Question

Analyze the worst-case complexity of the algorithm below when using an optimized adjacency list to store G.

**ComponentCount:**

**Input:** G = (V, E): an undirected graph with n
vertices and m edges

**Input:** n, m: the order and size of G,
respectively

**Output:** the number of connected components in
G

**Pseudocode:**

comp = n

uf = UnionFind(n)

For v in V:

For u in N(v):

If (uf.Find(v) != uf.Find(u))

uf.Union(u, v)

comp = comp - 1

End if

End for

End for

Return comp

Answer #1

**Answer:-**

comp = n

uf = UnionFind(n) **// O(log V)**

For v in V: **// O(V)**

For u in N(v): **// O(V) in worst
case**

If (uf.Find(v) != uf.Find(u))

uf.Union(u, v)

comp = comp - 1

End if

End for

End for

Return comp

**The total time complexity in worst case is =
O(V*V*logV)**

**i.e O(V^2logV)**

**Please UPVOTE thank you...!!!**

Analyze the worst-case complexity of the algorithm below when
using an optimized adjacency list to store G.
ComponentCount:
Input: G = (V, E): an undirected graph with n
vertices and m edges
Input: n, m: the order and size of G,
respectively
Output: the number of connected components in
G
Pseudocode:
comp = n
uf = UnionFind(n)
For v in V:
For u in N(v):
If (uf.Find(v) !=
uf.Find(u))
uf.Union(u, v)
comp = comp - 1...

You are given a directed acyclic graph G(V,E), where each vertex
v that has in-degree 0 has a value value(v) associated with it. For
every other vertex u in V, define Pred(u) to be the set of vertices
that have incoming edges to u. We now define value(u) = ?v∈P red(u)
value(v). Design an O(n + m) time algorithm to compute value(u) for
all vertices u where n denotes the number of vertices and m denotes
the number of edges...

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