I've been working on some problems/exercises on Project Euler hoping to practice/learn some optimal algorithms and programming idioms with python.
I came across a problem which asked to find all the unique combinations using at least two values to sum to 100. In researching this problem I came across people referring to the coin problem and the greedy algorithm which is what this question is about.
I had heard of the greedy algorithm before but, never understood or used it. I thought I would give it a try. I still am unsure of whether this is the proper way of doing it.
def greedy(amount):
combos = {}
ways = {}
denominations = [1,5,10,25]
## work backwards? ##
denominations.reverse()
for i in denominations:
## check to see current denominations maximum use ##
v = amount / i
k = amount % i
## grab the remainder in a variable and use this in a while loop ##
ways.update({i:v})
## update dictionarys ##
combos.update({i:ways})
while k != 0:
for j in denominations:
if j <= k:
n = k/j
k = k % j
ways.update({j:n})
combos.update({i:ways})
ways = {}
return combos
I know this isn't the way to go about solving the Euler question but, I wanted to understand and learn an optimal way to use this algorithm. My question is, would this be considered a proper greedy-algorithm? If not what am I doing wrong. If correct could I improve optimize?
The greedy coin algorithm computes the optimal way to make change for a given amount due. It works with our denominations of coins but could fail with made up denominations of coins (eg. a 7 cent coin and a 12 cent coin)
here is a recursive implementation of it
>>> def pickBest(coins,due):
... if due == 0: return []
... for c in coins:
... if c<= due: return [c] + pickBest(coins,due-c)
...
>>> coins = [1,5,10,25]
>>> coins = sorted(coins,reverse=True)
>>> coins
[25, 10, 5, 1]
>>> print pickBest(coins,88)
[25, 25, 25, 10, 1, 1, 1]
however I dont think this will help you much with the problem as you stated it
you would likely want to think of it as a recursive problem
100 = 99 + 1
100 = 98 + 2 (2 = 1 + 1)
100 = 98 + (1 + 1)
100 = 97 + 3 (3 = 1 + 2)
100 = 97 + 2+1 (recall 2 = 1+1)
100 = 97 + 1+1 + 1
...
at least thats what I think, I might be wrong..(in fact i think I am wrong)
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