Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 15.5, Problem 2E
Program Plan Intro
To findsthe structure and cost of the BST using
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Determine the cost and structure of an optimal binary search tree for a set of n = 4 keys with the following probabilities:
i
1
3
4
Pi
0.12
0.18
0.18
0.17
0.05
0.05
0.10
0.08
0.07
Any random element from the given Binary Search Tree is to be searched using the
standard algorithm. In the Binary Search Tree given in the above problem
(i) Determine the average or expected number of comparisons required to locate the
element.
(ii) determine the number of comparisons in the worst case.
O 2.8 and 3.5
O 2,89 and 3
2 and 3
2 and 4
2.89 and 4
Algorithm for Alpha-beta pruning using minimax.Minimax-Alpha-Beta(v, α, β)in: node v; alpha value α; beta value βout: utility value of node v
Chapter 15 Solutions
Introduction to Algorithms
Ch. 15.1 - Prob. 1ECh. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4ECh. 15.1 - Prob. 5ECh. 15.2 - Prob. 1ECh. 15.2 - Prob. 2ECh. 15.2 - Prob. 3ECh. 15.2 - Prob. 4ECh. 15.2 - Prob. 5E
Ch. 15.2 - Prob. 6ECh. 15.3 - Prob. 1ECh. 15.3 - Prob. 2ECh. 15.3 - Prob. 3ECh. 15.3 - Prob. 4ECh. 15.3 - Prob. 5ECh. 15.3 - Prob. 6ECh. 15.4 - Prob. 1ECh. 15.4 - Prob. 2ECh. 15.4 - Prob. 3ECh. 15.4 - Prob. 4ECh. 15.4 - Prob. 5ECh. 15.4 - Prob. 6ECh. 15.5 - Prob. 1ECh. 15.5 - Prob. 2ECh. 15.5 - Prob. 3ECh. 15.5 - Prob. 4ECh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Prob. 11PCh. 15 - Prob. 12P
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- Which one is the true statement? -A hash table can be used to make an algorithm run faster even in the worst case by trading space for time. -An iterative improvement algorithm starts with a sub-optimal feasible solution and seeks to improve it in each iteration until reaching a optimal feasible solution.arrow_forwardUsing the following data, construct an optimal binary search tree. You must show all your work. 1 2 3 4 words dawgs football library party study 0.2 0.25 0.01 0.25 0.01 0.05 0.04 0.06 0.08 0.01 0.04arrow_forwardThe heuristic function of greedy best-first search is Select one: a. f(n) > h(n) b. f(n) < h(n) c. f(n) = h(n) d. f(n) != h(n)arrow_forward
- illustrates the procedure to obtain the optimal binary search tree,given the list of keys ? = {a1,a2,.....an} and the probabilities Pi, 1≤ ? ≤? andQi,0≤ ? ≤narrow_forwardAnswer the following questions Question 1 A* is an informed search algorithm. What is an informed search? How is it different from uninformed search? Question 2 A* uses a heuristic function f(n) in its search for a solution. Explain the components of f(n). Why do you think f(n) is more effective than h(n), the heuristic function used by greedy best-first? Question 3 For A* to return the minimum-cost solution, the heuristic function used should be admissible and consistent. Explain what these two terms mean. Question 4 For the 9-tile soring problem, assume that you start from this initial state 7 2 4 5 6 8 3 1 The Goal State is: 1 2 3 4 5 6 7 8 The cost of moving any tile is 1. Let the heuristic function h(n) = number of misplaced tiles. For the shown configuration, there are four options for the next move: Move 5 to the right Move 6 to the left Move 2 down Move 3 up Each of these moves has a value f(n) = h(n) + g(n). If we choose to Move 5 to the right,…arrow_forwardFor the 8-queens problem, define a heuristic function, design a Best First Search algorithm in which the search process is guided by f(n) = g(n) + h(n), where g(n) is the depth of node n and h(n) is the heuristic function you define, and give the pseudo code description.arrow_forward
- What is the solution for the following search tree using the breadth-first strategy?asweredarrow_forwardGiven the recurrence relation: • T(n) = 8 if n 6. Find the value of T(495). [Hint: Use a recursion tree to solve the recurrence exactly and plug the argument into the function you obtain.] Answer: 493 The correct answer is: 336 Xarrow_forward1. Enter G = (V, E)Results: MIS I of G3. I ← ∅4. V ← V5. while V equals6. Give each vertex v V a random integer r(v).7. parallel V for all v8. if r(v) is the lowest value among all peers.9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}With a high degree of probability, this method ends in O(log n)rounds [3]. Lines 7–10 of the method can be executed in parallel, which will speed things up.Make the specified method in Python?arrow_forward
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