现在我正在尝试在 Python 3.2 中编写背包问题。我试图用矩阵动态地做到这一点。我尝试使用的算法如下
实现背包问题的memoryfunction方法 输入：一个非负整数 i 表示第一个 正在考虑的物品和一个表示背包容量的非负整数 j 输出：前 i 项的最优可行子集的值 注意：用作全局变量输入数组 Weights[1..n], Values[1...n] 和表 V[0...n, 0...W]，其条目用 -1 初始化，除了 用 0 初始化的第 0 行和第 0 列
if V[i, j] < 0
if j < Weights[i]
value <-- MFKnapsack(i - 1, j)
else
value <-- max(MFKnapsack(i -1, j),
Values[i] + MFKnapsack(i -1, j - Weights[i]))
V[i, j} <-- value
return V[i, j]
如果您运行下面的代码，您可以看到它尝试将权重插入列表中。由于这是使用递归，我很难发现问题。我也收到错误消息：无法使用“+”将整数与列表相加。我将矩阵初始化为从第一行和第一列的所有 0 开始，其他所有内容都初始化为 -1。任何帮助都感激不尽。
#Knapsack Problem
def knapsack(weight,value,capacity):
weight.insert(0,0)
value.insert(0,0)
print("Weights: ",weight)
print("Values: ",value)
capacityJ = capacity+1
## ------ initialize matrix F ---- ##
dimension = len(weight)+1
F = [[-1]*capacityJ]*dimension
#first column zeroed
for i in range(dimension):
F[i][0] = 0
#first row zeroed
F[0] = [0]*capacityJ
#-------------------------------- ##
d_index = dimension-2
print(matrixFormat(F))
return recKnap(F,weight,value,d_index,capacity)
def recKnap(matrix, weight,value,index, capacity):
print("index:",index,"capacity:",capacity)
if matrix[index][capacity] < 0:
if capacity < weight[index]:
value = recKnap(matrix,weight,value,index-1,capacity)
else:
value = max(recKnap(matrix,weight,value,index-1,capacity),
value[index] +
recKnap(matrix,weight,value,index-1,capacity-(weight[index]))
matrix[index][capacity] = value
print("matrix:",matrix)
return matrix[index][capacity]
def matrixFormat(*doubleLst):
matrix = str(list(doubleLst)[0])
length = len(matrix)-1
temp = '|'
currChar = ''
nextChar = ''
i = 0
while i < length:
if matrix[i] == ']':
temp = temp + '|\n|'
#double digit
elif matrix[i].isdigit() and matrix[i+1].isdigit():
temp = temp + (matrix[i]+matrix[i+1]).center(4)
i = i+2
continue
#negative double digit
elif matrix[i] == '-' and matrix[i+1].isdigit() and matrix[i+2].isdigit():
temp = temp + (matrix[i]+matrix[i+1]+matrix[i+2]).center(4)
i = i + 2
continue
#negative single digit
elif matrix[i] == '-' and matrix[i+1].isdigit():
temp = temp + (matrix[i]+matrix[i+1]).center(4)
i = i + 2
continue
elif matrix[i].isdigit():
temp = temp + matrix[i].center(4)
#updates next round
currChar = matrix[i]
nextChar = matrix[i+1]
i = i + 1
return temp[:-1]
def main():
print("Knapsack Program")
#num = input("Enter the weights you have for objects you would like to have:")
#weightlst = []
#valuelst = []
## for i in range(int(num)):
## value , weight = eval(input("What is the " + str(i) + " object value, weight you wish to put in the knapsack? ex. 2,3: "))
## weightlst.append(weight)
## valuelst.append(value)
weightLst = [2,1,3,2]
valueLst = [12,10,20,15]
capacity = 5
value = knapsack(weightLst,valueLst,5)
print("\n Max Matrix")
print(matrixFormat(value))
main()