Python-使用加法的所有列表组合

Question

I have a list that is in this form: ["Name/num1/num2/num3/num4/num5", ...]

For example: available = ["a/1/2/3/4/5", "b/5/4/3/2/4", "c/4/3/2/1/3"]

I am trying to create every possible combination of items in available , where the sum of num5 of each item in the combination (eg for a is 5 , for b is 1 , for c is 5 ) is less than MAXNUM (eg 3000).

To clarify with an example, the program will create a generator for available above and MAXNUM = 9 which can be turned into the following list:

[["a/1/2/3/4/5", "b/5/4/3/2/4"], ["a/1/2/3/4/5", c/4/3/2/1/3], [b/5/4/3/2/4, b/5/4/3/2/4], [b/5/4/3/2/4, "c/4/3/2/1/3"], ["c/4/3/2/1/3", "c/4/3/2/1/3", "c/4/3/2/1/3"]]

Note: This code needs to return a result with available having 100 items, and MAXNUM = 3000 within a reasonable time (No more than 10 minutes ideally)

Edit: Here is my code in a practical use, as requested:

import itertools
import sys
import time

sys.setrecursionlimit(10000000)

#["Name/Carbs/Protein/Fat/Vitamins/Calories"]
available = ['Fiddleheads/3/1/0/3/80', 'Fireweed Shoots/3/0/0/4/150', 'Prickly Pear Fruit/2/1/1/3/190', 'Huckleberries/2/0/0/6/80', 'Rice/7/1/0/0/90', 'Camas Bulb/1/2/5/0/120', 'Beans/1/4/3/0/120', 'Wheat/6/2/0/0/130', 'Crimini Mushrooms/3/3/1/1/200', 'Corn/5/2/0/1/230', 'Beet/3/1/1/3/230', 'Tomato/4/1/0/3/240', 'Raw Fish/0/3/7/0/200', 'Raw Meat/0/7/3/0/250', 'Tallow/0/0/8/0/200', 'Scrap Meat/0/5/5/0/50', 'Prepared Meat/0/4/6/0/600', 'Raw Roast/0/6/5/0/800', 'Raw Sausage/0/4/8/0/500', 'Raw Bacon/0/3/9/0/600', 'Prime Cut/0/9/4/0/600', 'Cereal Germ/5/0/7/3/20', 'Bean Paste/3/5/7/0/40', 'Flour/15/0/0/0/50', 'Sugar/15/0/0/0/50', 'Camas Paste/3/2/10/0/60', 'Cornmeal/9/3/3/0/60', 'Huckleberry Extract/0/0/0/15/60', 'Yeast/0/8/0/7/60', 'Oil/0/0/15/0/120', 'Infused Oil/0/0/12/3/120', 'Simple Syrup/12/0/3/0/400', 'Rice Sludge/10/1/0/2/450', 'Charred Beet/3/0/3/7/470', 'Camas Mash/1/2/9/1/500', 'Campfire Beans/1/9/3/0/500', 'Wilted Fiddleheads/4/1/0/8/500', 'Boiled Shoots/3/0/1/9/510', 'Charred Camas Bulb/2/3/7/1/510', 'Charred Tomato/8/1/0/4/510', 'Charred Corn/8/1/0/4/530', 'Charred Fish/0/9/4/0/550', 'Charred Meat/0/10/10/0/550', 'Wheat Porridge/10/4/0/10/510', 'Charred Sausage/0/11/15/0/500', 'Fried Tomatoes/12/3/9/2/560', 'Bannock/15/3/8/0/600', 'Fiddlehead Salad/6/6/0/14/970', 'Campfire Roast/0/16/12/0/1000', 'Campfire Stew/5/12/9/4/1200', 'Wild Stew/8/5/5/12/1200', 'Fruit Salad/8/2/2/10/900', 'Meat Stock/5/8/9/3/700', 'Vegetable Stock/11/1/2/11/700', 'Camas Bulb Bake/12/7/5/4/400', 'Flatbread/17/8/3/0/500', 'Huckleberry Muffin/10/5/4/11/450', 'Baked Meat/0/13/17/0/600', 'Baked Roast/4/13/8/7/900', 'Huckleberry Pie/9/5/4/16/1300', 'Meat Pie/7/11/11/5/1300', 'Basic Salad/13/6/6/13/800', 'Simmered Meat/6/18/13/5/900', 'Vegetable Medley/9/5/8/20/900', 'Vegetable Soup/12/4/7/19/1200', 'Crispy Bacon/0/18/26/0/600', 'Stuffed Turkey/9/16/12/7/1500']

global AllSP, AllNames
AllSP = []
AllNames = []

def findcombs(totalNames, totalCarbs, totalProtein, totalFat, totalVitamins, totalNutrients, totalCalories, MAXCALORIES):
    doneit = False
    for each in available:
        each = each.split("/")
        name = each[0]
        carbs = float(each[1])
        protein = float(each[2])
        fat = float(each[3])
        vitamins = float(each[4])
        nutrients = carbs+protein+fat+vitamins
        calories = float(each[5])
#        print(totalNames, totalCalories, calories, each)
        if sum(totalCalories)+calories <= MAXCALORIES:
            doneit = True
            totalNames2 = totalNames[::]
            totalCarbs2 = totalCarbs[::]
            totalProtein2 = totalProtein[::]
            totalFat2 = totalFat[::]
            totalVitamins2 = totalVitamins[::]
            totalCalories2 = totalCalories[::]
            totalNutrients2 = totalNutrients[::]

            totalNames2.append(name)
            totalCarbs2.append(carbs)
            totalProtein2.append(protein)
            totalFat2.append(fat)
            totalVitamins2.append(vitamins)
            totalCalories2.append(calories)
            totalNutrients2.append(nutrients)
#            print("    ", totalNames2, totalCarbs2, totalProtein2, totalFat2, totalVitamins2, totalNutrients2, totalCalories2)
            findcombs(totalNames2, totalCarbs2, totalProtein2, totalFat2, totalVitamins2, totalNutrients2, totalCalories2, MAXCALORIES)
        else:
            #find SP
            try:
                carbs    = sum([x * y for x, y in zip(totalCalories, totalCarbs)])    / sum(totalCalories)
                protein  = sum([x * y for x, y in zip(totalCalories, totalProtein)])  / sum(totalCalories)
                fat      = sum([x * y for x, y in zip(totalCalories, totalFat)])      / sum(totalCalories)
                vitamins = sum([x * y for x, y in zip(totalCalories, totalVitamins)]) / sum(totalCalories)
                balance  = (carbs+protein+fat+vitamins)/(2*max([carbs,protein,fat,vitamins]))
                thisSP   = sum([x * y for x, y in zip(totalCalories, totalNutrients)]) / sum(totalCalories) * balance + 12
            except:
                thisSP = 0
            #add SP and names to two lists
            AllSP.append(thisSP)
            AllNames.append(totalNames)

def main(MAXCALORIES):
    findcombs([], [], [], [], [], [], [], MAXCALORIES)
    index = AllSP.index(max(AllSP))
    print()
    print(AllSP[index], "  ", AllNames[index])

for i in range(100, 3000, 10):
    start = time.time()
    main(i)
    print("Calories:", i, ">>> Time:", time.time()-start)

Answer 1

Right, so the task for N foods has time and space complexity of O(exp(N)) . What you need is some heuristic search like A* (link) which follows some idea of 'how good' one incomplete combination is to direct its further search. As a result you will find not the best solution, but a practical good solution within limited time. Alternatives are genetic algorithms, simulated annealing, and other optimization algorithm. Note that you must define a metric of how good each combination is!

I was using the package astar ( https://github.com/jrialland/python-astar ) in my video game AI, and it exceeded my expectations.

Further suggestions: use namedtuple to make your code more readable, otherwise you will hate finding bugs and extending it:

from collections import namedtuple

food = namedtuple('Food', 'name carbs protein fat vitamins calories')

bananas = food('bananas', 10, 15, 20, 10, 100)
oranges = food('oranges', carbs=10, protein=15, fat=20, vitamins=10, calories=100)
print(bananas.calories, oranges.fat)

Answer 2

Given the high number of possibilities, perhaps you should approach the use of this information differently. For example, if the usage context is selection of foods given a prior selection, you could simply provide the information on how many of each food type can be had without going over the maximum

foofInfo = [ food.split("/") for food in available ]
foofInfo = { food[0]:tuple([int(v) for v in food[1:]]) for food in available } #name:(carbs,proteins,fat,vitamins,nutrients,calories)

calFood = {}
for name,(_,_,_,_,calories) in foofInfo.items():
    if calories not in calFood: calFood[calories] = []
    calFood[calories].append(name)

maxCalories = 3000
for calories,foods in calFood.items():
    maxCount = maxCalories//calories
    print("Up to ",maxCount," of ",", ".join(foods))

So you could propose a progressive refinement of the available options rather than a bazillion combinations:

Up to  37  of  Fiddleheads, Huckleberries
Up to  20  of  Fireweed Shoots
Up to  15  of  Prickly Pear Fruit
Up to  33  of  Rice
Up to  25  of  Camas Bulb, Beans, Oil, Infused Oil
Up to  23  of  Wheat
Up to  15  of  Crimini Mushrooms, Raw Fish, Tallow
Up to  13  of  Corn, Beet
Up to  12  of  Tomato
Up to  12  of  Raw Meat
Up to  60  of  Scrap Meat, Flour, Sugar
Up to  5  of  Prepared Meat, Raw Bacon, Prime Cut, Bannock, Baked Meat, Crispy Bacon
Up to  3  of  Raw Roast, Basic Salad
Up to  6  of  Raw Sausage, Camas Mash, Campfire Beans, Wilted Fiddleheads, Charred Sausage, Flatbread
Up to  150  of  Cereal Germ
Up to  75  of  Bean Paste
Up to  50  of  Camas Paste, Cornmeal, Huckleberry Extract, Yeast
Up to  7  of  Simple Syrup, Camas Bulb Bake
Up to  6  of  Rice Sludge, Huckleberry Muffin
Up to  6  of  Charred Beet
Up to  5  of  Boiled Shoots, Charred Camas Bulb, Charred Tomato, Wheat Porridge
Up to  5  of  Charred Corn
Up to  5  of  Charred Fish, Charred Meat
Up to  5  of  Fried Tomatoes
Up to  3  of  Fiddlehead Salad
Up to  3  of  Campfire Roast
Up to  2  of  Campfire Stew, Wild Stew, Vegetable Soup
Up to  3  of  Fruit Salad, Baked Roast, Simmered Meat, Vegetable Medley
Up to  4  of  Meat Stock, Vegetable Stock
Up to  2  of  Huckleberry Pie, Meat Pie
Up to  2  of  Stuffed Turkey