#! /bin/env python3

'''

The knapsack problem or the subset sum problem is known to be hard to
solve.

https://en.wikipedia.org/wiki/Knapsack_problem

https://en.wikipedia.org/wiki/Subset_sum_problem

Here we are given a list of positive integers and a single positive
integer We want to determine if the there is a subset of the list of
integers whose sum equals the given integer.

The brute force method is to try all possibilities.  That is,
calculate the sums of all the subsets of the list of integers. For
this, we use our new best friend: power set.

'''

from  itertools import chain, combinations

## for hw1 you are not allowed to use itertools
def powerset(iterable):
    "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
    s = list(iterable)
    return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))

def subsetsums(list):
    ps = powerset(list)
    sums = [sum(n) for n in ps]
    return sums

def allindices(lst, element):
    i = 0
    result = []
    if element in lst:
        i = lst.index(element)
        result.append(i)
        while element in lst[i+1:]:
            i = lst.index(element,i+1)
            result.append(i)
        return result
    return False

def lcallindices(lst,element):
    return [i for (i,item) in enumerate(lst) if item == element]


l = [1,3,5,7,9,11,13]

ps = powerset(l)

r = subsetsums(l)

ai = allindices(r,21)

lcai = lcallindices(r,21)