def q1_calc_max_profit(prices: list) -> float:
r"""Compute maximum profit from stock prices.
Args:
prices (list): List of prices as `float`. Index is number of minutes
since beginning of trading day.
Returns:
max_profit (float): Maximum profit possible from buying then selling.
Notes:
* interviewcake.com question #1, "Apple Stocks".
* Complexity:
* n = len(prices)
* Ideal: Time=O(n), Space=O(1)
* Realized: Time=O(n), Space=O(1)
References:
.. [1] https://www.interviewcake.com/question/stock-price
"""
# Check arguments.
utils.check_arguments(antns=q1_calc_max_profit.__annotations__,
lcls=locals())
# Calculate max_profit sequentially with min_price since the fund must be
# bought before being sold.
(min_price, max_profit) = (prices[0], 0.0)
for price in prices:
min_price = min(min_price, price)
max_profit = max(max_profit, price - min_price)
return max_profit
def calc_segi(seg1: tuple, seg2: tuple) -> tuple:
r"""Calculate the intersection of a line segment.
Args:
seg1 (tuple):
seg2 (tuple):
Segments are `tuple`s with ('x', 'width') for x-axis or
('y', 'height') for y-axis.
Returns:
segi (tuple):
Segment intersection as `tuple`. Same format as `seg1`, `seg2`.
All values are `None` if segments are disjoint.
"""
# Check arguments.
utils.check_arguments(antns=calc_segi.__annotations__, lcls=locals())
# Order segments by coordinates of leading edge.
# Disjoint if first trailing edge < second leading edge.
if seg1[0] < seg2[0]:
(seg1st, seg2nd) = (seg1, seg2)
else:
(seg1st, seg2nd) = (seg2, seg1)
if seg1st[0] + seg1st[1] < seg2nd[0]:
segi = (None, None)
else:
segi = (seg2nd[0],
min(seg1st[0] + seg1st[1], seg2nd[0] + seg2nd[1]) -
seg2nd[0])
return segi
def q1(pr_a: float = 0.28,
pr_b: float = 0.29,
pr_c: float = 0.19,
pr_aib: float = 0.14,
pr_aic: float = 0.12,
pr_bic: float = 0.10,
pr_aibic: float = 0.08) -> float:
r"""Calculate P(not(A union B union C)).
Args:
pr_[a,b,c] (float): [P(A), P(B), P(C)]
pr_[aib,aic,bic] (float): [P(A intr B), P(A intr C), P(B intr C)]
pr_aibic (float): P(A intr B intr C)
Returns:
pr_naubuc (float): P(not(A union B union C))
Notes:
* P(not(A union B union C)) = (1 - (
P(A) + P(B) + P(C) - P(A intr B) - P(A intr C)
- P(B intr C) + P(A intr B intr C)))
"""
# Check arguments.
utils.check_arguments(antns=q1.__annotations__, lcls=locals())
# Calculate probability of union complement.
pr_naubuc = 1.0 - (pr_a + pr_b + pr_c - pr_aib - pr_aic - pr_bic +
pr_aibic)
return pr_naubuc
def sum_ints(path: str) -> int:
r"""Sum the integers from a text file, one integer per line.
Args:
path(str): Path to file. File contains one `int` per line.
Returns:
total(int): Total sum of all `int`s in the file.
Notes:
* Example 4 from [1]_.
* Complexity:
* n = number of lines in `path` file.
* Time: O(n)
* Space: O(1)
References:
.. [1] https://sites.google.com/site/steveyegge2/
five-essential-phone-screen-questions
"""
# Check input.
utils.check_arguments(antns=sum_ints.__annotations__, lcls=locals())
if not os.path.exists(path):
raise ValueError(
("`path` does not exist:\n" + "path =\n{path}").format(path=path))
# Sum the lines in the file.
total = 0
with open(path, 'rt') as fobj:
for line in fobj:
total += int(line.strip())
return total
def q16_max_duffel_bag_value(cake_tuples: list, bag_capacity: int) -> int:
r"""Compute max value that the duffel bag can hold.
Args:
cake_tuples (list): `list` of `tuple`s (cake_weight, cake_value)
cake_weight, cake_value > 0
bag_capacity (int): Max weight that the duffel bag can hold.
Returns:
bag_value (int): Max value that the duffel bag can hold.
Returns `numpy.inf` if there is a cake with weight = 0.
Notes:
* interviewcake.com question #16, "The Cake Thief"
* Complexity:
* (n, k) = (len(cake_tuples), bag_capacity)
* Ideal:
* Time: O(n*k)
* Space: O(k)
* Realized:
* Time: O(n*k)
* Space: O(k)
References:
.. [1] https://www.interviewcake.com/question/python/cake-thief
"""
# Check arguments.
utils.check_arguments(antns=q16_max_duffel_bag_value.__annotations__,
lcls=locals())
for tup in cake_tuples:
for item in tup:
if item < 0:
raise ValueError(
("All items in `cake_tuples` must be >= 0:\n" +
"cake_tuples =\n" + "{ct}").format(ct=cake_tuples))
elif not isinstance(item, int):
raise ValueError(
("All items in `cake_tuples` must be type `int`:\n" +
"cake_tuples =\n" + "{ct}").format(ct=cake_tuples))
if bag_capacity < 0:
raise ValueError(("`bag_capacity` must be >= 0\n" +
"bag_capacity = {bc}").format(bc=bag_capacity))
# With dynamic programming:
bag_value = 0
for (cake_weight, cake_value) in cake_tuples:
if cake_weight == 0 and cake_value > 0:
bag_value = sys.maxsize
if bag_value != sys.maxsize:
bag_values_max = [0] * (bag_capacity + 1)
for bag_capacity_current in range(len(bag_values_max)):
for (cake_weight, cake_value) in cake_tuples:
if cake_weight <= bag_capacity_current:
bag_values_max[bag_capacity_current] = max(
bag_values_max[bag_capacity_current], cake_value +
bag_values_max[bag_capacity_current - cake_weight])
bag_value = bag_values_max[bag_capacity]
return bag_value
def q5_count_combinations(amount: int, denoms: list) -> int:
r"""Count the number of combinations of `denomiations` that sum to `amount`.
Args:
amount (int): Amount of money to partition.
denoms (list): `list` of demoninations to partition `amount`
Returns:
ncombos (int): Number of combinations.
Raises:
ValueError:
* Raised if not amount >= 1.
* Raised if not len(denoms) >= 1.
* Raised if any denoms are not `int`.
* Raised if any denoms are not >= 1.
Notes:
* interviewcake.com question #5, "Making Change".
* Complexity:
* n = amount; k = len(denoms)
* Complexity:
* Ideal: Time: O(n*k); Space: O(n)
* Realized: Time: O(n*k); Space: O(n)
References:
.. [1] https://www.interviewcake.com/question/python/coin
"""
# Check arguments.
utils.check_arguments(antns=q5_count_combinations.__annotations__,
lcls=locals())
if not amount >= 1:
raise ValueError(
("`amount` must be >= 1\n" + "amount = {amt}").format(amt=amount))
if not len(denoms) >= 1:
raise ValueError(("`len(denoms)` must be >= 1\n" +
"len(denoms) = {nden}").format(nden=len(denoms)))
for denom in denoms:
if not isinstance(denom, int):
raise ValueError(
("All `denoms` must be type `int`\n" + "denom = {den}\n" +
"type(denom) = {tden}").format(den=denom, tden=type(denom)))
if not denom >= 1:
raise ValueError(("All `denoms` must be >= 1\n" +
"denom = {den}").format(den=denom))
# For each denomination, iterate through the amounts to find the number of
# combinations per amount.
# Note: For each amount, iterating through denominations will instead find
# the number of permutations per amount.
amt_ncombos = [0] * (amount + 1)
amt_ncombos[0] = 1
for den in denoms:
for amt in range(den, amount + 1):
amt_ncombos[amt] += amt_ncombos[amt - den]
ncombos = amt_ncombos[amount]
return ncombos
def q14_movies_match_flight(flight_length: int, movie_lengths: list) -> bool:
r"""Check if the sum of two movie lengths exactly equals the flight length.
Args:
flight_length (int): Length (duration) of the flight. Units: minutes.
movie_lengths (list): List of `int` as the lengths (durations) of
movies. Units: minutes.
Returns:
found_match (bool):
True: There are two movies whose sum lengths exactly matches the
length of the flight.
False: There are not two movies...
Notes:
* interviewcake.com question #14, "Inflight Entertainment" [1]_.
* Complexity:
* Ideal:
* Time: O(n)
* Space: O(n)
* Realized:
* Time: O(n)
* Space: O(n)
References:
.. [1] https://www.interviewcake.com/question/python/
inflight-entertainment
"""
# Check arguments.
utils.check_arguments(antns=q14_movies_match_flight.__annotations__,
lcls=locals())
# Memoize movie lengths seen.
# Without `collections.defaultdict`:
# `in` calls `dict.__contains__`, which is O(1) lookup for Python 3x.
#found_match = False
#movie_lengths_seen = dict()
#for movie_length1 in movie_lengths:
# movie_length2 = flight_length - movie_length1
# if movie_length2 in movie_lengths_seen:
# found_match = True
# break
# # Add movie_length1 after testing for movie_length2 to avoid watching
# # movie1 twice.
# movie_lengths_seen[movie_length1] = True
# With `collections.defaultdict`:
movie_lengths_seen = collections.defaultdict(lambda: False)
for movie_length1 in movie_lengths:
movie_length2 = flight_length - movie_length1
found_match = movie_lengths_seen[movie_length2]
if found_match:
break
# Add movie_length1 after testing for movie_length2 to avoid watching
# movie1 twice.
movie_lengths_seen[movie_length1] = True
return found_match
def print_mult_table(max_fac: int = 12) -> None:
r"""Print a multiplication table to stdout.
Args:
max_fac (int, optional, default=12): Factor up to which to make table.
`max_fac` >= 0.
Example: max_fac=12 (default) makes multiplication table
0x0, 0x1, ..., 0x12
1x0, 1x1, ..., 1x12
..., ..., ..., ...
12x0, 12x1, ..., 12x12
Returns:
None: Prints table to `stdout`.
Raises:
ValueError: Raised if `max_fac` < 0.
Notes:
* Example 3 from [1].
* Complexity:
* n = max_fac
* Time: O(n^2)
* Space: O(1)
References:
.. [1] https://sites.google.com/site/steveyegge2/five-essential-phone-screen-questions
"""
# Check input
utils.check_arguments(antns=print_mult_table.__annotations__,
lcls=locals())
if max_fac < 0:
raise ValueError(("`max_fac` must be >= 0\n" +
"max_fac = {max_fac}").format(max_fac=max_fac))
# Define custom print function for factors and products (elements)
# of multiplication table,
max_prod = max_fac * max_fac
max_digits = len(str(max_prod))
fmt = "{elt:>" + str(max_digits) + "d}"
print_elt = lambda elt: print(fmt.format(elt=elt), end=' ')
# Print multiplication table.
for row_fac in range(max_fac + 1):
# Print header row
if row_fac == 0:
print(' ' * (max_digits - 1) + 'x', end=' ')
[print_elt(elt) for elt in range(max_fac + 1)]
print()
# Print header column element for every row.
print_elt(elt=row_fac)
# Print products
[print_elt(row_fac * col_fac) for col_fac in range(max_fac + 1)]
print()
return None
def q15_fib(idx: int) -> int:
r"""Compute the nth Fibonacci number.
Args:
idx (int): Nth Fibonacci number to compute.
`idx` >= 0.
Returns:
fnum (int): Nth Fibonacci number.
Raises:
ValueError: Raised if `idx` < 0 or is not `int`.
Notes:
* interviewcake.com question #15, "Compute Nth Fibonacci Number" [1]_.
* fib(n) = fib(n-1) + fib(n-2), fib(0) = 0, fib(1) = 1.
* Complexity:
* Ideal:
* Time: O(lg(n))
* Space: O(1)
* Realized:
* Time: O(n)
* Space: O(1)
References:
.. [1] https://www.interviewcake.com/question/python/nth-fibonacci
"""
# Check arguments.
utils.check_arguments(antns=q15_fib.__annotations__, lcls=locals())
if idx < 0:
raise ValueError(
("`idx` must be >= 0:\n" + "idx = {idx}").format(idx=idx))
# Compute nth Fibonacci number.
for inum in range(idx + 1):
if inum == 0:
fnum = 0
fnum_prev2 = 0
elif inum == 1:
fnum = 1
fnum_prev1 = 1
else:
fnum = fnum_prev1 + fnum_prev2
fnum_prev2 = fnum_prev1
fnum_prev1 = fnum
return fnum
def q2(pr_a: float = 0.30, pr_b: float = 0.40, pr_naub: float = 0.35) -> float:
r"""Calculate P(A intr B).
Args:
pr_[a,b] (float): [P(A), P(B)]
pr_naub (float): P(not(A union B))
Returns:
pr_aib (float): P(A intr B)
Notes:
* P(A union B) = P(A) + P(B) - P(A intr B)
P(A union B) = 1 - P(not(A union B))
=> P(A intr B) = P(A) + P(B) - (1 - P(not(A union B)))
"""
# Check arguments.
utils.check_arguments(antns=q2.__annotations__, lcls=locals())
# Calculate probability of intersection.
pr_aib = pr_a + pr_b - (1.0 - pr_naub)
return pr_aib
def q2_get_products_of_all_ints_except_at_index(ints: list) -> list:
r"""Calculate the products of all integers except for the one each index.
Args:
ints (list): `list` of `int` factors.
Returns:
prods (list): `list` of `int` products
Notes:
* interviewcake.com question #2, "Product of All Other Numbers".
* Complexity:
* n = len(prices)
* Ideal: Time=O(n), Space=O(n)
* Realized: Time=O(n), Space=O(n)
References:
..[1] https://www.interviewcake.com/question/product-of-other-numbers
"""
# Check arguments.
utils.check_arguments(
antns=q2_get_products_of_all_ints_except_at_index.__annotations__,
lcls=locals())
# Allocate a list of ones for `prods`. Multiply products at indexes by
# cumulative product then update cumulative product. Repeat iterating in
# opposite direction through `ints`.
idxs = range(len(ints))
prods = [1] * len(ints)
prod_cuml = 1
for idx in idxs:
prods[idx] = prod_cuml
prod_cuml *= ints[idx]
prod_cuml = 1
for idx in reversed(idxs):
prods[idx] *= prod_cuml
prod_cuml *= ints[idx]
return prods
def reverse_string(string: str) -> str:
r"""Reverse a string.
Args:
string (str): String with __getslice__ method.
Returns:
string_rev (str): Reversed `string`.
Notes:
* Example 1 from [1]_.
* Complexity:
* n = len(string)
* Time: O(n)
* Space: O(n)
References:
.. [1] https://sites.google.com/site/steveyegge2/five-essential-phone-screen-questions
"""
utils.check_arguments(antns=reverse_string.__annotations__, lcls=locals())
string_rev = string[::-1]
return string_rev
def calc_nth_fib(nth: int) -> int:
r"""Calculate the nth Fibonacci number (0-indexed).
Args:
nth (int): The index number of the Fibonacci number to calculate.
`nth` >= 0
Returns:
fib (int): The `nth` Fibonacci number in sequence.
Raises:
ValueError: Raised if `nth` < 0.
Notes:
* fib(0) = 0, fib(1) = 1, fib(n) = fib(n-1) + fib(n-2).
* Complexity:
* n = `nth`
* Time: O(n)
* Space: O(1)
"""
# Check arguments.
utils.check_arguments(antns=calc_nth_fib.__annotations__, lcls=locals())
if nth < 0:
raise ValueError(
("`nth` must be >= 0\n" + "nth = {nth}").format(nth=nth))
# Initialize Fibonacci sequence to reach nth Fibonacci number.
maxlen = 2
fibs_prev = collections.deque(maxlen=maxlen)
fibs_prev.extend(range(maxlen))
if nth < maxlen:
fib = fibs_prev[nth]
else:
idxs_res = range((nth - maxlen) + 1)
[fibs_prev.append(sum(fibs_prev)) for idx in idxs_res]
fib = fibs_prev[-1]
return fib
def q6_calc_intersection(rect1: dict, rect2: dict) -> dict:
r"""Calculate the intersection of two rectangles.
Args:
rect1 (dict):
rect2 (dict):
Rectangles are `dicts` with keys `x`, `y`, `width`, `height`.
`x`, `y` are the coordinates of the bottom-left corner.
Values are `int`.
Returns:
recti (dict):
Rectangle intersection as `dict`. Same format at `rect1`, `rect2`.
All values are `None` if rectangles are disjoint.
Raises:
ValueError:
* Raised if missing required keys.
* Raised if values are not `int`.
* Raised if width or height < 0
Notes:
* interviewcake.com question #6, "Rectangular Love".
* Complexity:
* Ideal: Time: O(1); Space: O(1)
* Realized: Time: O(1); Space: O(1)
References:
.. [1] https://www.interviewcake.com/question/rectangular-love
"""
# Check arguments.
utils.check_arguments(antns=q6_calc_intersection.__annotations__,
lcls=locals())
keys = set(['x', 'y', 'width', 'height'])
if not keys.issubset(set(rect1.keys())):
raise ValueError(
("`rect1` is missing required keys:\n" +
"required_keys = {keys}\n" + "rect1.keys() = {r1keys}").format(
keys=keys, r1keys=set(rect1.keys())))
if not keys.issubset(set(rect2.keys())):
raise ValueError(
("`rect2` is missing required keys:\n" +
"required_keys = {keys}\n" + "rect2.keys() = {r2keys}").format(
keys=keys, r2keys=set(rect2.keys())))
for key in keys:
if not isinstance(rect1[key], int):
raise ValueError(
("All values must be `int`:\n" +
"type(rect1[{key}]) = {tp}").format(key=key,
tp=type(rect1[key])))
if not isinstance(rect2[key], int):
raise ValueError(
("All values must be `int`:\n" +
"type(rect2[{key}]) = {tp}").format(key=key,
tp=type(rect2[key])))
for key in ['width', 'height']:
if not rect1[key] >= 0:
raise ValueError(
("'width' and 'height' values must be >= 0:\n" +
"type(rect1[{key}]) = {tp}").format(key=key,
tp=type(rect1[key])))
if not rect2[key] >= 0:
raise ValueError(
("'width' and 'height' values must be >= 0:\n" +
"type(rect2[{key}]) = {tp}").format(key=key,
tp=type(rect2[key])))
# Define a method to compute the intersection of two segments.
def calc_segi(seg1: tuple, seg2: tuple) -> tuple:
r"""Calculate the intersection of a line segment.
Args:
seg1 (tuple):
seg2 (tuple):
Segments are `tuple`s with ('x', 'width') for x-axis or
('y', 'height') for y-axis.
Returns:
segi (tuple):
Segment intersection as `tuple`. Same format as `seg1`, `seg2`.
All values are `None` if segments are disjoint.
"""
# Check arguments.
utils.check_arguments(antns=calc_segi.__annotations__, lcls=locals())
# Order segments by coordinates of leading edge.
# Disjoint if first trailing edge < second leading edge.
if seg1[0] < seg2[0]:
(seg1st, seg2nd) = (seg1, seg2)
else:
(seg1st, seg2nd) = (seg2, seg1)
if seg1st[0] + seg1st[1] < seg2nd[0]:
segi = (None, None)
else:
segi = (seg2nd[0],
min(seg1st[0] + seg1st[1], seg2nd[0] + seg2nd[1]) -
seg2nd[0])
return segi
# Calculate the rectangle intersections for x-axes and y-axes.
# If any axes are disjoint, then all axes are disjoint (`None` values).
recti = dict()
(recti['x'], recti['width']) = calc_segi(seg1=(rect1['x'], rect1['width']),
seg2=(rect2['x'], rect2['width']))
(recti['y'],
recti['height']) = calc_segi(seg1=(rect1['y'], rect1['height']),
seg2=(rect2['y'], rect2['height']))
for val in recti.values():
if val is None:
recti = {'x': None, 'y': None, 'width': None, 'height': None}
break
return recti
def q4_condense_meeting_times(times: list) -> list:
r"""Condense meeting times into contiguous blocks.
Args:
times (list): `list` of `tuple`s of `int`s as meeting times. `int`s are
number of 30-minute blocks since 9:00am. Does not need to be sorted.
Example: `times = [(0, 1), (3, 5), (2, 4)]`
Returns:
condensed (list): `list` of combined meeting times as `tuple`s.
Example: `condensed = [(0, 1), (2, 5)]`
Notes:
* interviewcake.com question #4, "Merging Meeting Times".
* Complexity:
* n = len(times)
* Ideal: Time=O(n*lg(n)), Space=O(n)
* Realized: Time=O(n*lg(n)), Space=O(n)
References:
.. [1] https://www.interviewcake.com/question/merging-ranges
"""
# Check arguments.
utils.check_arguments(antns=q4_condense_meeting_times.__annotations__,
lcls=locals())
# #########################################
# # Without sorting: Time: O(n**2); Space: O(n)
# # Iterate through `times` comparing current time to:
# # * condensed times in `condensed`, iterating forwards
# # * uncondensed times in `times`, iterating forwards
# # * uncondensed times in `times`, iterating backwards
# # * condensed times in `condensed`, iterating backwards
# # Backwards and forwards iteration is necessary for unsorted `times`.
# def do_overlap(time1:tuple, time2:tuple) -> bool:
# # Check arguments.
# utils.check_arguments(
# antns=do_overlap.__annotations__,
# lcls=locals())
# # Order meeting times by start time.
# # Overlap if first stop time >= second start time.
# if time1[0] < time2[0]:
# (time1st, time2nd) = (time1, time2)
# else:
# (time1st, time2nd) = (time2, time1)
# if time1st[1] >= time2nd[0]:
# overlap = True
# else:
# overlap = False
# return overlap
# # Compare current time to seen condensed times.
# condensed = [times[0]]
# for (idx, time) in enumerate(times):
# idx_olap = None
# # Compare current time with condensed times, forward.
# for idx_cmp in range(len(condensed)):
# time_cmp = condensed[idx_cmp]
# overlap = do_overlap(time1=time, time2=time_cmp)
# if overlap:
# time = (min(time[0], time_cmp[0]), max(time[1], time_cmp[1]))
# if idx_olap is None:
# idx_olap = idx_cmp
# # Compare current time with uncondensed times, forward and backward.
# for idx_cmp in itertools.chain(
# range(idx+1, len(times)), reversed(range(idx+1, len(times)-1))):
# time_cmp = times[idx_cmp]
# overlap = do_overlap(time1=time, time2=time_cmp)
# if overlap:
# time = (min(time[0], time_cmp[0]), max(time[1], time_cmp[1]))
# # Compare current time with condensed times, backward.
# for idx_cmp in reversed(range(len(condensed))):
# time_cmp = condensed[idx_cmp]
# overlap = do_overlap(time1=time, time2=time_cmp)
# if overlap:
# time = (min(time[0], time_cmp[0]), max(time[1], time_cmp[1]))
# if idx_olap is None:
# idx_olap = idx_cmp
# # Update condensed times if overlap, else append.
# if idx_olap is not None:
# condensed[idx_olap] = time
# else:
# condensed.append(time)
########################################
# With sorting: Time: O(n*lg(n)); Space: O(n)
# Sort times first by meeting start then by meeting end
# to avoid needing to compare all meeting times to each other.
times = sorted(times, key=operator.itemgetter(0, 1))
condensed = [times[0]]
for time in times:
cond = condensed[-1]
# If time is disjoint, append as new meeting.
# Else change condensed meeting time.
if cond[1] < time[0]:
condensed.append(time)
else:
condensed[-1] = (cond[0], max(cond[1], time[1]))
return condensed
def q3_calc_highest_product_of_3(ints: list) -> int:
r"""Calculate the highest product from integers.
Args:
ints (list): List of `ints` with `len(ints) >= 3`
Returns:
prod (int): Highest product from 3 `int`s.
Raises:
ValueError: Raised if `len(ints) < 3`.
Notes:
* interviewcake.com question #3, "Highest Product of 3".
* Complexity:
* n = len(ints)
* Ideal: Time=O(n), Space=O(1)
* Realized: Time=O(n), Space=O(1)
References:
..[1] https://www.interviewcake.com/question/highest-product-of-3
"""
# Check arguments.
utils.check_arguments(antns=q3_calc_highest_product_of_3.__annotations__,
lcls=locals())
if len(ints) < 3:
raise ValueError(("`ints` must have at least 3 items:\n" +
"ints =\n{ints}").format(ints=ints))
# #########################################
# # With collections, itertools; Python 3.5.
# max_3 = collections.deque(iterable=[1]*3, maxlen=3)
# min_2 = collections.deque(iterable=[1]*2, maxlen=2)
# for item in ints:
# # Find the 3 most positive integers.
# for idx in range(len(max_3)):
# if item > max_3[idx]:
# max_3.insert(item, index=idx)
# break
# # Find the 2 most negative integers.
# for idx in range(len(min_2)):
# if item < min_2[idx]:
# min_2.insert(item, index=idx)
# break
# prod_max_3 = functools.reduce(operator.mul, max_3, 1)
# prod_min_2 = functools.reduce(operator.mul, min_2, 1)
# prod_minmax_3 = prod_min_2 * max_3[0]
# prod = max(prod_max_3, prod_minmax_3)
# #########################################
# # With extreme integers ranked.
# (max_1st, max_2nd, max_3rd) = (1, 1, 1)
# (min_1st, min_2nd) = (1, 1)
# for item in ints:
# # Find the 3 most positive integers.
# if item > max_3rd:
# if item > max_2nd:
# if item > max_1st:
# max_3rd = max_2nd
# max_2nd = max_1st
# max_1st = item
# else:
# max_3rd = max_2nd
# max_2nd = item
# else:
# max_3rd = item
# # Find the 2 most negative integers.
# if item < min_2nd:
# if item < min_1st:
# min_2nd = min_1st
# min_1st = item
# else:
# min_2nd = item
# prod = max(max_1st*max_2nd*max_3rd, max_1st*min_1st*min_2nd)
#########################################
# With bottom-up approach.
(prod_1_pos, prod_2_pos, prod_3_pos) = (0, 0, 0)
(prod_1_neg, prod_2_neg) = (0, 0)
for item in ints:
# Find the 3 most positive integers.
if item >= 0:
prod_3_pos = max(item * prod_2_pos, prod_3_pos)
prod_2_pos = max(item * prod_1_pos, prod_2_pos)
prod_1_pos = max(item, prod_1_pos)
# Find the 2 most negative integers.
else:
item *= -1
prod_2_neg = max(item * prod_1_neg, prod_2_neg)
prod_1_neg = max(item, prod_1_neg)
prod = max(prod_3_pos, prod_1_pos * prod_2_neg)
return prod
def myfunc(arg0: int, arg1: str) -> float:
utils.check_arguments(antns=myfunc.__annotations__, lcls=locals())
return 1.0
