Manufacturing Anxiety: Breaking the Illusion
Recently, this Google interview question has been circulating in job hunting groups everywhere.
Many people's first reaction: "Isn't this just sorting + simulation? Easy!"
Dead wrong.
If you just write a brute force simulation, congratulations โ the interviewer will smile and hit you with three Followups, then you'll get rejected.
Our oavoservice team obtained this question immediately and discovered it's packed with Greedy Algorithm, Binary Search, and Edge Case challenges.
Question Breakdown: Demonstrating Expertise
๐ Original Problem
You're on a remote island that needs evacuation due to pending flooding. The government is sending planes tomorrow to get some people out. If you miss the last plane you'd have to take a slower boat the following day which you don't want. Given the plane schedule and the schedule of all your fellow islanders, What is the latest you could get to the airport tomorrow and still get evacuated?
๐ Problem Analysis
You're stranded on a remote island about to be flooded.
The government is sending multiple planes tomorrow to evacuate some islanders.
If you miss all flights, you'll have to take a slow boat the next day (you definitely don't want that).
Given:
- All flight departure times and seat capacities
- All other islanders' planned airport arrival times
Rule: First come, first served, limited seats
Question: What's the latest you can arrive at the airport and still guarantee a seat?
Deep Dive: Building Trust
๐ง Problem Essence Analysis
This problem appears to be a "scheduling problem," but actually tests:
| Test Point | Specific Content |
|---|---|
| Greedy Thinking | How to allocate passengers to flights? |
| Binary Search | How to efficiently find the critical time point? |
| Edge Case Handling | Full flights, no flights, time conflicts |
| Complexity Optimization | From O(nยฒ) brute force to O(n log n) optimization |
๐ Input/Output Format
Input:
- flights: List[(departure_time, capacity)] # Flight list: (departure time, seats)
- arrivals: List[int] # Other islanders' airport arrival times
Output:
- int: Latest arrival time that guarantees boarding
- Return -1 if impossible to board any flight
๐ฏ Example Analysis
Example 1:
flights = [(100, 2), (200, 1)] # Flight 1: departs at 100, 2 seats; Flight 2: departs at 200, 1 seat
arrivals = [50, 80] # Two islanders arrive at times 50 and 80
Output: 199
Explanation:
- Flight 1 (departs 100, 2 seats): Islanders arriving before 100 can board
- Islander A(50), Islander B(80) both board, filling 2 seats
- Flight 2 (departs 200, 1 seat): People arriving before 200 can board
- No one else competing for this flight, you just need to arrive by 199
So the answer is 199
Example 2:
flights = [(100, 1)] # Only one flight, 1 seat
arrivals = [50] # One islander arrives at time 50
Output: 49
Explanation:
- The only flight departs at 100, with just 1 seat
- Islander A arrives at 50; if you arrive after 50, the seat is taken
- So you must arrive at 49 or earlier
Example 3:
flights = [(100, 1)]
arrivals = [50, 60] # Two islanders
Output: -1
Explanation:
- Only 1 seat, but 2 islanders arrive before you can
- No matter when you arrive, there's no seat left
- Return -1
Solution: Core Algorithm
Approach 1: Brute Force Simulation O(n ร m ร log m)
The most intuitive idea: enumerate your arrival time and simulate the entire boarding process.
def latest_arrival_brute_force(flights, arrivals):
"""
Brute force: enumerate all possible arrival times
flights: List[(departure_time, capacity)]
arrivals: List[int] - other islanders' arrival times
"""
# Collect all possible time points
all_times = set(arrivals)
for dep, _ in flights:
all_times.add(dep - 1) # moment before departure
all_times.add(dep)
all_times = sorted(all_times, reverse=True) # enumerate from late to early
for my_time in all_times:
if can_board(flights, arrivals, my_time):
return my_time
return -1
But this is too slow! Let's optimize...
Approach 2: Correct Greedy Strategy
Core Insight:
- Sort flights by departure time
- Sort passengers by arrival time
- Each passenger greedily chooses the "earliest available flight"
- Binary search for your latest arrival time
Approach 3: Final Correct Version
def latest_arrival_time(flights, arrivals):
"""
Google Interview Question: Island Evacuation
Args:
flights: List[Tuple[int, int]] - (departure_time, capacity)
arrivals: List[int] - other islanders' arrival times
Returns:
int: Latest arrival time guaranteeing evacuation, -1 if impossible
"""
if not flights:
return -1
# Sort by departure time
flights = sorted(flights, key=lambda x: x[0])
n_flights = len(flights)
# Total seats
total_seats = sum(cap for _, cap in flights)
# If not enough seats for everyone (including you)
if total_seats <= len(arrivals):
return -1
def simulate(my_time):
"""
Simulate whether you can board if arriving at my_time
Returns True if successful evacuation
"""
# Everyone sorted by arrival time
everyone = sorted(arrivals + [my_time])
# Remaining seats per flight
seats = [cap for _, cap in flights]
# Pointer to current flight being considered
flight_ptr = 0
for person_arrival in everyone:
# Find first flight with departure_time > arrival_time
while flight_ptr < n_flights and flights[flight_ptr][0] <= person_arrival:
flight_ptr += 1
# From flight_ptr, find a flight with available seats
boarded = False
for i in range(flight_ptr, n_flights):
if seats[i] > 0:
seats[i] -= 1
boarded = True
break
if not boarded and person_arrival == my_time:
return False
return True
# Binary search for latest arrival time
# Earliest possible is 0, latest is one moment before last flight departs
lo, hi = 0, flights[-1][0] - 1
result = -1
while lo <= hi:
mid = (lo + hi) // 2
if simulate(mid):
result = mid
lo = mid + 1
else:
hi = mid - 1
return result
๐งช Test Cases
# Test 1: Basic case
flights1 = [(100, 2), (200, 1)]
arrivals1 = [50, 80]
print(latest_arrival_time(flights1, arrivals1)) # Expected: 199
# Test 2: Tight situation
flights2 = [(100, 1)]
arrivals2 = [50]
print(latest_arrival_time(flights2, arrivals2)) # Expected: 49
# Test 3: Impossible to evacuate
flights3 = [(100, 1)]
arrivals3 = [50, 60]
print(latest_arrival_time(flights3, arrivals3)) # Expected: -1
# Test 4: Complex multi-flight scenario
flights4 = [(50, 1), (100, 2), (150, 1)]
arrivals4 = [30, 40, 60, 90]
print(latest_arrival_time(flights4, arrivals4)) # Needs careful analysis
# Test 5: Edge case - no other people
flights5 = [(100, 1)]
arrivals5 = []
print(latest_arrival_time(flights5, arrivals5)) # Expected: 99
# Test 6: Edge case - no flights
flights6 = []
arrivals6 = [50]
print(latest_arrival_time(flights6, arrivals6)) # Expected: -1
Complexity Analysis
| Method | Time Complexity | Space Complexity |
|---|---|---|
| Brute Force | O(T ร n ร m) | O(n + m) |
| Binary Search + Simulation | O(log T ร (n + m) log(n + m)) | O(n + m) |
Where:
- T = maximum time range
- n = number of flights
- m = number of other islanders
๐คฏ Interviewer's Followup Traps
Followup 1: What if there are many flights?
Test Point: Optimize the simulation process
Current solution's simulation is O((n + m) log(n + m)). With large n, use Segment Tree or Binary Indexed Tree to optimize seat allocation.
Followup 2: What if you need to return which flight you should take?
def latest_arrival_with_flight(flights, arrivals):
"""Return (latest_arrival_time, flight_index_to_board)"""
# ... record which flight you board in the simulate function
pass
Followup 3: What if multiple "you"s all want to arrive as late as possible?
Test Point: Game Theory / Multi-agent Optimization
This becomes a more complex scheduling problem requiring Nash Equilibrium considerations.
Followup 4: What if flights might be delayed?
Test Point: Robustness Design
Need to consider probability models and risk assessment.
๐ฅ Why Most People Fail
| Common Mistake | Correct Approach |
|---|---|
| Only consider "can I board" | Need to simulate everyone's boarding process |
| Brute force enumerate all time points | Binary search optimization |
| Ignore "first come first served" rule | Greedy strategy: early arrivals board early flights |
| Poor Edge Case handling | No flights, full capacity, time boundaries |
๐ oavoservice Services
This combination of scenario modeling + greedy + binary search is classic Google interview style.
If you encounter similar problems in interviews, we can provide:
- โ OA Assistance: CodeSignal / HackerRank perfect score guarantee
- โ VO Support: Live Coding real-time off-screen assistance
- โ Strategy Guidance: Help you build proper problem decomposition thinking
๐ Add WeChat Now: Coding0201
Don't let one scheduling problem ruin your Google Offer.
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