How to convert algorithm to python

Question

I'm having trouble converting a script to a more effective algorithm I was given.

Here's the python code:

#!/usr/bin/env python

import itertools
target_sum = 10
a = 1
b = 2
c = 4
a_range = range(0, target_sum + 1, a)
b_range = range(0, target_sum + 1, b)
c_range = range(0, target_sum + 1, c)
for i, j, k in itertools.product(a_range, b_range, c_range):
    if i + j + k == 10:
        print a, ':', i/a, ',', b, ':',  j/b, ',', c, ':',  k/c

(it only does 3 variables just for example, but I want to use it on thousands of variables in the end).

Here's the result I am looking for(all the combo's that make it result to 10):

1 : 0 , 2 : 1 , 4 : 2
1 : 0 , 2 : 3 , 4 : 1
1 : 0 , 2 : 5 , 4 : 0
1 : 2 , 2 : 0 , 4 : 2
1 : 2 , 2 : 2 , 4 : 1
1 : 2 , 2 : 4 , 4 : 0
1 : 4 , 2 : 1 , 4 : 1
1 : 4 , 2 : 3 , 4 : 0
1 : 6 , 2 : 0 , 4 : 1
1 : 6 , 2 : 2 , 4 : 0
1 : 8 , 2 : 1 , 4 : 0
1 : 10 , 2 : 0 , 4 : 0

In question Can brute force algorithms scale? a better algorithm was suggested but I'm having a hard time implementing the logic within python. The new test code:

    # logic to convert
    #for i = 1 to k
    #for z = 0 to sum:
    #    for c = 1 to z / x_i:
    #        if T[z - c * x_i][i - 1] is true:  #having trouble creating the table...not sure if thats a matrix
    #            set T[z][i] to true
    
#set the variables
sum = 10
data = [1, 2, 4]
# trying to find all the different ways to combine the data to equal the sum

for i in range(len(data)):
    print(i)
    if i == 0:
        continue
    for z in range(sum):
        for c in range(z/i):
            print("*" * 15)
            print('z is equal to: ', z)
            print('c is equal to: ', c)
            print('i is equal to: ', i)
            print(z - c * i)
            print('i - 1: ', (i - 1))
            
            if (z - c * i) == (i - 1):
                print("(z - c * i) * (i - 1)) match!")
                print(z,i)

Sorry its obviously pretty messy, I have no idea how to generate a table in the section that has:

if T[z - c * x_i][i - 1] is true:
    set T[z][i] to true

In other places while converting the algo, I had more problems because in lines like 'or i = 1 to k' converting it to python gives me a TypeError: 'int' object is not utterable.

Answer 1

You can get that block which creates the table for dynamic programming with this:

from collections import defaultdict

# T[x, i] is True if 'x' can be solved
# by a linear combination of data[:i+1]
T = defaultdict(bool)           # all values are False by default
T[0, 0] = True                # base case

for i, x in enumerate(data):    # i is index, x is data[i]
    for s in range(sum + 1):
        for c in range(s / x + 1):
            if T[s - c * x, i]:
                T[s, i + 1] = True