Rob - 5 months ago 17

Python Question

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
```