用贪婪的python算法求解背包问题

Question

我试图用Python解决背包问题，实现一个贪婪的算法。我得到的结果对我来说毫无意义。

背包：

20
    1    91    29
    2    60    65
    3    61    71
    4     9    60
    5    79    45
    6    46    71
    7    19    22
    8    57    97
    9     8     6
   10    84    91
   11    20    57
   12    72    60
   13    32    49
   14    31    89
   15    28     2
   16    81    30
   17    55    90
   18    43    25
   19   100    82
   20    27    19
524

import os 

def constructive():     
    knapsack = []
    Weight = 0
    while(Weight <= cap):
        best = max(values)
        i = values.index(best)
        knapsack.append(i)
        Weight = Weight + weights[i]
        del values[i]
        del weights[i]
    return knapsack, Weight


def read_kfile(fname):
    with open(fname, 'rU') as kfile:
        lines = kfile.readlines()     # reads the whole file
    n = int(lines[0])
    c = int(lines[n+1])
    vs = []
    ws = []
    lines = lines[1:n+1]   # Removes the first and last line
    for l in lines:
        numbers = l.split()   # Converts the string into a list
        vs.append(int(numbers[1]))  # Appends value, need to convert to int
        ws.append(int(numbers[2]))  # Appends weigth, need to convert to int
    return n, c, vs, ws

dir_path = os.path.dirname(os.path.realpath(__file__))  # Get the directory where the file is located
os.chdir(dir_path)  # Change the working directory so we can read the file

knapfile = 'knap20.txt'
nitems, cap, values, weights = read_kfile(knapfile)
val1,val2 =constructive()
print ('knapsack',val1)
print('weight', val2)
print('cap', cap)

结果：

knapsack [18, 0, 8, 13, 3, 8, 1, 0, 3]
weight 570
cap 524

Answer 1

欢迎光临。程序给出的权重超过上限的原因是因为在最后一个项目上，你放进背包里，你没有检查它是否能放进去。为此，只需添加一个if语句，还应检查值列表是否为空。请注意，我有append(I+1)，因为文本文件的索引从1开始，而Python的列表索引从0开始：

def constructive():
    knapsack = []
    Weight = 0

    while(Weight <= cap and values):
        best = max(values)
        i = values.index(best)
        if weights[i] <= cap-Weight:
            knapsack.append(i+1)
            Weight = Weight + weights[i]
        del values[i]
        del weights[i]

    return knapsack, Weight