Question
Q8. Explain DFS and BDS Graph traversal algorithms with the help of a suitable example.
Answer :
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Depth-First Search (DFS) and Breadth-First Search (BFS) are fundamental graph traversal algorithms used to explore nodes and edges of a graph systematically. DFS explores a graph by moving as far as possible along each branch before backtracking. It uses a stack data structure, either explicitly or via recursion. Starting from a source vertex, DFS visits a vertex, marks it as visited, and recursively explores all unvisited adjacent vertices. For example, consider a graph with vertices {A, B, C,
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Related Questions
Solve the following recurrence Using Recursion tree method
(i) T(n) = 3T(n/3) + n
(ii) T(n) = 2T(n/2) + n²
(iii) T(n) = T(n/2) + T(n/4) + T(n/8) + n
Q8. Explain DFS and BDS Graph traversal algorithms with the help of a suitable example.
Prove the following proposition using induction:
P(n): 1² + 2² + 3² + 4² + ... ... ... ... . + n² = n(n+1)(2n+1) / 6
Binary sort
) Merge sort
. For the function defined by f(n) = 2n³ + 3n² + 1 and g(n) = 2n² +3, show that
(i) f(n) = Ω(g(n))
(ii) g(n) != Ω(f(n))
(iii) n³ = Ω(g(n))
(iv) f(n) != Ω(n⁴)
Binary search