Devise an efficient divide-and-conquer algorithm for the Towers of Hanoi problem when the disks are colored alternately red and blue, and we add the extra rule that no disk may be placed on any other disk of the same color
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Devise an efficient divide-and-conquer
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- using Python programming language. The Towers of Hanoi is a classic puzzle that consists of 3 towers, and n disks of different sizes that can slide onto any tower. The puzzle starts with the disks sorted in ascending order of size from top to bottom. It has the following constraints:a. Only one disk can be moved at a time.b. A disk can only be moved from the top of one tower to another tower.c. A disk can only be placed on top of a larger disk. Write a pseudo-code.We can generalize two-pass multiway merge-sort to use more than two passes. On the first pass, we divide the file into as many groups as we can merge in one pass. Then, recursively sort each group, using as many passes as necessary, and finally merge the sorted groups.A file of 1000 blocks is to be externally sorted, using 40 main-memory buffers. How many passes are needed? How many runs remain at the last pass? Find the correct number in the list below. a) The number of passes required is 2.b) The number of passes required is 3.c) The number of runs at the last pass is 10.d) The number of passes required is 1.Text reading is an integral component in our counting algorithms, and it is also ubiquitous in daily applications. The following is a very bad algorithm for reading from a text file, although it is correct and straightforward. It reads from a file line by line, and concatenate them into text. Then we split it using a regular expression. The split part is fast in linear complexity (we will learn it in Comp-2140), hence that is not our concern. Note that trim() is needed to remove empty strings. static String [] readTextBAD (String PATH) throws Exception { BufferedRe ader br=new BufferedReader (new FileReader(PATH)); String text=""; String line=""; while ((line=br.readLine ())!=null) text=text+" "+line.trim(); String tokens []=text.trim().split("[^a-zA -Z]+"); return tokens; } 5.4.1 Time complexity of readTextBAD Write below the time complexity of readTextBAD in terms of the text word length n, and explain your answer. Refer to repeat1 example in the textbook for the cause of low speed…
- Write an efficient algorithm for the following problem, and describe your reasoning. Determine the Time complexity and if you cannot find any polynomial time algorithm, then give a backtracking algorithm. Problem: Tower of Hanoi with Every Tower having some Disks Input: Each of the three towers contains roughly n/3 disks. Tower A contains floor(n/3) largest disks. Tower C contains ceiling(n/3) smallest disks. Tower B contains the remaining disks. The disks at each tower are already sorted according to the typical Tower of Hanoi rule. Output: A set of moves that transfers all the n disks to C maintaining the Tower of Hanoi rule that after each move, the smaller disks at a tower will always be above the larger ones.to the code below by using javaScript! Compare two approaches to partition in quickselect: Sedgewick and Lumoto . Assume that the numbers range from 0 to 100. Use the recursive version of quickselect. Always select the median at |1+r/2|Regardless of even/odd array size.you must collect both operation count and timing data. Check if both measurements do indeed have the same order of growth. please read it carfully and solve it by folowing all the requiremntsTowers of Hanoi Every budding computer scientist must grapple with certain classic problems, and the Towers of Hanoi (see Figure below) is one of the most famous of these. Legend has it that in a temple in the Far East, priests are attempting to move a stack of disks from one peg to another. The initial stack had 64 disks threaded onto one peg and arranged from bottom to top by decreasing size. The priests are attempting to move the stack from this peg to a second peg under the constraints that exactly one disk is moved at a time, and at no time may a larger disk be placed above a smaller disk. A third peg is available for temporarily holding the disks. Supposedly the world will end when the priests complete their task, so there is little incentive for us to facilitate their efforts. Let's assume that the priests are attempting to move the disks from peg 1 to peg 3. We wish to develop an algorithm that will print the precise sequence of disk-to-disk peg transfers. If we were
- You are the sysadmin for a big tech company, and you have to estimate the amount of servers you need to handle some long-running jobs. One server can handle only one job at once. One job can only be executed by one server at once. Once a server has finished executing its current job, it can be reassigned to a new job. Given an array of time intervals intervals where intervals[i] = [starti, endi], representing the start and end time for a particular job that needs to be executed, return the minimum number of servers required to run all jobs. Constraints: 1 <= intervals.length <= 104 0 <= starti < endi <= 106 Function definition for Java: public int minMeetingRooms(int[][] intervals) { // Your code here } Function definition for Python: def minMeetingRooms(self, intervals: List[List[int]]) -> int: #Your code here Announced Test Cases: Input: intervals = [[0,30],[5,10],[15,20]] Output: 2Explanation: We need one server for the job that starts at 0. For the job…Consider the following problem: You have a large collection of music files (e.g., MP3 files), and for each file you know the artist name (as a string) and the song title (also as a string). You wish to find the name of the artist who has the largest number of songs featured in the collection. Describe an algorithm for this problem.the algorithm should be as efficient as possible. State the running time of your algorithm, assuming that there are in total n songs, across t different artistsPlease do not give solution in image formate thanku. Write a Python code for the following scenario : 1: Use Breadth First Search and Recursive Best First Search and implement the algorithms in Python. The program should be able to dynamically take in start and goal nodes from the user at run time. Compare to interpret the results in terms of the algorithm working, performance & shortest path if obtained relevant to the given problem 2: Print the minimum connections that keep the whole network up and running. For each incremental depth limit, the corresponding node generating sequence should be legibly printed in the result Consider Heuristic Value as : The edge cost is an approximation towards the transmission cost between any pair of nodes. For heuristic design, consider all the possible paths between any arbitrary node n to the goal node. The average of the total transmission cost across all these paths is the heuristic value h(n) Consider the following undirected graph…
- Consider a satellite moving around the earth along the equator and recording some data (air-pressure, temperature, height etc.) for scientific investigation. The data thus obtained is stored in a database where the key to each data entry is the longitude of the point. We require this data to be sorted, but each of the n data entries might have been misplaced by no more than k positions from the correct sorted order (k is a predefined constant, depending on the speed of the satellite). Design a worst-case time and space efficient algorithm for sorting such a dataset.Please explain What is the worse-case performance of quicksort? Select the correct answer with the correct justification. Group of answer choices a. O(n*n), because during the partitioning stage it is possible that we select a 'bad' random pivot point that only sorts one item at a time. If we continuously do this over and over again, we are effectively only sorting 1 item each time. We then need to perform this pivot step n more times to sort the remaining n-1 items, thus giving us an O(n*n) complexity. b. O(n*n), because quicksort is a comparison-based sorting algorithm in which we have to compare every possible element against every other element in order to swap each element into the correct position. c. O(n*log(n)), because each time we are selecting a pivot point, on the average-case we are able to split our problem into roughly two collections, and sort half of our elements at the pivot point.A common implementation of sequential files on disk has each block point to its successor, which may be any block on the disk. This method requires a constant amount of time to write a block (as the file is originally written), to read the first block in the file, and to read the ith block, once you have read the 1 - 1” block. Reading the lth block therefore requires time proportional to 1. Show how by adding just one additional pointer per node, you can keep all the other properties, but allow the lth block to be read in time proportional to log I. [Hint: heaps have implicit pointers from node I to what other nodes?] Explain what the algorithm for reading the th block has in common with an algorithm for raising a number to the ith power in time proportional to log 1.