How do you solve Second Minimum Time to Reach Destination on LeetCode?

Second Minimum Time to Reach Destination (LeetCode #2045) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(E log V) time complexity and O(V) space complexity. Key insight: Understanding traffic signal timing is crucial for calculating wait times.

What is the brute force solution for Second Minimum Time to Reach Destination?

The brute force approach for Second Minimum Time to Reach Destination is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves exploring all possible paths from the start vertex to the destination vertex and calculating the time taken for each path. This is straightforward but inefficient, as it doesn't account for the traffic signal changes effectively. The optimal Optimal Solution approach improves this to O(E log V).

What algorithm or data structure is used to solve Second Minimum Time to Reach Destination?

Second Minimum Time to Reach Destination uses the following concepts: Breadth-First Search, Graph Theory, Shortest Path. The recommended patterns to study are: Graph Traversal, Dijkstra's Algorithm, Priority Queue.

What are the interview tips for Second Minimum Time to Reach Destination?

Always clarify the problem constraints and requirements. Discuss your thought process and approach before jumping into coding. Test your solution with edge cases to ensure robustness.

What are common mistakes when solving Second Minimum Time to Reach Destination?

Not considering the wait time at each vertex properly. Forgetting to track both minimum and second minimum times.

#2045

Second Minimum Time to Reach Destination

Hard

Breadth-First SearchGraph TheoryShortest PathGraph TraversalDijkstra's AlgorithmPriority Queue

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(E log V)
Space	O(1)	O(V)

💡

Intuition

Time O(E log V)Space O(V)

The optimal solution uses a modified Dijkstra's algorithm to efficiently find the second minimum time by considering the traffic signal changes. This approach allows us to explore paths while keeping track of the minimum and second minimum times without exhaustively searching all paths.

⚙️

Algorithm

3 steps

1Step 1: Initialize a priority queue to explore paths based on time.
2Step 2: For each vertex, track the minimum and second minimum time to reach it.
3Step 3: For each edge, calculate the time considering the traffic signal changes and update the priority queue.

solution.py29 lines

1# Full working Python code
2import heapq
3from collections import defaultdict
4
5def second_min_time(n, edges, time, change):
6    graph = defaultdict(list)
7    for u, v in edges:
8        graph[u].append(v)
9        graph[v].append(u)
10
11    min_time = [[float('inf'), float('inf')] for _ in range(n + 1)]
12    min_time[1][0] = 0
13    pq = [(0, 1)]  # (current_time, node)
14
15    while pq:
16        current_time, node = heapq.heappop(pq)
17        for neighbor in graph[node]:
18            wait_time = (change - (current_time % change)) % change
19            leave_time = current_time + wait_time + time
20            if leave_time < min_time[neighbor][0]:
21                min_time[neighbor][1] = min_time[neighbor][0]
22                min_time[neighbor][0] = leave_time
23                heapq.heappush(pq, (leave_time, neighbor))
24            elif min_time[neighbor][0] < leave_time < min_time[neighbor][1]:
25                min_time[neighbor][1] = leave_time
26                heapq.heappush(pq, (leave_time, neighbor))
27
28    return min_time[n][1] if min_time[n][1] != float('inf') else -1
29

ℹ

Complexity note: The time complexity is O(E log V) due to the priority queue operations, where E is the number of edges and V is the number of vertices. The space complexity is O(V) for storing the minimum times for each vertex.

1Understanding traffic signal timing is crucial for calculating wait times.
2Using a priority queue can significantly optimize the pathfinding process.

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