How do you solve Bus Routes on LeetCode?

Bus Routes (LeetCode #815) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding how to map bus stops to the buses that serve them is crucial for efficient traversal.

What is the brute force solution for Bus Routes?

The brute force approach for Bus Routes is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves exploring all possible bus routes from the source to the target. We can simulate taking each bus and checking if we can reach the target, but this method can be very slow and inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Bus Routes?

Bus Routes uses the following concepts: Array, Hash Table, Breadth-First Search. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Bus Routes?

Always clarify the problem constraints and edge cases before diving into coding. Think about how to represent the problem using graphs or maps for better clarity. Practice explaining your thought process as you code; it helps solidify your understanding.

What are common mistakes when solving Bus Routes?

Failing to track visited stops and buses, leading to infinite loops. Not considering the case where the source is the same as the target.

#815

Bus Routes

Hard

ArrayHash TableBreadth-First SearchHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

The optimal solution uses a breadth-first search (BFS) approach to explore bus routes efficiently. By treating bus stops as nodes and buses as edges, we can find the shortest path in terms of bus transfers.

⚙️

Algorithm

5 steps

1Step 1: Create a mapping of bus stops to the buses that serve them.
2Step 2: Initialize a queue for BFS starting from the source stop.
3Step 3: Track visited stops and buses to avoid cycles.
4Step 4: For each stop, explore all buses that can be taken and enqueue the next stops.
5Step 5: If the target stop is reached, return the number of buses taken.

solution.py32 lines

1# Full working Python code
2from collections import defaultdict, deque
3
4def numBusesToDestination(routes, source, target):
5    if source == target:
6        return 0
7
8    stop_to_buses = defaultdict(list)
9    for bus, stops in enumerate(routes):
10        for stop in stops:
11            stop_to_buses[stop].append(bus)
12
13    visited_stops = set()
14    visited_buses = set()
15    queue = deque([(source, 0)])  # (current stop, bus count)
16
17    while queue:
18        current_stop, bus_count = queue.popleft()
19        if current_stop in visited_stops:
20            continue
21        visited_stops.add(current_stop)
22
23        for bus in stop_to_buses[current_stop]:
24            if bus in visited_buses:
25                continue
26            visited_buses.add(bus)
27            for next_stop in routes[bus]:
28                if next_stop == target:
29                    return bus_count + 1
30                queue.append((next_stop, bus_count + 1))
31
32    return -1

ℹ

Complexity note: The time complexity is linear because we are processing each bus stop and bus exactly once, making it efficient for large inputs.

1Understanding how to map bus stops to the buses that serve them is crucial for efficient traversal.
2Using BFS allows us to find the shortest path in terms of bus transfers.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.