Second Minimum Time to Reach Destination | 2 Approaches | FULL DRY RUN | Leetcode 2045
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Dijkstra's - • Dijkstra's Algorithm | PART-1 | (Micr...
In this video we will try to solve a very good Graph Problem : Second Minimum Time to Reach Destination | 2 Approaches | FULL DRY RUN | Leetcode 2045 | codestorywithMIK
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Problem Name : Second Minimum Time to Reach Destination | 2 Approaches | FULL DRY RUN | Leetcode 2045 | codestorywithMIK
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Summary :
Approach 1: Using Modified Dijkstra's Algorithm
Time Complexity: O(ElogV) - where E is the number of edges and V is the number of vertices.
Space Complexity: O(V+E)
Description:
This approach uses a priority queue (min-heap) to implement a modified version of Dijkstra's algorithm.
Each node keeps track of two distances: the minimum distance (d1) and the second minimum distance (d2).
For each node, if it is reached through a shorter path, update d1; if it is reached through a path that is not the shortest but shorter than the current second shortest, update d2.
The algorithm also accounts for traffic lights, adjusting the travel time if the light is red.
The goal is to find the second minimum time to reach the target node n.
Approach 2: Using Breadth-First Search (BFS)
Time Complexity: O(V+E) - where E is the number of edges and V is the number of vertices.
Space Complexity: O(V+E)
Description:
This approach uses a queue to implement BFS, which processes nodes layer by layer.
Similar to the Dijkstra's approach, it maintains two distances for each node: the minimum distance (d1) and the second minimum distance (d2).
For each node, it processes the current path, updating d1 or d2 as needed.
The algorithm adjusts the travel time based on traffic lights, ensuring that travel only proceeds during green lights.
The goal is to find the second minimum time to reach the target node n.
Key Differences:
Priority Queue vs. Queue:
Approach 1 uses a priority queue to always expand the node with the smallest current distance, ensuring the shortest path is found first.
Approach 2 uses a regular queue, expanding nodes in the order they were discovered, making it simpler but potentially less efficient for weighted graphs.
Efficiency:
Approach 1 is more efficient in terms of finding the shortest paths due to the priority queue but involves higher computational complexity with log V factor.
Approach 2 is straightforward BFS with linear time complexity, but it might not handle weights as optimally as the priority queue method.
Both approaches effectively find the second minimum travel time by leveraging the properties of shortest path algorithms, adjusted for the specific problem constraints such as traffic lights.
✨ Timelines✨
00:00 - Introduction
00:30 - Problem Explanation
08:35 - Thought Process - Dijkstra's
15:26 - How to calculate Green time
25:32 - FULL DRY RUN - Dijkstra's
43:01 - Coding it up - Dijkstra's
48:55 - Thought Process - BFS
52:30 - FULL DRY RUN - BFS
01:01:58 - Coding it up - BFS
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