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#equations.py

For a given collection of numbers and operations, generate equations that evaluate to a given goal.

##Usage

solve(goals: int | Iterable[int], numbers: Collection[int], operations: Iterable[str]='+-*/', unary: Callable | None=None, *, singles: bool=False, insert_paras: bool=True, fixed_order: bool=False, max_consecutive_powers: int=1, max_factorials: int=1) -> dict[int, list[str]]

For one or more given numeric goals, numbers and operations, return an int: list dictionary of all possible equations that can be made from the numbers and operations to make each goal.

goal must be an int or a collection of ints.

numbers must be a collection of ints.

operations must be an iterable of str mathemathical symbols. It defaults to "+-*/". The full range of tested operations is ['+', '-', '*', '/', '', '.', '**', '%', '//']. The empty string concatenates numbers. The period concatenates with a decimal point.

unary is an optional unary function eg abs, operator.neg, math.floor, math.ceil, math.sqrt, math.factorial. It defaults to None. All permutations of applying it over two or more consecutive operands will be generated. The program can currently only accept one unary function at a time. Also see singles parameter.

The following parameters are keyword-only:

If singles is True, all permutations of applying unary to individual operands will also be generated. This boolean option is useful because some unary functions eg math.floor and math.ceil do not alter integers. It defaults to False.

The insert_paras bool determines whether to allow parentheses in the generated equations. Parantheses will not be used in the equation if this is False, except as required for unary with singles. It defaults to True.

If fixed_order is True, the numbers will not be rearranged. It defaults to False.

Using too many powers (**) or too many math.factorial functions in equations can cause the program to crash or run for too long. The max_consecutive_powers and max_factorials int parameters (both default=1) restrain this issue.

##Examples

In:

numbers = range(1, 4)
goal = 6
for eqs in solve(goal, numbers, fixed_order=True).values():
    for eq in eqs:
        print(eq)

Output:

1+2+3
(1+2)+3
1+(2+3)
1*2*3
(1*2)*3
1*(2*3)

In:

numbers = [100, 23, 56, 40, 6]
goal = 49
for eqs in solve(goal, numbers).values():
    for eq in eqs:
        print(eq)

Output:

(100-23)*(40/56)-6
((100-23)*(40/56))-6
(100-23)*40/56-6
(((100-23)*40)/56)-6
((100-23)*40)/56-6
((100-23)*40/56)-6
(100-23)/56*40-6
(((100-23)/56)*40)-6
((100-23)/56)*40-6
((100-23)/56*40)-6
(100-23)/(56/40)-6
((100-23)/(56/40))-6
40*((100-23)/56)-6
(40*((100-23)/56))-6
((40*(100-23))/56)-6
(40*(100-23))/56-6
40*(100-23)/56-6
(40*(100-23)/56)-6
(40/56)*(100-23)-6
(40/56*(100-23))-6
((40/56)*(100-23))-6
40/56*(100-23)-6
(40/(56/(100-23)))-6
40/(56/(100-23))-6