Please help with the following python programming problems Line with most pointsdef line_with_most_points (points):A point on the two-dimensional grid of integers is given as a two-tuple of x- and y-coordinates, forexample (2, 5) or (10, 1). As originally postulated by Euclid, given any two distinct points onthe plane, there exists exactly one straight line that goes through both points. (In differently shapedspaces, different rules and their consequences apply) Of course, this same line, being shamelesslyinfinite to both directions, will also pass through an infinity of other points on that plane.Given a list of points on the integer grid, find the line that contains the largest number of pointsfrom this list. To guarantee the uniqueness of the expected result for every test case, this functionshould not return the line itself, but merely the count of how many of these points lie on that line.The list of points is guaranteed to contain at least two points and that all points in the list aredistinct, but otherwise these points are not given in any specific order.To get started, consult the example program geometry-py for the cross product function that canbe used to quickly determine whether three given points on the plane are collinear.pointsExpected result[ (42, 1), (7, 5)]2[(1, 4), (2, 6), (3, 2), (4, 10)]3[(x, y) for x in range (10) for y in range (10)]10[ (3, 5), (1, 4), (2, 6), (7, 7), (3, 8)]3[(5, 6), (7, 3), (7, 1), (2, 1), (7, 4), (2, 6), (7, 7)1 4 Double troubledef double_trouble(items, n):Suppose, if just for the sake of argument, that the following operation is repeated n times for thegiven list of iteme: remove the first element, and append that same element twice to the end ofitems. Which one of the items would be removed and copied in the last operation performed?Sure, this problem could be finger-quotes "solved" by actually performing that operation n times,but the point of this exercise is to come up with an analytical solution to compute the result muchfaster than actually going through that whole rigmarole. To gently nudge you towards thinking insymbolic and analytical solutions, the automated tester is designed so that anybody trying to bruteforce their way through this problem by performing all n operations one by one for real will run outof time and memory long before receiving the answer, as will the entire universe.To come up with this analytical solution, tabulate some small cases (you can implement the bruteforce function to compute these) and try to spot the pattern that generalizes to arbitrarily largevalues of n. You can again also check out Wolfram Alpha or similar systems capable of manipulationof symbolic formulas to simplify combinatorial and summing formulas.Expected resultitemsn['joe', 'bob', 42]10'joe'[17, 42, 99]100017[17, 42, 99]10**2099['only', 'the', 'number', 'of',"matters' ]10**1000 'the''items'

Given the coordinate points as list find the maximum count of points which belong to same line if…

Line with most polnts def line_with_most_points(points): 4 point on the two-dimensional grid of integers is given as a two-tuple of x- and y-coordinates, for example (2, 5) or (10, 1). As originaly postulated by Euclid, given any two distinct points on the plane, there exists exactly one straight line that goes through both points. (In differently shaped spaces, different rules and their consequences apply:) Of course, this same line, being shamelessly nfinite to both directions, will also pass through an infinity of other points on that plane. Given a list of pointa on the integer grid, find the line that contains the largest number of points rom this list. To guarantee the uniqueness of the expected result for every test case, this function should not return the line itself, but merely the count of how many of these points lie on that line. The list of points is guaranteed to contain at least two points and that all points in the list are distinct, but otherwise these points are not given in any specific order. To get started, consult the example program geometry.pyfor the cross product function that can be used to quickly determine whether three given points on the plane are collinear. points Expected result [(42, 1), (7, 5)] 2 [(1, 4), (2, 6), (3, 2), (4, 10)] [(x, y) for x in range (10) for y in range(10)] 10 [(3, 5), (1, 4), (2, 6), (7, 7), (3, 8)1 3 (7 3) (7 A 2

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE