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Let G = (V, G) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighed edge (u, v) ∈ V×V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph is
- a)Θ(∣E∣ + ∣V∣)
- b)Θ(∣E∣.∣V∣)
- c)Θ(E∣ log ∣V∣)
- d)Θ(∣V∣)
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Let G = (V, G) be a weighted undirected graph and let T be a Minimum S...
Is added to G with weight w. In order to update the MST T, we can follow the following steps:
1. Add the edge (u, v) to G with weight w.
2. If the weight of (u, v) is greater than the weight of the maximum weight edge in T, then the MST T remains unchanged.
3. Otherwise, find the cycle C in T that is formed by adding the edge (u, v).
4. Find the maximum weight edge e in cycle C. Remove edge e from T.
5. Add the edge (u, v) to T.
6. Repeat steps 3-5 until there are no cycles formed by adding edges.
By following these steps, we can update the MST T in O(log^2(V)) time complexity, where V is the number of vertices in the graph. This is because finding the cycle and the maximum weight edge in the cycle can be done in O(log(V)) time using a union-find data structure.
Note: If the graph is not connected, we need to consider each connected component separately and update the MST for each component.
1. Add the edge (u, v) to G with weight w.
2. If the weight of (u, v) is greater than the weight of the maximum weight edge in T, then the MST T remains unchanged.
3. Otherwise, find the cycle C in T that is formed by adding the edge (u, v).
4. Find the maximum weight edge e in cycle C. Remove edge e from T.
5. Add the edge (u, v) to T.
6. Repeat steps 3-5 until there are no cycles formed by adding edges.
By following these steps, we can update the MST T in O(log^2(V)) time complexity, where V is the number of vertices in the graph. This is because finding the cycle and the maximum weight edge in the cycle can be done in O(log(V)) time using a union-find data structure.
Note: If the graph is not connected, we need to consider each connected component separately and update the MST for each component.
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Community Answer
Let G = (V, G) be a weighted undirected graph and let T be a Minimum S...
As T is a minimum spanning tree and we need to add a new edge to existing spanning tree.
Later we need to check still T is a minimum spanning tree or not, So we need to check all vertices whether there is any cycle present after adding a new edge.
All vertices need to traverse to confirm minimum spanning tree after adding new edge then time complexity is O(V).
Later we need to check still T is a minimum spanning tree or not, So we need to check all vertices whether there is any cycle present after adding a new edge.
All vertices need to traverse to confirm minimum spanning tree after adding new edge then time complexity is O(V).
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Let G = (V, G) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighed edge (u, v) ∈ V×V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph isa)Θ(E + V)b)Θ(E.V)c)Θ(E log V)d)Θ(V)Correct answer is option 'D'. Can you explain this answer?
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Let G = (V, G) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighed edge (u, v) ∈ V×V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph isa)Θ(E + V)b)Θ(E.V)c)Θ(E log V)d)Θ(V)Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let G = (V, G) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighed edge (u, v) ∈ V×V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph isa)Θ(E + V)b)Θ(E.V)c)Θ(E log V)d)Θ(V)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G = (V, G) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighed edge (u, v) ∈ V×V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph isa)Θ(E + V)b)Θ(E.V)c)Θ(E log V)d)Θ(V)Correct answer is option 'D'. Can you explain this answer?.
Let G = (V, G) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighed edge (u, v) ∈ V×V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph isa)Θ(E + V)b)Θ(E.V)c)Θ(E log V)d)Θ(V)Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let G = (V, G) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighed edge (u, v) ∈ V×V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph isa)Θ(E + V)b)Θ(E.V)c)Θ(E log V)d)Θ(V)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G = (V, G) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighed edge (u, v) ∈ V×V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph isa)Θ(E + V)b)Θ(E.V)c)Θ(E log V)d)Θ(V)Correct answer is option 'D'. Can you explain this answer?.
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