https://github.com/emahtab/topological-sort-problems

Topological Sort Problems
https://github.com/emahtab/topological-sort-problems

kahns-alogrithm leetcode topological-sort

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Topological Sort Problems

• Host: GitHub
• URL: https://github.com/emahtab/topological-sort-problems
• Owner: eMahtab
• Created: 2024-10-28T02:25:11.000Z (about 2 months ago)
• Default Branch: main
• Last Pushed: 2024-10-28T02:41:32.000Z (about 2 months ago)
• Last Synced: 2024-10-28T06:15:11.009Z (about 2 months ago)
• Topics: kahns-alogrithm, leetcode, topological-sort
• Homepage:
• Size: 5.86 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Topological Sort Problems : O(V+E)

Topological sort of a directed graph is a linear ordering of its vertices such that for every directed edge (u,v) from vertex u to vertex v, u comes before v in the ordering.

When topological sort is implemented using **Kahn's Algorithm (BFS with a queue)**, the time complexity and space complexity are as follows:

### Time Complexity : O(V+E)

##### Explanation:

1. Counting in-degrees takes 𝑂(𝐸) time because we iterate over each edge once.

2. Enqueueing and dequeueing each vertex takes 𝑂(𝑉) time.

3. Processing each neighbor of each vertex (decreasing in-degrees and enqueuing zero in-degree nodes) takes 𝑂(𝐸) time as each edge is visited once.

### Space Complexity : : O(V+E)

##### Explanation:

The space complexity is also 𝑂(𝑉+𝐸) because:

1. We need space to store the graph (using an adjacency list) with 𝑉 vertices and 𝐸 edges, which takes 𝑂(𝑉+𝐸).

2. We maintain an in-degree array of size 𝑉, taking 𝑂(𝑉).

3. The queue holds vertices with zero in-degrees, and in the worst case, all vertices could be added to the queue, so it also takes 𝑂(𝑉) space.

## Problems :

1. https://leetcode.com/problems/course-schedule

2. https://leetcode.com/problems/course-schedule-ii

3. https://leetcode.com/problems/parallel-courses

4. https://leetcode.com/problems/find-all-possible-recipes-from-given-supplies

5. https://leetcode.com/problems/alien-dictionary