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- 4 a) Dijkstra's algorithm solves the SSSP problem. Describe how your choice of data structure to implement the Dijkstra's algorithm affects the time complexity of the algorithm b) Apply the Dijkstra's algorithm to compute the shortest path from the source vertex S and comment whether it solves the SSSP problem. You should use the table below to update d[v] and n[v] for each vertex 2 3 4 -3 5 y You should show all your updates using the following table as you apply the algorithm Vertex, v d[v] n[v] y 2.Sequential and binary search have pros and cons.0 A ladder tournament L can be split into two separate ladder tournaments L and L byassigning each player either to L or to L. The new ranks of the players are adjustedso that they do not contradict the relative rankings in L. However, there are manyways to define the inverse operation, joining two tournaments of disjoint players.Design algorithm Join-Ladder-Tournaments(L, L) that gives both tournamentsan equal value. This means, for example, that the joining does not force the championof L to compete against the worst players in L before she can have a match withthe champion of L
- 26 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following pair of graphs: X o1:02 48 V3 us V4 If the given graphs are isomorphic, then identify the correct mapping between the sets of vertices of the two graphs. Multiple Choice Aun) = v1, Au2) = v2, luz) = v3, fU4) = V5, and fu5) = v4 uiz Tools AU) = V, Au2) = v3, Auz) = v2, fu4) = V5, and fug) = v4 The two graphs are not isomorphic. 00% Aun) = V1, Au2) = V3, Auz) = v2, Au4) = v4, and flu5) = v5 seAnswer the questions for the following algorithm. ("weight matrix" is a weighted adjacency matrix with Os on the diagonal) ALGORITHM Floyd(W[1.n, 1.n]) /Implements Floyd's algorithm for the all-pairs shortest-paths problem I/Input: The weight matrix W of a graph with no negative-length cycle 1/Output: The distance matrix of the shortest paths' lengths D-W lis not necessary if W can be overwritten for k +1 to n do for i +1 to n do for j+1 to n do D[i. j] + min(D[i, j), D[i, k] + D[k. j]} return D a) What is the input size? b) Are there different best/worst/average cases of different orders of growth? c) Construct a sum describing the number of basic op calls, but do not solve:Course Title: Data Structures and Algorithms Topic: Algorithm Complexity Please solve it on urgent basis: Analyze the following codes for Time and space complexity. Determine Big O for the following code fragments in the average case. Assume that all variables are of type int. (d) for (i=0; i< n-1; i++) for (j=i+1; j < n; j++) { tmp = A[i][j]; A[i][j] = A[j][i]; A[j][i] = tmp; }
- Which of the following statements are true? Select one: a. None b. KNN is a clustering algorithm c. Clustering is a unsupervised learning method since it does not require labeled training data. d. When clustering, we want to put two dissimilar data objects into the same clusteri)- Write an algorithm to find the longest path in a DAG, where the length of the path is measured by the number of edges that it contains. What is the asymptotic complexity of your algorithm? ii) - Write an algorithm to find a maximum cost spanning tree, that is, the spanning tree with highest possible cost.[Breadth-first search run-time complexity: adjacency matrix] Analyze the run-time of the following BFS algorithm when the graph is represented as an adjacency matrix (instead of adjacency list). State the run-time complexity using a big-O notation and write the steps of its derivation. Please explain your steps. Will leave review BFS (s) : Set Discovered[s] = true and Discovered[u] = false for all other u Initialize L[0] to consist of the single element s Set the layer counter i=0 Set the current BFS tree T= Ø While L[i] is not empty Initialize an empty list L[i+1] For each node u E L[i] Consider each edge (u, v) incident to u If Discovered[v] = false then Set Discovered[v] = true Add edge (u,v) to the tree T Add v to the list L[i+1] Endif Endfor Increment the layer counter i by one Endwhile
- C++ - 11.) Prove that if n keys are uniformly distributed in m buckets, the number of comparisons in an unsuccessful search is given by n/m.Q6)k-means clustering 8 6 4 2 0 -2 -4 * * * * * X * 10 * 8 0 2 12 14 16 18 X1 | Consider the data plotted above, which consist of two rows of equally spaced points. If k-means clustering (k = 2) is initialised with the two blue points whose coordinates are (9, 3) and (11, 3), indicate the final clusters obtained (after the algorithm converges) on the figure. * * * * 10 *algorithm MatrixMultiplication (A1, A2, ... , An) pre-cond: An instance is a sequence of n matrices. post-cond: optSol is a bracketing that requires the fewest multiplications, andoptCost is the resulting number of multiplications.