在 Python 中计算 15^6 组合的 for 循环的替代方法

Question

Today, I have a nested for loop in python to calculate the value of all different combinations in a horse racing card consisting of six different races; ie six different arrays (of different lengths, but up to 15 items per array). It can be up to 11 390 625 combinations (15^6).

For each horse in each race, I calculate a value (EV) which I want to multiply.

Array 1: 1A,1B,1C,1D,1E,1F
Array 2: 2A,2B,2C,2D,2E,2F
Array 3: 3A,3B,3C,3D,3E,3F
Array 4: 4A,4B,4C,4D,4E,4F
Array 5: 5A,5B,5C,5D,5E,5F
Array 6: 6A,6B,6C,6D,6E,6F

1A * 1B * 1C * 1D * 1E * 1F = X,XX
.... .... .... .... ... ...
6A * 6B * 6C * 6D * 6E * 6F 0 X,XX

Doing four levels is OK. It takes me about 3 minutes. I have yet not been able to do six levels.

I need help in creating a better way of doing this, and have no idea how to proceed. Does numpy perhaps offer help here? Pandas? I've tried compiling the code with Cython, but it did not help much.

My function takes in a list containing the horses in numerical order and their EV. (Since horse starting numbers do not start with zero, I add 1 to the index). I iterate through all the different races, and save the output for the combination into a dataframe.

    def calculateCombos(horses_in_race_1,horses_in_race_2,horses_in_race_3,horses_in_race_4,horses_in_race_5,horses_in_race_6,totalCombinations, df):
        totalCombinations = 0
        for idx1, hr1_ev in enumerate(horses_in_race_1):
            hr1_no = idx1 + 1
            for idx2, hr2_ev in enumerate(horses_in_race_2):
                hr2_no = idx2 + 1
                for idx3, hr3_ev in enumerate(horses_in_race_3):
                    hr3_no_ = idx3 + 1
                    for idx4, hr4_ev in enumerate(horses_in_race_4):
                        hr4_no = idx4 + 1
                        for idx5, hr5_ev in enumerate(horses_in_race_5):
                            hr5_no = idx5 + 1
                            for idx6, hr6_ev in enumerate(horses_in_race_6):
                                hr6_no = idx6 + 1
                                totalCombinations = totalCombinations + 1
                                combinationEV = hr1_ev * hr2_ev * hr3_ev * hr4_ev * hr5_ev * hr6_ev
                                new_row = {'Race1':str(hr1_no),'Race2':str(hr2_no),'Race3':str(hr3_no),'Race4':str(hr4_no),'Race5':str(hr5_no),'Race6':str(hr6_no), 'EV':combinationEV}
                                df = appendCombinationToDF(df, new_row)
        return df   

Answer 1

Why don't you try this and see if you can run the function without any issues? This works on my laptop (I'm using PyCharm). If you can't run this, then I would say that you need a better PC perhaps. I did not encounter any memory error.

Assume that we have the following:

horses_in_race_1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
horses_in_race_2 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
horses_in_race_3 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
horses_in_race_4 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
horses_in_race_5 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
horses_in_race_6 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]

I have re-written the function as follows - made a change in enumeration. Also, not using df as I do not know what function this is - appendCombinationToDF

def calculateCombos(horses_in_race_1,horses_in_race_2,horses_in_race_3,horses_in_race_4,horses_in_race_5,horses_in_race_6):
    for idx1, hr1_ev in enumerate(horses_in_race_1, start = 1):
        for idx2, hr2_ev in enumerate(horses_in_race_2, start = 1):
            for idx3, hr3_ev in enumerate(horses_in_race_3, start = 1):
                for idx4, hr4_ev in enumerate(horses_in_race_4, start = 1):
                    for idx5, hr5_ev in enumerate(horses_in_race_5, start = 1):
                        for idx6, hr6_ev in enumerate(horses_in_race_6, start = 1):
                            combinationEV = hr1_ev * hr2_ev * hr3_ev * hr4_ev * hr5_ev * hr6_ev
                            new_row = {'Race1':str(idx1),'Race2':str(idx2),'Race3':str(idx3),'Race4':str(idx4),'Race5':str(idx5),'Race6':str(idx6), 'EV':combinationEV}
                            l.append(new_row)
                            #df = appendCombinationToDF(df, new_row)
l = [] # df = ...
calculateCombos(horses_in_race_1, horses_in_race_2, horses_in_race_3, horses_in_race_4, horses_in_race_5, horses_in_race_6)

Executing len(l) , I get:

11390625 # maximum combinations possible. This means that above function ran successfully and computation succeeded.

If the above can be executed, replace list l with df and see if function can execute without encountering memory error. I was able to run the above in less than 20-30 seconds.