9) Determine the cost and structure of an optimal binary search tree for a set of n = 7 keys with the following probabilities: i 0 1 2 3 4 5 6 7 Pi 0.04 0.06 0.08 0.02 0.10 0.12 0.14 qi 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.05

Luby’s Algorithm: 1. Input: G = (V, E)2. Output: MIS I of G3. I ← ∅4. V ← V5. while V = ∅6. assign a random number r(v) to each vertex v ∈ V7. for all v ∈ V in parallel8. if r(v) is minimum amongst all neighbors9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}Make Implementation of this algorithm in sequential form in Python. dont copy ans from bartleby its wrong

Problem 8: Optimal Binary Search Tree Find the optimal binary search tree (BST) for the following keys and frequencies: Key: 1 2 3 4 5 6 7 Frequencies: 3 5 9 2 11 13 16

What is the solution for the following search tree using the breadth-first strategy?aswered

The table shows the distances, in units of 100 m, between seven houses, A to G. A В D E F G A 4 3 B 4 1 2 4 7 5 1 3 7 D 3 2 6 4 E 2 4 4 2 6 F 7 6 10 G 6 6 7 4 10 Use Prim's algorithm on the table in the insert to find a minimum spanning tree. Start by crossing out row A. Show which entries in the table are chosen and indicate the order in which the rows are deleted. Draw your minimum spanning tree and state its total weight. 4) LO

1. Input: G = (V, E)2. Output: MIS I of G3. I ← ∅4. V ← V5. while V = ∅6. assign a random number r(v) to each vertex v ∈ V7. for all v ∈ V in parallel8. if r(v) is minimum amongst all neighbors9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}This algorithm terminates in O(log n)rounds with good probability. The stepsof the algorithm between lines 7–10 can be performed in parallel which will providea speedup.Make Python Implementation this algorithm in sequential form

1. Input: G = (V, E)2. Output: MIS I of G3. I ← ∅4. V ← V5. while V = ∅6. assign a random number r(v) to each vertex v ∈ V7. for all v ∈ V in parallel8. if r(v) is minimum amongst all neighbors9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}This algorithm terminates in O(log n)rounds with good probability [3]. The stepsof the algorithm between lines 7–10 can be performed in parallel which will providea speedup.Make a Python Implementation of given algorithm?

Implement RBFS algorithm and draw the search tree for the following search space. (Assume start state S and goal state G) 150 42 B H 6 2 66 105 A G 10 7 10 E 30 36 100 1 63 1. 2.

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Answer the given question with a proper explanation and step-by-step solution. Question 1 What is the worst time complexity for inserting an arbitrary item into a AVL tree? 0(n) 0 (log2 (n)) 0(1) 0(n^2) 0 (n log2 (n))   Question 2 What is the worst time complexity for inserting an arbitrary item into a binary search tree? 0(n) 0 (log2(n)) 0(1) 0 (n^2) 0 (n log2 (n))   Question 13 What is the time complexity for efficiently ordering elements (sorting) from a binary search tree? 0 (n) 0 (Log2 (n)) 0(1) 0(n^2) 0 (n log2 (n))   Question 11 The average Big O runtime to find an arbitrary element in an arbitrary AVL tree is roughly equal to the element in which other data structure or structures? Queue Hash Table Sorted Array LinkedList None of the above   Question 13 What is the time complexity for efficiently ordering elements (sorting) from a binary search tree? 0 (n) 0 (log2 (n)) 0(1) 0 (n^2) 0 (n log2 (n))   Question 23 What is the time complexity of the most time efficient algorithm for…