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 16.1, Problem 2E
Program Plan Intro
To describe the given approach is greedy
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Write and implement the best first search algorithm where we have given the Start state and Goal state and we want to reach the goal state.
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7
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1
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Initial state
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Goal state
Consider navigating the maze shown below (same maze used in the homework).
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M
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2
2
2
E
B
G
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H
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The maze is represented as a graph with edge costs as shown on the edges. The edge cost is 1 for all edges where the cost is not shown. Let B be the initial state and G is the goal state. The heuristic cost of every node to reach G is :
h(n)
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A
5.1
B
4.1
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3.9
D
14
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3.8
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7
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14
IM
0.5
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IP
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4.5
Show the steps of an A* search starting from B to goal G:
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Show the frontier and explored set in every iteration (i.e., complete the above table)
List the vertices in the order they are expanded.
I need to implement a python code for Q learning and SARSA method. My example involves a cliff walking experiment where the rewards are -1 except for the region marked as cliff if the agent steps there the reward is -100 and the agent is sent back to the start. The values used are alpha = 0.1, y or gamma = 1 and the e- greedy action is 0.1. After using these values on both algorithm the results needs to be shown by using matplot. The graph should have episodes in the x axis and sum of rewards during episode on the y axis. It needs to be smoothed out by averaging over 10 runs and, plotting moving average over last 10 episodes. This needs to be done in python using numpy and panda but I'm not allowed to use gym library or any other library.
Chapter 16 Solutions
Introduction to Algorithms
Ch. 16.1 - Prob. 1ECh. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Prob. 4ECh. 16.1 - Prob. 5ECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5E
Ch. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.3 - Prob. 1ECh. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16 - Prob. 1PCh. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5P
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- Consider the same maze shown above with the same start and goal nodes. Let the heuristic cost of every node to reach G be: ANSWER THIS Question AND I WILL GIVE A thumbs up IF IT CORRarrow_forwardX-Kingdom has trapped n number of soldiers of their opponent. They want to execute them. They created a strategy so that the prisoners will kill each other and at the end one prisoner will be alive and eventually released. As part of the process, they assigned each trapped soldier a sequence number starting from 1 and ending at n. If n = 5 and k = 2, then the safe position is 3. Firstly, the person at position 2 is killed, then person at position 4 is killed, then person at position 1 is killed. Finally, the person at position 5 is killed. So, the person at position 3 survives. If n = 7 and k = 3, then the safe position is 4. The people at positions 3, 6, 2, 7, 5, 1 are killed in order, and the person at position 4 survives. Input:n and k Output:Print the list of prisoners in reverse order from n to 1Then reverse the list to print it in correct order from 1 to nDisplay the position number who will survive. You must have to use circular doubly linked list for your solution. You…arrow_forwardThe classic example of following a greedy algorithm is making change. Let’ssay you buy some items at the store and the change from your purchase is63 cents. How does the clerk determine the change to give you? If the clerkfollows a greedy algorithm, he or she gives you two quarters, a dime, andthree pennies. That is the smallest number of coins that will equal 63 cents(given that we don’t allow fifty-cent pieces).It has been proven that an optimal solution for coin changing can alwaysbe found using the current American denominations of coins. However, if weintroduce some other denomination to the mix, the greedy algorithm doesn’tproduce an optimal solution.Write a program that uses a greedy algorithm to make change (this codeassumes change of less than one dollar):arrow_forward
- Write and implement the best first search algorithm where we have given the Start state and Goal state and we want to reach the goal state.arrow_forwardA bottle factory produces bottles of equal mass. During a production, the weight of one of the bottles is set incorrectly. The factory scale will be used to find this bottle. Design a decrease-andconquer algorithm which finds the that bottle. Analyze the worst-case, best-case and average-case complexities of your algorithm. Explain your algorithm.arrow_forwardYou are given the midsem and endsem marks for the N Students in the course. A student P is said to dominate a student Q, if the midsem and endsem marks of P are both greater than the respective midsem and endsem marks of Q. Design an efficient algorithm for finding all the students that are not dominated by any other student in the class.arrow_forward
- The classic example of following a greedy algorithm is making change. Let’s say you buy some items at the store and the change from your purchase is 63 cents. How does the clerk determine the change to give you? If the clerkfollows a greedy algorithm, he or she gives you two quarters, a dime, and three pennies. That is the smallest number of coins that will equal 63 cents (given that we don’t allow fifty-cent pieces). It has been proven that an optimal solution for coin changing can always be found using the current American denominations of coins. However, if we introduce some other denomination to the mix, the greedy algorithm doesn’t produce an optimal solution.Write a program that uses a greedy algorithm to make change (this code assumes change of less than one dollar).arrow_forwardIs it true that a greedy algorithm always finds the best solution? Justify your response.arrow_forwardDoes a greedy algorithm always find an optimal solution? Justify your answer.arrow_forward
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