Design an efficient algorithm to find the closest pair of points in a set of points on a plane using Divide and conquer. Input: A list of n points on a plane. Output: The minimum distance between a pair of these points.
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- 5. Given # > 3 points P₁ = (x₁, y₁), …….‚ P₂ = (x₂‹ Yn) in the coordinate plane, design an algorithm to check whether all the points lie within a triangle with its vertices at three of the points given. (You can either design an algorithm from scratch or reduce the problem to another one with a known algorithm.)algorithm for Interval point cover. pre-cond: P is a set of points, and I is a set of intervals on a line. post-cond: The output consists of the smallest set of intervals that covers all ofthe points.The greatest common divisor of two positive integers, A and B, is the largest number that can be evenly divided into both of them. Euclid's algorithm can be used to find the greatest common divisor (GCD) of two positive integers. You can use this algorithm in the following manner: 1. Compute the remainder of dividing the larger number by the smaller number. 2. Replace the larger number with the smaller number and the smaller number with the remainder. 3. Repeat this process until the smaller number is zero. The larger number at this point is the GCD of A and B. Write a program that lets the user enter two integers and then prints each step in the process of using the Euclidean algorithm to find their GCD. An example of the program input and output is shown below: Enter the smaller number: 5 Enter the larger number: 15 The greatest common divisor is 5
- Need help in python. Problem: 2D random walk. A two dimensional random walk simulates the behavior of a particle moving in a grid of points. At each step, the random walker moves north, south, east, or west with probability 1/4, independently of previous moves. Compose a program that takes a command-line argument n and estimates how long it will take a random walker to hit the boundary of a 2n+1-by-2n+1 square centered at the starting point. //Given codeImport stdioImport randomImport sysn = int(sys.argv[1])//write code herestdio.write('The walker took ')stdio.write(c)stdio.writeln(' steps')Input: A set of n movies. A positive integer k. A positive integer q. A function f that takes two movies X, Y, and gives a positive similarity score f(X, Y) in constant time. Task: Design an efficient algorithm that partitions the movies into exactly k disjoint sets such that movies from different sets have a similarity score at most q. If such groups cannot be made, then print 'Unsatisfiable'. Yeah, please what is the time complexity for this algorithm, thanks.Problem 2: Postman Harry Harry is a postman. He's got a post office with a size of n rows and m columns. Each slot at the post office contains a number of letters. Harry can only go right and down. He starts at (0, 0), and ends at (n-1, m-1). Write a program that calculates the maximum amount of letters Harry can pick up. He can only pick up letters from a slot if he is on that slot. If the amount of letters is the same down and right, go right. Sample input/output: Enter the number of rows and columns: 35 Enter the number of letters in the 5 slots of row number 1: 5 2 60 1 Enter the number of letters in the 5 slots of row number 2: 2 4 3 9 2 Enter the number of letters in the 5 slots of row number 3: 8 72 3 4 The maximum number of letters Harry can pick is 32 solve using c++; (chapter 9: Variables / Assignments)
- Start with a pile of n stones and successively split a pile into two smaller piles until each pile has only one Each time a split happens, multiply the number of stones in each of the two smaller piles. (For example, if a pile has 15 stones and you split it into a pile of 7 and another pile of 8 stones, multiply 7 and 8.) The goal of this problem is to show that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2. Using strong mathematical induction, prove that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2.Let A = {a, b, c} and B = {u, v}. Write a. A × B b. B × A# Exercise 1. Implement the algorithm covered in lectures that determines if an integer n is prime. Your function should return True, if n is prime, and False otherwise. Your algorithm has to be effective for n ~ 1,000,000,000,000.def isPrime(n):
- Tiling: The precondition to the problem is that you are given threeintegers n, i, j, where i and j are in the range 1 to 2n. You have a 2n by 2n squareboard of squares. You have a sufficient number of tiles each with the shape . Your goalis to place nonoverlapping tiles on the board to cover each of the 2n × 2n tiles except forthe single square at location i, j. Give a recursive algorithm for this problem in whichyou place one tile yourself and then have four friends help you. What is your base case?Union-Find: Maze Write a program that generates mazes of arbitrary size using the union-find algorithm. A simple algorithm to generate the maze is to start by creating an N x M grid of cells separated by walls on all sides, except for entrance and exit. Then continually choose a wall randomly, and knock it down if the cells are not already connected to each other. If we repeat the process until the starting and ending cells are connected, we have a maze. It is better to continue knocking down the walls until every cell is reachable from every cell as this would generate more false leads in the maze. Test you algorithm by creating a 15 x 15 grid, and print all the walls that have been knocked down. DWeighted Intervals Problem EXAMPLE:Suppose we have the following weighted intervals. start finish weight 11 14 4 10 13 5 9 11 5 11 14 3 8 9 2 To solve the problem, we start out by sorting the intervals by finish time. This gives us the following. start finish weight 8 9 2 9 11 5 10 13 5 11 14 4 11 14 3 Next we calculate the p-values. P(j) = k where interval k is the last interval prior to interval j in the list below which does not conflict with interval j, or P(j) = 0 if all intervals prior to interval j conflict with it. # start finish weight P 1 8 9 2 0 2 9 11 5 1 3 10 13 5 1 4 11 14 3 2 5 11 14 4 2 Finally, we use the formula OPT(j) = max{OPT(j-1), weight(j)+ OPT(P(j))} to fill in the OPT value for each j. (The…