Suppose, we have n integers in an array nums. We have to find out if the numbers in the array are pairwise coprime, setwise coprime, or not coprime.Two numbers nums[i] and nums[j] are said to be pairwise coprime if gcd(nums[i], nums[j]) = 1. This should hold for every number pair in the array and i < j.The numbers are said to be setwise coprime if gcd(nums[i]) = 1.If they are neither, we say that they are not coprime.So, if the input is like n = 4, nums = {7, 11, 13, 17}, then the output will be the numbers are ... Read More

To integrate a Laguerre series, use the laguerre.lagint() method in Python. The method returns the Laguerre series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The scaling factor is for use in a linear change of variable.The 1st parameter, c is an array of Laguerre series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. The 2nd parameter, m is an order of integration, must be positive. (Default: ... Read More

To generate a Chebyshev series with given roots, use the chebyshev.chebfromroots() method in Python Numpy. The method returns 1-D array of coefficients. If all roots are real then out is a real array, if some of the roots are complex, then out is complex even if all the coefficients in the result are real. The parameter roots are the sequence containing the roots.StepsAt first, import the required library −import numpy as np from numpy.polynomial import chebyshev as CTo generate a Chebyshev series with given roots, use the chebyshev.chebfromroots() method in Python Numpy −print("Result...", C.chebfromroots((-1, 0, 1)))Get the datatype −print("Type...", C.chebfromroots((-1, ... Read More

To Integrate a Chebyshev series, use the chebyshev.chebint() method in Python. Returns the Chebyshev series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The 1st parameter, c is an array of Chebyshev series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.The 2nd parameter, m is an order of integration, must be positive. (Default: 1). The 3rd parameter, k is an Integration constant(s). The value of the first ... Read More

To evaluate a Laguerre series at points x, use the polynomial.laguerre.lagval() method in Python Numpy. The 1st parameter is x. If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c.The 2nd parameter, C, an array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the ... Read More

Suppose, there are 2n number of letters and each of them has an integer number between 1 to n written on them. There are exactly two letters that have the same number written on them. These letters are arranged into m stacks and stack i has letters stack[i] on it. Our task is to empty all the stacks in the following mannerWe have to choose any two stacks and remove the top letter from both of them.The letters that we have removed must have the same number on both of them.If we can empty the m stacks in this manner, ... Read More

To evaluate a Laguerre series at points x, use the polynomial.laguerre.lagval() method in Python Numpy. The 1st parameter is x. If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c.The 2nd parameter, C, an array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the ... Read More

Suppose, there is a demand for red and blue cars for sale. An automobile company decides to sell p red cars and q blue cars of different prices. Currently, the company has 'a' number of red cars, 'b' number of blue cars, and 'c' numbers of colorless cars (the cars are yet to be painted) in their stock. The values of the different cars are given in arrays A, B, and C. So, the company has to sell p + q number of cars in a day and they have to make maximum profit from them. The colorless cars can ... Read More

Suppose, there are two n * n pixel square images first and second. The pixels can either be black or white. The images are given in a matrix representation where if a pixel is black it is represented as 'x' and if it is white, it is represented as '.'. We have to check the second image matches with the first image after 90° rotations and translations. If it does we return true, otherwise, we return false.So, if the input is like n = 4, first = {"..x.", "x.x.", "x.xx", "xx.."}, second = {"..xx", "x.xx", ".x.x", "..x."}, then the output ... Read More

To evaluate a Laguerre series at points x, use the polynomial.laguerre.lagval() method in Python Numpy. The 1st parameter is x. If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c.The 2nd parameter, C, an array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional case the ... Read More