# Traffic speed limit check for intervals

Given 2 lists of tuples limits and speeds, both have the format of [(speed1, time1), (speed2, time2)]. My goal is to write a function to check whether the there is a period of time that the speed exceeds the limit (Return True if exceeds). For example, Given limits = [(50,100), (30, 20)], speeds = [(30, 80), (10, 30), (40, 10)], return True.

The example inputs imply that during the first 100 miles, the speed limit is 50. In the 101-120 mile, speed limit is 30. Since in the speeds list, the last 10 miles have speed 40 > 30, so we return True.

We can assume the inputs are valid, so the limits and speeds list always start and end at the same time.

Can I have some pointers on the correctness and how the code can be refactored?

def speed_check(limits, speeds):
i, j = 0, 0
prev_limit_range, prev_speed_range = 0, 0
while j < len(speeds) and i < len(limits):
if limits[i][0] < speeds[j][0]:
return True
if limits[i][1] + prev_limit_range < speeds[j][1] + prev_speed_range:
prev_limit_range += limits[i][1]
i += 1
elif limits[i][1] + prev_limit_range > speeds[j][1] + prev_speed_range:
prev_speed_range += speeds[j][1]
j += 1
else:
prev_limit_range += limits[i][1]
prev_speed_range += speeds[j][1]
i += 1
j += 1

return False

assert speed([(30, 15), (55, 20)], [(30, 15), (55, 20)]) == False
assert speed([(30, 15), (55, 20)], [(30, 14), (65, 20)]) == True

• " both have the format of [(speed1, time1)" "during the first 100 miles," This is contradictory. Did you mean to say that the format is [(speed1, distance1), ...]? Commented Apr 2, 2018 at 16:24

def speed_check(limits, speeds):
# Explicit assignment of temporary variables
i, j = 0, 0
prev_limit_range, prev_speed_range = 0, 0
# Assumption that speeds and limits will not change during iteration
while j < len(speeds) and i < len(limits):
# Multiple if statements make it so that we can't just swap lines of
# code without breaking things.
if limits[i][0] < speeds[j][0]: # speed > limit would be more readable
return True
if limits[i][1] + prev_limit_range < speeds[j][1] + prev_speed_range:
prev_limit_range += limits[i][1]
i += 1
elif limits[i][1] + prev_limit_range > speeds[j][1] + prev_speed_range:
prev_speed_range += speeds[j][1]
j += 1
else:
# Manual incrementation of local variables.
prev_limit_range += limits[i][1]
prev_speed_range += speeds[j][1]
i += 1
j += 1

return False


Python-wise there are multiple parts of your implementation that could be tackled differently. Let's see what we could do.

If you think about this problem graphically, drawing an x-axis for distance and a y-axis for speed, then all you want is to check whether the curve for actual speed ever crosses the curve for speed limits.

You could break down your problem into subparts:

def get_graph(speedlist):
"""Generate a list of tuples into a flatten list as in:
[(1,2), (3, 4)] -> [1, 1, 3, 3, 3, 3]
"""
return [item for x in [y[1]*[y[0]] for y in speedlist] for item in x]

def check_exceeds(speeds, limits):
speed_graph = get_graph(speeds)
limits_graph = get_graph(limits)
return any([x > y for x, y in zip(speed_graph, limits_graph)])


This approach avoids three issues I see in your implementation: excess of if-statements, explicit indexing, and explicit iteration. Why are these issues? Well, it's easy to make mistakes when indexing and manually iterating, and it's easy to forget possible branches when using if/else clauses. Python offers a lot of tooling so that you don't have to do everything yourself, and it's considered good practice to leverage that tooling to make your code both more readable and safe.

For your assertions, there is also no need to compare to True nor False, in case your function is defined in such a way that it returns a boolean:

assert check_exceeds([(30, 15), (55, 20)], [(30, 15), (55, 20)])
assert not check_exceeds([(30, 15), (55, 20)], [(30, 14), (65, 20)])


(quick answer as I was answering the post in StackOverflow before it migrated)

• Welcome to Code Review! Please take a look at the how to answer to avoid common pitfalls while answering this on CR and you'll be fine.
– Mast
Commented Apr 2, 2018 at 9:05
• the name of the function is a little confusing, get_speed_graph because it's used for both speeds and limits, perhaps it should be called get_graph or flatten_list or something more generic. Commented Apr 2, 2018 at 12:45
• Agreed. I changed it to get_graph, even though I think there must still be a better name for it (since we aren't getting any "graphs" per see). Commented Apr 2, 2018 at 12:48
• It might be worthwhile to note that flattening the list and comparing in this way can be a little inefficient in terms of memory and time, in the worst case. When the "distance" for a given "speed" is a very high value, there will be a lot of repetition of the same "speed" value in the list. Perfectly fine for low values though, and certainly very readable and pythonic imho. Commented Apr 2, 2018 at 19:17
• @Drgabble agreed. A possibly better solution would be to have get_graph return a generator and check_exceeds exit early if the limit is ever exceeded (in fact early exits are implemented in the OP). Seems a bit of an overkill for such a contrived example as readability seems more important here. Commented Apr 2, 2018 at 22:04

Your code seems to be working fine on the test cases (one the function name is fixed), let's see how it can be improved.

## Style

There is an official standard Python style guide called PEP 8. This is highly recommended reading. It gives guidelines to help writing code that is both readable and consistent. The Python community tries to follow these guidelines, more or less strictly (a key aspect of PEP 8 is that it provides guidelines and not strict rules to follow blindly).

Among other things, it advised to

Use 4 spaces per indentation level.

## Logic simplification

The comparisons seems complicated but it is actually fairly simple: you compare 2 values and consider 3 situations: they are equal or the first number is smaller or the first number is bigger. To avoid repeating (and computing) the different numbers, you could compute the difference once.

    diff = (limits[i][1] + prev_limit_range) - (speeds[j][1] + prev_speed_range)
if diff < 0:
prev_limit_range += limits[i][1]
i += 1
elif diff > 0:
prev_speed_range += speeds[j][1]
j += 1
else:
prev_limit_range += limits[i][1]
prev_speed_range += speeds[j][1]
i += 1
j += 1


By re-organising the terms, we have:

diff = limits[i][1] - speeds[j][1] + prev_limit_range - prev_speed_range


and it appears that only the different between prev_limit_range and prev_speed_range is relevant: we could use a single variable for it.

prev_diff = 0
while j < len(speeds) and i < len(limits):
if limits[i][0] < speeds[j][0]:
return True
diff = limits[i][1] - speeds[j][1] + prev_diff
if diff < 0:
prev_diff += limits[i][1]
i += 1
elif diff > 0:
prev_diff += -speeds[j][1]
j += 1
else:
prev_diff += limits[i][1] - speeds[j][1]
i += 1
j += 1


But then, prev_diff += limits[i][1] - speeds[j][1] corresponds to prev_diff = prev_diff + limits[i][1] - speeds[j][1] = diff = 0.

Also, storing the relevant data in variable, things get a bit cleaner.

    lim, speed = limits[i][1], speeds[j][1]
diff = speed - lim
if diff > prev_diff:
prev_diff += lim
i += 1
elif diff < prev_diff:
prev_diff += -speed
j += 1
else:
prev_diff = 0
i += 1
j += 1


## Iterator

Instead of dealing with indices explicitly, you could use iterators and just decide which iterator you "advance" on (I am not 100% convinced it makes things better in your case but it is always a good technique to know):

def speed_check(limits, speeds):
prev_diff = 0
speed_iter, limit_iter = iter(speeds), iter(limits)
try:
speed_val = next(speed_iter)
limit_val = next(limit_iter)
while limit_val[0] >= speed_val[0]:
diff = speed_val[1] - limit_val[1]
if diff > prev_diff:
prev_diff += limit_val[1]
limit_val = next(limit_iter)
elif diff < prev_diff:
prev_diff += -speed_val[1]
speed_val = next(speed_iter)
else:
prev_diff = 0
limit_val = next(limit_iter)
speed_val = next(speed_iter)
return True
except StopIteration:  # no more values
return False