33.1-4 Show how to find an optimal k-clustering in polynomial time when there is just one attribute (d = 1).
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- to write some code: Cluster MNIST with k-means (you know optimal k already). Assign a label to each cluster by the most popular y (classes from 0 to 9) in that cluster. Now we can compute accuracy_score of our cluster labels comparing them with true label of each point. This way we can get an idea of how good our clustering is without looking at it (because you can't really look at 64 dimensional points, right?). q1: What accuracy_score did you get? Hint: you can use np.bincount(x): Count number of occurrences of each value in array of non-negative ints. Each bin gives the number of occurrences of its index value in `x`. Hint: use KMeans(..., random_state=0) for reproducible results. from sklearn.metrics import accuracy_score # YOUR CAN WRITE CODE HERELet G be a graph, where each edge has a weight. A spanning tree is a set of edges that connects all the vertices together, so that there exists a path between any pair of vertices in the graph. A minimum-weight spanning tree is a spanning tree whose sum of edge weights is as small as possible. Last week we saw how Kruskal's Algorithm can be applied to any graph to generate a minimum-weight spanning tree. In this question, you will apply Prim's Algorithm on the graph below. You must start with vertex A. H 4 4 1 3 J 2 C 10 4 8 B 9 F 18 8 There are nine edges in the spanning tree produced by Prim's Algorithm, including AB, BC, and IJ. Determine the exact order in which these nine edges are added to form the minimum-weight spanning tree. 3.Let G be a graph, where each edge has a weight. A spanning tree is a set of edges that connects all the vertices together, so that there exists a path between any pair of vertices in the graph. A minimum-weight spanning tree is a spanning tree whose sum of edge weights is as small as possible. Last week we saw how Kruskal's Algorithm can be applied to any graph to generate a minimum-weight spanning tree. In this question, you will apply Prim's Algorithm on the same graph from the previous quiz. You must start with vertex A. H 4 G D J 9 4 7 10 6 8 В F A 18 E There are nine edges in the spanning tree produced by Prim's Algorithm, including AB, BC, and IJ. Determine the exact order in which these nine edges are added to form the minimum-weight spanning tree. 3.
- Create an SP client that analyses the edge-weighted digraph's edges in relation to a specified pair of vertices, s and t: Create a V-by-V boolean matrix where each item in row v and column w is true if and only if v->w is an edge in the edge-weighted digraphs whose weight can be raised without increasing the length of the shortest path from v to w, and false otherwise.• Let L, R be two sets, with cardinalities |Z| = 1 and |R| = r. What is the maximum number of edges in a bipartite graph G=(L_R_E). • Let L, R be two sets, with cardinalities |Z| = 1 and |R| = r. Give the formula for the number of bipartite graphs G=(L_R_E) ?Sensitivity. Create an SP client that runs a sensitivity analysis on the edges of an edge-weighted digraph in relation to a given pair of vertices s and t: Create a V-by-V boolean matrix so that, for each v and w, the entry in row v and column w is true if v->w is an edge in the edge-weighted digraphs whose weight can be raised without increasing the shortest-path length from v to w, and false otherwise.
- Correct answer will be upvoted else downvoted. Computer science. It might have been a simple undertaking, yet it worked out that you ought to observe a few guidelines: Before all else, you select any sure integer x. Then, at that point, you do the accompanying activity n times: select two components of cluster with total equivalents x; eliminate them from an and supplant x with limit of that two numbers. For instance, if at first a=[3,5,1,2], you can choose x=6. Then, at that point, you can choose the second and the third components of a with total 5+1=6 and toss them out. After this activity, x equivalents 5 and there are two components in cluster: 3 and 2. You can toss them out on the following activity. Note, that you pick x before the beginning and can't transform it as you need between the activities. Decide how could you act to toss out all components of a. Input The main line contains a solitary integer t (1≤t≤1000) — the number of experiments.…Is A ⊆ B if A = {8, 10, 12, 14} and B = {8, 10, 12, 16, 20}?Correct answer will be upvoted else downvoted. Computer science. You are given a cluster an of length n. You are approached to deal with q inquiries of the accompanying organization: given integers I and x, duplicate computer based intelligence by x. In the wake of handling each inquiry you really wanted to output the best normal divisor (GCD) of all components of the cluster a. Since the appropriate response can be excessively huge, you are approached to output it modulo 109+7. Input The principal line contains two integers — n and q (1≤n,q≤2⋅105). The subsequent line contains n integers a1,a2,… ,an (1≤ai≤2⋅105) — the components of the cluster a preceding the changes. The following q lines contain inquiries in the accompanying arrangement: each line contains two integers I and x (1≤i≤n, 1≤x≤2⋅105). Output Print q lines: in the wake of handling each inquiry output the GCD of all components modulo 109+7 on a different line.
- In the Euclidean (metric) Traveling Salesperson Problem (TSP), we started with a DFS traversal of the minimum spanning tree (MST) and then skipped vertices that we had already visited. Why were we able to allow skipping of nodes? O Because DFS run on an MST adds an exponential number of vertices O In a metric space the triangle inequality states that removing a vertex cannot lengthen the path O In the Euclidean metric, distance in measured in the number of edges, so removing edges makes the path shorter O It feels rightCreate an SP client that analyses the edge-weighted digraph's edges in relation to a specified pair of vertices, s and t: Create a V-by-V boolean matrix where each item in row v and column w is true for each v and w if the edge v->w is an edge in the edge-weighted digraphs whose weight can be raised without increasing the length of the shortest path from v to w, and false otherwise.Please answer in c++. Correct answer will upvoted else downvoted. The OmkArray of a cluster a with components a1,a2,… ,a2k−1, is the exhibit b with components b1,b2,… ,bk to such an extent that bi is equivalent to the middle of a1,a2,… ,a2i−1 for all I. Omkar has discovered a cluster b of size n (1≤n≤2⋅105, −109≤bi≤109). Given this cluster b, Ray needs to test Omkar's case and check whether b really is an OmkArray of some exhibit a. Would you be able to help Ray? The middle of a bunch of numbers a1,a2,… ,a2i−1 is the number ci where c1,c2,… ,c2i−1 addresses a1,a2,… ,a2i−1 arranged in nondecreasing request. Input Each test contains various experiments. The main line contains a solitary integer t (1≤t≤104) — the number of experiments. Depiction of the experiments follows. The primary line of each experiment contains an integer n (1≤n≤2⋅105) — the length of the cluster b. The subsequent line contains n integers b1,b2,… ,bn (−109≤bi≤109) — the components of b. It is…