function that finds operations in between numbers such that equation is satisfied

find_placeholders.py

from numpy import *
import itertools

__all__ = ['find_placeholders']
__author__ = "Tim Herfurth <timherfurth87@gmail.com>"

# # function that finds operations in between numbers such that equation is satisfied

# possible operations
list_of_all = [add, subtract, multiply, divide]
list_of_all = ['+',"-","*","/"]

def find_placeholders(a,c):
    '''
    Finds a combination of basic mathematical operations (+,-,*,/) between numbers in a that yields c
    
    Parameters
    ----------
        a: List of numbers on left-hand side of equation in between which mathematical operation is to be determined
        c: Number that represents right-hand side of equation
        
    Returns
    ---------
        List of mathematical operations that satisfy equation. If no solution can be found an according string is returned.
        
    Example
    ---------
        Task to solve: 5_3_6=10 where _ have to be determined
        >>> find_placeholders([5,3,6],10)
        ['/', '*']
    '''
    n = len(a)
    # create all possible combinations of signs and append 0, which is later removed
    operations = [p for p in itertools.product(list_of_all, repeat=n-1)]
    operations = [list(x)+['0'] for x in operations]
    # combine numbers and operations to one string per combination
    str1 = list(map(str, a))
    left_hand_expressions = array([''.join(''.join(x) for x in zip(str1,x))[:-1] for x in operations])
    # evaluate equations (and taking care of division by zero); stop after first equality is found
    equation_holds = -1
    for eq_n, eq in enumerate(left_hand_expressions):
        try:
            if eval(eq)==c:
                equation_holds = eq_n
                break
        except ZeroDivisionError:
            pass
    # return operations that satisfy equation
    if equation_holds == -1:
        return 'no solution found'
    else:
        return operations[eq_n][:-1]