Simple math equation solver
Level: Advanced (score: 4)
Your task is to write a simple math equation solver. Given a list of operators and an integer result, find all the number combinations that can be used with operators to produce the result.
Numbers must be integers in the range of 1 to 9 and no number may be repeated in a solution. The solver should return a list of solutions, each solution a list of integers which produce the result with the given operators.
Consider the following examples:
>>> # i1 + i2 = 6
>>> list(find_all_solutions(["+"], 6))
[
[1, 5], # 1 + 5 = 6
[2, 4], # 2 + 4 = 6
[4, 2], # 4 + 2 = 6
[5, 1], # 5 + 1 = 6
# 3 + 3 is not valid, as each number can only be used once
]
>>> # i1 - i2 = 5
>>> list(find_all_solutions(["-"], 5))
[
[6, 1], # 6 - 1 = 5
[7, 2], # 7 - 2 = 5
[8, 3], # 8 - 3 = 5
[9, 4], # 9 - 4 = 5
]
>>> # i1 * i2 * i3 + i4 = 181
>>> list(find_all_solutions(["*", "*", "+"], 181))
[
[4, 5, 9, 1], # 4 * 5 * 9 + 1 = 181
[4, 9, 5, 1], # 4 * 9 * 5 + 1 = 181
[5, 4, 9, 1], # 5 * 4 * 9 + 1 = 181
[5, 9, 4, 1], # 5 * 9 * 4 + 1 = 181
[9, 4, 5, 1], # 9 * 4 * 5 + 1 = 181
[9, 5, 4, 1], # 9 * 5 * 4 + 1 = 181
]
- Allowed operations are addition +, subtraction - or multiplication *.
- Result is always an int (positive or negative).
- i1, i2, i3 [...] are ints between 1 and 9 (included) but can only be used once in a solution.
Task
- Write a function that receives a list of operators & result and returns all possible solutions as a list / generator of a list of int as shown above.
- Make sure to implement the order of operations correctly (multiplication before addition or subtraction).
- Using operators other than +, - or * should raise a ValueError.
- Using non int as a result should raise ValueError.
Good luck and keep calm and code in Python!