For any positive m, n, a method was created to find integers a, b such that am+bn = gcd(m, n). Python-program this algorithm
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For any positive m, n, a method was created to find integers a, b such that am+bn = gcd(m, n). Python-program this
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- Write and test a Java/Python recursive method for finding the minimum element in an array, A, of n elements. What the running time? Hint: an array of size 1 would be the stop condition. The implementation is similar to linearSum method in lecture 5 examples. You can use the Math.min method for finding the minimum of two numbers.Java - Write an iterative method that calculates the SUM of all integers between 1 and a given integer N (input into the method). Write a corresponding recursive solution. (return answer, don’t print)An algorithm was introduced for finding integers a, b for anym, n where m, n are positive such that am+bn = gcd(m, n). Implementthis algorithm as a Python program
- mplement a Java program that applies the Newton-Raphson's method xn+1 = xn – f(xn) / f '(xn) to search the roots for this polynomial function ax6 – bx5 + cx4 – dx3+ ex2 – fx + g = 0. Fill out a, b, c, d, e, f, and g using the first 7 digits of your ID, respectively. For example, if ID is 4759284, the polynomial function would be 4x6 – 7x5 + 5x4 – 9x3+ 2x2 – 8x + 4 = 0. The program terminates when the difference between the new solution and the previous one is smaller than 0.00001 within 2000 iterations. Otherwise, it shows Not Found as the final solution.Jacobi method is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. Further details of the method can be found at Jacobi Method with a formal algorithm and examples of solving a system of 2/3 linear equations. This also includes a python implementation of the algorithm using numpy. But, in this assignment, you are required to write python implementation using list/nested list data structure without using any of the built-in python libraries for matrix operations. Write a python function Jacobi(A, b, x_init) where A is a diagonal dominant matrix, b is list of constants (right-hand side of the equations), and x_init (a list) is an initial guess to the solution. The function returns the solution as a list (each value of the list is rounded off to two decimal places). >>> Jacobi([[2, 1, 1], [0, 2, 1],…The factorial of a positive integer n —which we denote as n!—is the product of n and the factorial of n 1. The factorial of 0 is 1. Write two different recursive methods in Java that each return the factorial of n. Analyze your algorithm in Big-Oh notation and provide the appropriate analysis, ensuring that your program has a test class.
- An method found integers a, b for every positive m, n such that am+bn = gcd(m, n). Pythonize this algorithm.The following Python program solves Sudoku using backtracking. The method that starts the solution is "solve_sudoku(matrix)" and receives as input an n x n matrix where the empty inputs are represented by -1 from pprint import pprint def search_next_void(puzzle): for r in range(9): for c in range(9): if puzzle[r][c] == -1: return r, c return None, None def is_valid(puzzle, guess, row, col): row_vals = puzzle[row] if guess in row_vals: return False col_vars = [puzzle[i][col] for i in range(9)] if guess in col_vars: return False row_start = (row // 3) * 3 col_start = (col // 3) * 3 for r in range(row_start, row_start + 3): for c in range(col_start, col_start + 3): if puzzle[r][c] == guess: return False return True def solve_sudoku(puzzle): row, col = search_next_void(puzzle) if row is None: return True for guess in range(1, 10): if…A matrix's trace is equal to its trace transposed. The diag method of Numpy may be used to extract the elements along the diagonal of a square matrix. Retrieving data from diagonals above or below the primary diagonal is possible using the optional parameter k. The call trace, just like in Python programming, may be used to get a matrix's trace.
- The following Python program solves Sudoku using backtracking. The method that starts the solution is "solve_sudoku(matrix)" and receives as input an n x n matrix where the empty inputs are represented by -1 from pprint import pprint def search_next_void(puzzle): for r in range(9): for c in range(9): if puzzle[r][c] == -1: return r, c return None, None def is_valid(puzzle, guess, row, col): row_vals = puzzle[row] if guess in row_vals: return False col_vars = [puzzle[i][col] for i in range(9)] if guess in col_vars: return False row_start = (row // 3) * 3 col_start = (col // 3) * 3 for r in range(row_start, row_start + 3): for c in range(col_start, col_start + 3): if puzzle[r][c] == guess: return False return True def solve_sudoku(puzzle): row, col = search_next_void(puzzle) if row is None: return True for guess in range(1, 10): if…Suppose you are to make change for the amount 1234 with the smallest possible number of coins. The coin values you have available to you are 1, 17, and 29. In implementing a recursive solution mincoins( n ), what three values of n would be used for the three recursive calls of mincoins()? Smallest: Next: Largest: This straight recursive implementation would have exponential runtime because results are computed repeatedly. One speedup technique would be to make a table and store intermediate results when they are computed, so they don't need to be computed again. What is this technique called? Another speedup technique involves computing mincoins(1), mincoins(2), mincoins(1234). What is this technique called?Write Java solution for below problem Given a list of integers return largest and smallest number from it