Python 投资组合动态规划的背包问题和回溯

我正在从事一个python项目，利用背包问题和动态规划，根据可以投资多少资金来找到最佳投资.到目前为止，我能够按名称列出最佳投资，但我在格式化和获取其余信息以及实现回溯表方面遇到了困难.以下是我到目前为止得到的信息和输出:

import pandas as pd
from itertools import chain

def investmentFilename(file):
    df = pd.read_csv(file)
    frame = pd.DataFrame(df)
    frame = frame.drop(0) # dropping the United States
    # print(frame)
    return frame

def loadInvestments(frame):
    portfolio = []
    state = frame['RegionName'].tolist()
    avg = frame['Zhvi'].tolist()
    dfAvg = pd.DataFrame(avg)
    # print(dfAvg)
    tenyr = (frame['10Year'].tolist())
    tenyr = pd.DataFrame(tenyr)
    roi = tenyr.multiply(dfAvg, axis='columns', level=None, fill_value=None)
    # print(roi)
    # roi = pd.DataFrame(roi)
    ROI = roi.values.tolist()
    ROI = list(chain.from_iterable(ROI))
    print("InvestmentName InvestmentCost EstimatedReturnOnInvestment")
    for i in range(len(state)):
        portfolio.append([state[i], int(avg[i]), int(ROI[i])])
        print(state[i], '\t', avg[i], '\t', ROI[i])

    # print(portfolio)
    # portfolio = list(chain.from_iterable(portfolio))
    # print(portfolio)

    # printing list data
    # print("Investment Name:",state)
    # print("Investment Cost:", avg)
    # print("Estimated Return on Investment:", ROI)
    return portfolio

def optimizeInvestments(invstmt, money):
    """ knapsack problem """
    n = len(invstmt)
    val = []
    name = []
    roi = []

    for i in invstmt:
        name.append(i[0])
        val.append(i[1])
        roi.append(i[2])

    K = [[0 for x in range(money + 1)] for x in range(n + 1)]
    I = [[0 for x in range(money + 1)] for x in range(n + 1)]

    for i in range(n + 1):
        for w in range(money + 1):
            if i == 0 or w == 0:
                K[i][w] = 0
                I[i][w] = ""

            elif roi[i - 1] <= w:

                if (val[i - 1] + K[i - 1][w - roi[i - 1]] > K[i - 1][w]):
                    K[i][w] = val[i - 1] + K[i - 1][w - roi[i - 1]]
                    I[i][w] = name[i - 1] + I[i - 1][w - roi[i - 1]]
                else:
                    K[i][w] = K[i - 1][w]
                    I[i][w] = I[i - 1][w]

            else:
                K[i][w] = K[i - 1][w]
                I[i][w] = I[i - 1][w]

    return (I[n][money])

dataFrame = investmentFilename('zhvi-short.csv')
items = loadInvestments(dataFrame)
print(items)
money = 15000 # change the amount of money you want to invest here
# items = [["A", 60, 120], ["B", 100, 20],["C", 120, 30]] # test
# print(items)
val = []
roi = []
for i in items:
    val.append(i[1])
    roi.append(i[2])
print(optimizeInvestments(items, money))

这将提供以下输出:

我想用"and"或逗号分隔.然后，我还希望输出每个名称的特定ROI.

我还需要为最佳投资实施回溯表.我知道如何在理论上实现回溯表，但我不确定如何实现背包问题.