op/recursion invariant alongwith the runtime of the algorithm that you would write for the below question:- You are given
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State the PSEUDOCODE and the loop/recursion invariant alongwith the runtime of the
You are given data about a friendship network. For every pair of friends, you are given the number of times they have exchanged messages in the last year. Give an efficient algorithm for partitioning the people in the network into k clusters, or communities in such a way that the minimum number of messages exchanged by any two members in different communities is maximized.
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- You are given a N*N maze with a rat placed at maze[0][0]. Find whether any path exist that rat can follow to reach its destination i.e. maze[N-1][N-1]. Rat can move in any direction ( left, right, up and down).Value of every cell in the maze can either be 0 or 1. Cells with value 0 are blocked means rat cannot enter into those cells and those with value 1 are open.Input FormatLine 1: Integer NNext N Lines: Each line will contain ith row elements (separated by space)Output Format :The output line contains true if any path exists for the rat to reach its destination otherwise print false.Sample Input 1 :31 0 11 0 11 1 1Sample Output 1 :trueSample Input 2 :31 0 11 0 10 1 1Sample Output 2 : false Solution: //// public class Solution { public static boolean ratInAMaze(int maze[][]){ int n = maze.length; int path[][] = new int[n][n]; return solveMaze(maze, 0, 0, path); } public static boolean solveMaze(int[][] maze, int i, int j, int[][] path) {//…A graph is a collection of vertices and edges G(V, E). A weighted graph has weights (numbers, etc.) on every edge. A multigraph can have more than one edges between any vertices. Explain why a person should use a weighted graph instead of a multigraph. Give examples. An adjacency matrix might be a better choice for speeding up a program, however, it consumes huge memory for large graphs. How this situation can be improved? What programming constructs better suit graph representation? Explain with exampleCorrect answer will be upvoted else downvoted. Computer science. You are given an exhibit a comprising of n (n≥3) positive integers. It is realized that in this exhibit, every one of the numbers with the exception of one are something very similar (for instance, in the cluster [4,11,4,4] all numbers aside from one are equivalent to 4). Print the list of the component that doesn't rise to other people. The numbers in the cluster are numbered from one. Input The main line contains a solitary integer t (1≤t≤100). Then, at that point, t experiments follow. The main line of each experiment contains a solitary integer n (3≤n≤100) — the length of the exhibit a. The second line of each experiment contains n integers a1,a2,… ,an (1≤ai≤100). It is ensured that every one of the numbers aside from one in the an exhibit are something very similar. Output For each experiment, output a solitary integer — the list of the component that isn't equivalent to other people.
- Let's say you're going to invite some people to a party. You're considering n friends, but you know that they will have a good time only if each of them knows at least k others at the party. (Assume that if A knows B, then B automatically knows A.) Solve your problem by designing an algorithm for finding the largest possible subset of your friends where everyone knows at least k of the others, if such a subset exists. Please comment on code and show all work so I can better understand the problem and please use python thank you, To help you get started l've made a graph of "my friends": G={'Rachel':['Ross Monica'], 'Ross':['Rachel', 'Monica'], 'Monica':['Rachel', 'Ross'], 'Jon Snow':['Daenerys' "Sansa' "Arya'), 'Daenerys':['Jon Snow "Sansa "Arya' Khal Drogo'), 'Sansa':['Jon Snow DaenerysArya'), 'Arya':['Jon Snow "Daenerys' Sansa'), 'Khal Drogo':['Daenerys'], 'Cersei':['Jaime'], 'Jaime':['Cersei'], 'Bart':['Milhouse'], 'Milhouse':['Bart','Lisa'], 'Lisa':['Milhouse'],…Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. each individual has a rating chart portrayed by a variety of integers an of length n. You are currently refreshing the foundation, so you've made a program to pack these diagrams. The program functions as follows. Given an integer boundary k, the program takes the base of each adjoining subarray of length k in a. All the more officially, for a cluster an of length n and an integer k, characterize the k-pressure exhibit of an as a cluster b of length n−k+1, to such an extent that bj=minj≤i≤j+k−1ai For instance, the 3-pressure cluster of [1,3,4,5,2] is [min{1,3,4},min{3,4,5},min{4,5,2}]=[1,3,2]. A stage of length m is an exhibit comprising of m unmistakable integers from 1 to m in subjective request. For instance, [2,3,1,5,4] is a stage, however [1,2,2] isn't a change (2 shows up twice in the exhibit) and [1,3,4] is likewise not a stage (m=3 but rather there is 4 in the…Imagine there are N teams competing in a tournament, and that each team plays each of the other teams once. If a tournament were to take place, it should be demonstrated (using an example) that every team would lose to at least one other team in the tournament.
- There are n students who studied at a late-night study for final exam. The time has come to order pizzas. Each student has his own list of required toppings (e.g. mushroom, pepperoni, onions, garlic, sausage, etc). Everyone wants to eat at least half a pizza, and the topping of that pizza must be in his reqired list. A pizza may have only one topping. How to compute the minimum number of pizzas to order to make everyone happy?This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played altogether, in all the rounds of the tournament? Your answer: Hint: This is much simpler than you think. When you see the answer you will say "of course".Given a deck of 52 playing cards, we place all cards in random order face up next to each other. Then we put a chip on each card that has at least one neighbour with the same face value (e.g., on that has another queen next to it), we put a chip. Finally, we collect all chips that were each queen placed on the cards. For example, for the sequence of cards A♡, 54, A4, 10O, 10♡, 104, 94, 30, 3♡, Q4, 34 we receive 5 chips: One chip gets placed on each of the cards 100, 10♡, 104, 30, 3♡. (a) Let p5 be the probability that we receive a chip for the 5th card (i.e., the face value of the 5th card matches the face value of one of its two neighbours). Determine p5 (rounded to 2 decimal places). (b) Determine the expected number of chips we receive in total (rounded to 2 decimal places). (c) For the purpose of this question, you can assume that the expectation of part (b) is 6 or smaller. Assume that each chip is worth v dollars. Further, assume that as a result of this game we receive at least…
- In a tournament, there are n participating teams are labelled from 1 to n. Each pair of teams will play against each other exactly once. Thus, a total of [n(n-1)/2] matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match: 1. The match ends in a draw, in which case both teams will get 1 point. 2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points. Design an algorithm which runs in O(n2 ) time and provides a list of results in all [n(n-1)/2] matches which: (a) ensures that all n teams finish with the same points total, and (b) includes the fewest drawn matches among all lists satisfying (a). Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain EnglishIn a tournament, there are n participating teams are labelled from 1 to n. Each pair of teams will play against each other exactly once. Thus, a total of [n(n-1)/2] matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match: 1. The match ends in a draw, in which case both teams will get 1 point. 2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points. Design an algorithm which runs in O(n2 ) time and provides a list of results in all [n(n-1)/2] matches which: (a) ensures that all n teams finish with the same points total, and (b) includes the fewest drawn matches among all lists satisfying (a). Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English. PLease give the total time complexity.Algorithm design with sorting. Each of n users spends some time on a social media site. For each i = 1, . . . , n, user i enters the site at time ai and leaves at time bi ≥ ai. You are interested in the question: how many distinct pairs of users are ever on the site at the same time? (Here, the pair (i, j) is the same as the pair (j, i)).Example: Suppose there are 5 users with the following entering and leaving times: Then, the number of distinct pairs of users who are on the site at the same time is five: these pairs are (1, 2), (1, 3), (2, 3), (4, 6), (5, 6). (Drawing the intervals on a number line may make this easier to see).(a) Given input (a1 , b1),(a2 , b2), . . . ,(an, bn) as above in no particular order (i.e., not sorted in any way), describe a straightforward algorithm that takes Θ(n2)-time to compute the number of pairs of users who are ever on the site at the same time, and explain why it takes Θ(n2)-time. [We are expecting pseudocode and a brief justification for its…