Question

Right now I am attempting to code the knapsack problem in Python 3.2. I am trying to do this dynamically with a matrix. The algorithm that I am trying to use is as follows

Implements the memoryfunction method for the knapsack problem 
Input: A nonnegative integer i indicating the number of the first
items being considered and a nonnegative integer j indicating the knapsack's capacity
Output: The value of an optimal feasible subset of the first i items
Note: Uses as global variables input arrays Weights[1..n], Values[1...n]
and table V[0...n, 0...W] whose entries are initialized with -1's except for
row 0 and column 0 initialized with 0's

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]

If you run the code below that I have you can see that it tries to insert the weight into the the list. Since this is using the recursion I am having a hard time spotting the problem. Also I get the error: can not add an integer with a list using the ‘+’. I have the matrix initialized to start with all 0’s for the first row and first column everything else is initialized to -1. Any help will be much appreciated.

#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()

Answer 1

F = [[-1]*capacityJ]*dimension

does not properly initialize the matrix. [-1]*capacityJ is fine, but [...]*dimension creates dimension references to the exact same list. So modifying one list modifies them all.

Try instead

F = [[-1]*capacityJ for _ in range(dimension)]

This is a common Python pitfall. See this post for more explanation.