Rob Rob - 2 months ago 9
Python Question

trying all combinations of operations on list of variables

I have a list of values like:

values = [1, 2, 3, 4]


and I want to try all combinations on this list like:

1 + 2
1 + 3
1 + 4
1 * 2
1 * 3
1 * 4
1 + 2 * 3
1 + 2 * 4
1 + 3 * 4


etc.

What would be the most straightforward way to get all these possible combinations of operations in the most succinct way possible?

I would imagine having two lists, [1,2,3,4] and [+, *, -, /] and then taking all combinations of the numbers of all lengths, and then filling in the blanks with all combinations.

So selecting [1, 2, 3] and then selecting all permutations of the operations and combining them together. This seems messy and I'm hoping there's a clearer way to code this?

Answer

Here's a recursive solution that builds the expression from numbers & operators and then uses eval to calculate it:

vals = [1, 2, 3]
operators = ['+', '*', '-', '/']

def expressions(values):
    # Base case, only one value left
    if len(values) == 1:
        yield values

    # Iterate over the indexes
    for i in range(len(values)):
        # Pop value from given index and store the remaining values
        # to be used with next recursion
        forward = values[:]
        val = forward.pop(i)

        # Yield all value, operator, subexpression combinations
        for op in operators:
            for rest in expressions(forward):
                yield [val, op] + rest

for expr in expressions(vals):
    expr = ' '.join(str(x) for x in expr)
    print('{} = {}'.format(expr, eval(expr)))

Output (partial):

1 + 2 + 3 = 6
1 + 2 * 3 = 7
1 + 2 - 3 = 0
1 + 2 / 3 = 1.6666666666666665
1 + 3 + 2 = 6
1 + 3 * 2 = 7
1 + 3 - 2 = 2
1 + 3 / 2 = 2.5
1 * 2 + 3 = 5
1 * 2 * 3 = 6
1 * 2 - 3 = -1
1 * 2 / 3 = 0.6666666666666666
1 * 3 + 2 = 5
1 * 3 * 2 = 6
1 * 3 - 2 = 1
1 * 3 / 2 = 1.5
1 - 2 + 3 = 2
1 - 2 * 3 = -5
1 - 2 - 3 = -4
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