#
# Name: CS 111 Course Staff
#
# lab3btask3.py
#
# negate_evens([2, 3, 5, 8])
#
# * what is the solution?
#     [-2, 3, 5, -8]
#
# * what is the next smaller subproblem?
#     negate_evens([3, 5, 8])
#
# * what is the solution to that subproblem?
#     [3, 5, -8]
#
# * how can we use the solution to the subproblem to construct the
#   solution to the original problem?
#     return [-1 * 2] + [3, 5, -8]
#
# negate_evens([1, -4, -7, 6])
#
# * what is the solution?
#     [1, 4, -7, -6]
#
# * what is the next smaller subproblem?
#     negate_evens([-4, -7, 6])
#
# * what is the solution to that subproblem?
#     [4, -7, -6]
#
# * how can we use the solution to the subproblem to construct the
#   solution to the original problem?
#     return [1] + [4, -7, -6]

def negate_evens(vals):
    """ uses recursion to return a version of the list vals in which 
        all even number have been multiplied by -1
        input: vals is an arbitrary list of integers
    """
    if vals == []:
        return []
    else:
        rest_negated = negate_evens(vals[1:])
        if vals[0] % 2 == 0:
            return [-1 * vals[0]] + rest_negated
        else:
            return [vals[0]] + rest_negated