How do you solve Time to Cross a Bridge on LeetCode?

Time to Cross a Bridge (LeetCode #2532) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log k) time complexity and O(k) space complexity. Key insight: Using a priority queue allows us to efficiently manage worker availability and prioritize the least efficient workers.

What is the brute force solution for Time to Cross a Bridge?

The brute force approach for Time to Cross a Bridge is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach simulates each worker's actions sequentially, calculating the total time taken for each box to be moved. This method is straightforward but inefficient, as it doesn't optimize the order in which workers operate. The optimal Optimal Solution approach improves this to O(n log k).

What algorithm or data structure is used to solve Time to Cross a Bridge?

Time to Cross a Bridge uses the following concepts: Array, Heap (Priority Queue), Simulation. The recommended patterns to study are: Priority Queue, Simulation.

What are the interview tips for Time to Cross a Bridge?

Always clarify the problem constraints and requirements before jumping into coding. Think about edge cases, such as when there are more boxes than workers. Explain your thought process clearly while coding, as it helps the interviewer understand your approach.

What are common mistakes when solving Time to Cross a Bridge?

Not managing the state of workers properly, leading to incorrect time calculations. Failing to prioritize workers correctly based on their efficiency.

#2532

Time to Cross a Bridge

Hard

ArrayHeap (Priority Queue)SimulationPriority QueueSimulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n log k)Space O(k)

The optimal solution uses a priority queue to efficiently manage worker availability and prioritize the least efficient workers. This reduces the time complexity significantly by avoiding unnecessary checks.

⚙️

Algorithm

3 steps

1Step 1: Create a priority queue to manage workers based on their efficiency.
2Step 2: While there are boxes to move, dispatch the least efficient worker available to pick up a box.
3Step 3: Update the total time based on the worker's actions and repeat until all boxes are moved.

solution.py15 lines

1# Full working Python code
2import heapq
3
4def timeToCrossBridge(n, k, time):
5    pq = []
6    for i in range(k):
7        heapq.heappush(pq, (time[i][0] + time[i][2], i, time[i]))
8    total_time = 0
9    while n > 0:
10        _, worker_idx, worker_time = heapq.heappop(pq)
11        total_time += worker_time[0] + worker_time[1] + worker_time[2] + worker_time[3]
12        n -= 1
13        heapq.heappush(pq, (worker_time[0] + worker_time[2], worker_idx, worker_time))
14    return total_time
15

ℹ

Complexity note: The complexity is O(n log k) because we are using a priority queue to manage k workers, and for each of the n boxes, we perform log k operations to manage the queue.

1Using a priority queue allows us to efficiently manage worker availability and prioritize the least efficient workers.
2Understanding the problem constraints helps in designing the simulation accurately.

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