this:
use as many 25¢ as possible, then
use as many 10¢ as possible, then
use as many 5¢ as possible, then finally
use as many 1¢ as possible.For example, to make change for 30¢, the greedy algorithm uses 6 coins (25 + 1 + 1 + 1 + 1 + 1). However, we can use 3 coins (10 + 10 + 10) instead.
High-level algorithm
1. Sort the classes into nondecreasing order using their finish times as key.
Now we have classes j = 1, ⋯ , n with start times S[j], and finish times F[j],
with F[1] ≤ F[2] ≤ ⋯ ≤ F[n-1] ≤ F[n].
2. Find the optimum schedule as follows.
Sc ← ∅
/*
* We maintain variable f equal to the finish time
* of the last class scheduled.
*/
f ← -∞
for j ← 1 to n do {
if S[j] ≥ f then {
Sc ← Sc ∪ {j}
f ← F[j]
}
}
return Sc as the desired schedule