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- You are given an n ×n square matrix. Each cell contains a number (positive,negative, or zero); you may assume they are integers if that helps. Now you are thrown into one of the square cells. Your task is to escape the board and at the same time collect as much value as you can. Every time you reach a cell, you gain/lose by the amount stored in that cell. From a cell, you can traverse to a cell below or to the right. You can escape the board fromthe the right boundary or from the bottom. Note that you cannot go back to a cell that you have already visited; otherwise, you can just keeping visiting two consecutive positive cells and obtain infinite value, yet never escaping – you are filthy rich but alone forever!Give an algorithm to escape as rich as you can be. State the complexity. Your explanation/pseudo-code (if you choose to write one) should be clear; remember that I can only grade based on what you write, not what you thought. You should also provide substantial reasoning as to…A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, theprincipal plays the following game: She asks the first student to open all the lockers. She then asks the secondstudent to close all the even-numbered lockers. The third student is asked to check every third locker. If it isopen, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourthlocker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continuethis game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed,the student opens it. After all the students have taken turns, some of the lockers are open and some are closed.The program below, when ran, will prompt the user to enter the number of lockers in the school. After thegame is over, the program will output the number of lockers and the lockers numbers of the lockers…Implement keys() for SeparateChainingHashST and LinearProbingHashST. 0 Add a method to LinearProbingHashST that computes the average cost of a search hit in the table, assuming that each key in the table is equally likely to be sought.
- You are given a 2 by n grid, where the cell on row i column j contains a non-negative number ai,j . You can start at either cell in the lefttmost column, and your goal is to reach either cell in the rightmost column by a sequence of moves. You can move to an adjacent cell (if it exists) in each of the 4 cardinal directions (up,down, left and right). A path achieves a score equal to the sum of values in its cells. Note that a cell which is used twice in a path only counts its value once to the score of that path.Design an algorithm which runs in O(n) time and finds a path of minimum score from the leftmost column to the rightmost column.When Bobby’s friends visit her on the farm, she likes to show them around. Thefarm consists of n fields numbered 1, 2, . . . , n, the first of which contains her house and the n-th of whichcontains the big barn. A total of m directed paths connect the fields. The i-th path is from field ui to fieldvi, and has a nonzero length wi.1 Suppose there are k friends coming today. To show off the farm in the best way, Bobby designs a tourfor each friend that starts at her house, potentially travels through some fields, and ends at the barn.Bobby wants the total length of the k tours to be as short as possible, where the length of a tour is thetotal length of paths in the tour. However, she doesn’t want any two friends to share any path. That is,for any two friends, their tours should not have any common paths (but they can travel through the samefields). Write an LP that can calculate the shortest total length of k tours that satisfies Bobby. You canassume that at least one feasible…Suppose, you have been given a non-negative integer which is the height of a ‘house ofcards’. To build such a house you at-least require 8 cards. To increase the level (or height)of that house, you would require four sides and a base for each level. Therefore, for the toplevel, you would require 8 cards and for each of the rest of the levels below you wouldrequire 5 extra cards. If you were asked to build level one only, you would require just 8cards. Of course, the input can be zero; in that case, you do not build a house at all.Complete the recursive method below to calculate the number of cards required to builda ‘house of cards’ of specific height given by the parameter.
- X-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…X-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.A safe is locked by a combination of of four binary digits (that is, 0 or 1), but theowner has forgotten the combination. The safe is designed in such a way that nomatter how many digits have been pressed, if the correct combination of three digitsis pressed at any point, then the safe automatically opens (there is no ”enter” key).Our goal is to find the minimum number of digits that one needs to key in in order toguarantee that the safe opens. In other words, we wish to find the smallest possiblelength of a binary sequence containing every four-digit sequence in it.(a) Create a digraph whose vertex set consists of three-digit binary sequences. Fromeach vertex labelled xyz, there is one outgoing edge (labelled 0) leading to vertexyz0, and another outgoing edge (labelled 1) leading to vertex yz1.(b) Explain why every edge represents a four digit sequence and why an Euleriantour of this graph represents the desired sequence of keystrokes.(c) Find the minimum number of digits that one…
- There are m towns in a straight line, with a road joining each pair of consecutive towns. Legends say that an ordinary person in one of these towns will become a hero by completing a sequence of n quests. The first quest will be completed in their home town, but after each quest they may complete their next quest either in the same town or after moving to a neighbouring town.For example, if n = 5 and m = 4, a resident of town 2 may become a hero as follows:• begin in town 2 for quest 1,• then move to town 3 for quest 2,• stay in town 3 for quest 3,• return to town 2 for quest 4, and• move to town 1 for quest 5.Design an algorithm which runs in O(nm) time and finds the total number of waysto complete n quests.We have a list that stores the repeated heart-rate measurements for the same patient over several tests. Each inner-list is a test and for that test, the heart rate is monitored for some time while taking a few measurements. Next, we would like to calculate the average of the measurements for each test.heart_rate = [ [ 72, 75, 71, 73], # resting[ 91, 90, 94, 93], # walking slowly[ 130, 135, 139, 142], # running on treadmill[ 120, 118, 110, 105, 100, 98]] # after minute recoveryIn your code, define a function calculate_average_heart_rates() that accepts the list heart_rate as its only input argument. Inside the function, use nested loops to calculate the average heart rate during each test scenario. This function should return a list that contains the average heart rate values of a patient for the four test scenarios.Write unit testsThere are four medals (Gold, Silver, Bronze and Wood) on a table, but they are all wrapped with dark wrapping paper, such that it is impossible to distinguish them. You would like to find the gold medal.The game starts as follows. You pick one medal without unwrapping it, and then the game host unwraps one of the remaining medals and reveals that it is a silver medal. (Assume here that the host unwraps a medal with equal probability, but knowing where the gold medal was and avoiding unwrapping the gold medal if still on the table, to keep the game interesting to watch until the end.)You have now three medals left to unwrap (one in your hand, two on the table). At this point, the host gives you the option to change your mind and swap your medal for one of the two left on the table. What would you do at this point? Would you keep your medal, or swap it with one of the two medals left on the table? If so, which one? Hints: Find the solution by using Bayes’ theorem, calculating all the…