Update(July 2020): Question is 9 years old but still one that I'm deeply interested in. In the time since, machine learning(RNN's, CNN's, GANS,etc), new approaches and cheap GPU's have risen that enable new approaches. I thought it would be fun to revisit this question to see if there are new approaches.
I am learning programming (Python and algorithms) and was trying to work on a project that I find interesting. I have created a few basic Python scripts, but I’m not sure how to approach a solution to a game I am trying to build.
Here’s how the game will work:
Users will be given items with a value. For example,
Apple = 1
Pears = 2
Oranges = 3
They will then get a chance to choose any combo of them they like (i.e. 100 apples, 20 pears, and one orange). The only output the computer gets is the total value (in this example, it's currently $143). The computer will try to guess what they have. Which obviously it won’t be able to get correctly the first turn.
Value quantity(day1) value(day1)
Apple 1 100 100
Pears 2 20 40
Orange 3 1 3
Total 121 143
The next turn the user can modify their numbers but no more than 5% of the total quantity (or some other percent we may chose. I’ll use 5% for example.). The prices of fruit can change(at random) so the total value may change based on that also (for simplicity I am not changing fruit prices in this example). Using the above example, on day 2 of the game, the user returns a value of $152 and $164 on day 3. Here's an example:
Quantity (day2) %change (day2) Value (day2) Quantity (day3) %change (day3) Value(day3)
104 104 106 106
21 42 23 46
2 6 4 12
127 4.96% 152 133 4.72% 164
*(I hope the tables show up right, I had to manually space them so hopefully it's not just doing it on my screen, if it doesn't work let me know and I'll try to upload a screenshot.)
I am trying to see if I can figure out what the quantities are over time (assuming the user will have the patience to keep entering numbers). I know right now my only restriction is the total value cannot be more than 5% so I cannot be within 5% accuracy right now so the user will be entering it forever.
What I have done so far
Here’s my solution so far (not much). Basically, I take all the values and figure out all the possible combinations of them (I am done this part). Then I take all the possible combos and put them in a database as a dictionary (so for example for $143, there could be a dictionary entry {apple:143, Pears:0, Oranges :0}..all the way to {apple:0, Pears:1, Oranges :47}. I do this each time I get a new number so I have a list of all possibilities.
Here’s where I’m stuck. In using the rules above, how can I figure out the best possible solution? I think I’ll need a fitness function that automatically compares the two days data and removes any possibilities that have more than 5% variance of the previous days data.
Questions:
So my question with user changing the total and me having a list of all the probabilities, how should I approach this? What do I need to learn? Is there any algorithms out there or theories that I can use that are applicable? Or, to help me understand my mistake, can you suggest what rules I can add to make this goal feasible (if it's not in its current state. I was thinking adding more fruits and saying they must pick at least 3, etc..)? Also, I only have a vague understanding of genetic algorithms, but I thought I could use them here, if is there something I can use?
I'm very very eager to learn so any advice or tips would be greatly appreciated (just please don't tell me this game is impossible).
UPDATE: Getting feedback that this is hard to solve. So I thought I'd add another condition to the game that won't interfere with what the player is doing (game stays the same for them) but everyday the value of the fruits change price (randomly). Would that make it easier to solve? Because within a 5% movement and certain fruit value changes, only a few combinations are probable over time.
Day 1, anything is possible and getting a close enough range is almost impossible, but as the prices of fruits change and the user can only choose a 5% change, then shouldn't (over time) the range be narrow and narrow. In the above example, if prices are volatile enough I think I could brute force a solution that gave me a range to guess in, but I'm trying to figure out if there's a more elegant solution or other solutions to keep narrowing this range over time.
UPDATE2: After reading and asking around, I believe this is a hidden Markov/Viterbi problem that tracks the changes in fruit prices as well as total sum (weighting the last data point the heaviest). I'm not sure how to apply the relationship though. I think this is the case and could be wrong but at the least I'm starting to suspect this is a some type of machine learning problem.
Update 3: I am created a test case (with smaller numbers) and a generator to help automate the user generated data and I am trying to create a graph from it to see what's more likely.
Here's the code, along with the total values and comments on what the users actually fruit quantities are.
#!/usr/bin/env python
import itertools
# Fruit price data
fruitPriceDay1 = {'Apple':1, 'Pears':2, 'Oranges':3}
fruitPriceDay2 = {'Apple':2, 'Pears':3, 'Oranges':4}
fruitPriceDay3 = {'Apple':2, 'Pears':4, 'Oranges':5}
# Generate possibilities for testing (warning...will not scale with large numbers)
def possibilityGenerator(target_sum, apple, pears, oranges):
allDayPossible = {}
counter = 1
apple_range = range(0, target_sum + 1, apple)
pears_range = range(0, target_sum + 1, pears)
oranges_range = range(0, target_sum + 1, oranges)
for i, j, k in itertools.product(apple_range, pears_range, oranges_range):
if i + j + k == target_sum:
currentPossible = {}
#print counter
#print 'Apple', ':', i/apple, ',', 'Pears', ':', j/pears, ',', 'Oranges', ':', k/oranges
currentPossible['apple'] = i/apple
currentPossible['pears'] = j/pears
currentPossible['oranges'] = k/oranges
#print currentPossible
allDayPossible[counter] = currentPossible
counter = counter +1
return allDayPossible
# Total sum being returned by user for value of fruits
totalSumDay1=26 # Computer does not know this but users quantities are apple: 20, pears 3, oranges 0 at the current prices of the day
totalSumDay2=51 # Computer does not know this but users quantities are apple: 21, pears 3, oranges 0 at the current prices of the day
totalSumDay3=61 # Computer does not know this but users quantities are apple: 20, pears 4, oranges 1 at the current prices of the day
graph = {}
graph['day1'] = possibilityGenerator(totalSumDay1, fruitPriceDay1['Apple'], fruitPriceDay1['Pears'], fruitPriceDay1['Oranges'] )
graph['day2'] = possibilityGenerator(totalSumDay2, fruitPriceDay2['Apple'], fruitPriceDay2['Pears'], fruitPriceDay2['Oranges'] )
graph['day3'] = possibilityGenerator(totalSumDay3, fruitPriceDay3['Apple'], fruitPriceDay3['Pears'], fruitPriceDay3['Oranges'] )
# Sample of dict = 1 : {'oranges': 0, 'apple': 0, 'pears': 0}..70 : {'oranges': 8, 'apple': 26, 'pears': 13}
print graph
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