Explain the Longest Common Subsequence problem with an example.
The Longest Common Subsequence (LCS) problem is about finding the longest subsequence common to two given sequences. A subsequence is a sequence derived by deleting some or no elements of the original sequence without changing the order of the remaining elements.
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Explain the breadth first search algorithm using the graph given below with v1 as the source vertex:
For each stage of the algorithm give:
i) ),v(d π )v( for each vertex, where )v(d is the distance from the source to the vertex v and is the predecessor of v.
ii) White and gray vertices
iii) Vertices in the queue
Also, give the breadth search tree.
Let me NO {0} and n∈ N. Let the god of x, y ∈ Z be denoted by (x, y). Prove that (m, n) = (m (mod n), n).
Find an optimal parenthesisation of the matrix chain product whose sequence of dimensions is 10, 25, 10, 5, 17.
Write the steps to search the numbers 18 and 45 in the binary search tree:
Check whether the following array represents a max-heap. If not run an algorithm to convert it into a max-heap:
6, 20, 18, 15, 17, 11, 12, 13
Find a minimal spanning tree for the following graph using the Prim’s algorithm, showing all the steps. Take v1 as the root.
What is the weight of the minimal spanning tree you get? Give reasons for your answer.
Consider the following undirected graph G with vertices labeled from 1 to 5:
Determine if there exists a clique of size 3 in the graph G. If yes, provide the vertices forming the clique.