tree path finder

Write a function, path_finder, that takes in the root of a binary tree and a target value. The function should return an array representing a path to the target value. If the target value is not found in the tree, then return None.

You may assume that the tree contains unique values.

test_00:

a = Node("a")
b = Node("b")
c = Node("c")
d = Node("d")
e = Node("e")
f = Node("f")

a.left = b
a.right = c
b.left = d
b.right = e
c.right = f

#      a
#    /   \
#   b     c
#  / \     \
# d   e     f

path_finder(a, 'e') # -> [ 'a', 'b', 'e' ]

test_01:

a = Node("a")
b = Node("b")
c = Node("c")
d = Node("d")
e = Node("e")
f = Node("f")

a.left = b
a.right = c
b.left = d
b.right = e
c.right = f

#      a
#    /   \
#   b     c
#  / \     \
# d   e     f

path_finder(a, 'p') # -> None

test_02:

a = Node("a")
b = Node("b")
c = Node("c")
d = Node("d")
e = Node("e")
f = Node("f")
g = Node("g")
h = Node("h")

a.left = b
a.right = c
b.left = d
b.right = e
c.right = f
e.left = g
f.right = h

#      a
#    /   \
#   b     c
#  / \     \
# d   e     f
#    /       \
#   g         h

path_finder(a, "c") # -> ['a', 'c']

test_03:

a = Node("a")
b = Node("b")
c = Node("c")
d = Node("d")
e = Node("e")
f = Node("f")
g = Node("g")
h = Node("h")

a.left = b
a.right = c
b.left = d
b.right = e
c.right = f
e.left = g
f.right = h

#      a
#    /   \
#   b     c
#  / \     \
# d   e     f
#    /       \
#   g         h

path_finder(a, "h") # -> ['a', 'c', 'f', 'h']

test_04:

x = Node("x")

#      x

path_finder(x, "x") # -> ['x']

test_05:

path_finder(None, "x") # -> None

test_06:

root = Node(0)
curr = root
for i in range(1, 19500):
  curr.right = Node(i)
  curr = curr.right

#      0
#       \
#        1
#         \
#          2
#           \
#            3
#             .
#              .
#               .
#              19498
#                \
#                19499

path_finder(root, 16281) # -> [0, 1, 2, 3, ..., 16280, 16281]