. Implement Euclidean Algorithm for calculating greatest common divisor First write and test a function that calculates the greatest common divisor of two nonnegative integers, as follows: /* precondition: a>=b>=0 */ /* postcondition: return d=gcd(a,b) */ int EuclidAlgGCD (int a, int b); Then implement the extended Euclidean Algorithm to find not only the greatest common divisor of two integers, but also find the integer coefficients that expresses the gcd in terms of the integers, as illustrated below: /* precondition: a>=b>=0 */ /* postcondition: return d=gcd(a,b), s and t are set so that d=sa+tb */ int ExtendedEuclidAlgGCD (int a, int b, int & s, int & t);

3. Given the function void f(n, m): input: two integers n, m, both of which are in form of 2 i← 1; j←m; k← 0; while i 1: j-j/2; k←k + j; return k; a. Calculate the value of k. b. Compute the computational complexity of the function and express your result using Big-Oh notation.

Exercise D Implement abs that returns the absolute value of a number NOTE You are NOT ALLOWED to use Basics.abs absolute : number -> number absolute x = 0 --remove this line and implement your absolute function here

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a) Implement a function start( ) that takes as input a positive number a, rounds its logarithm base 4 to the nearest integer n, and returns the value of 1.0 x 2^n.

Write a function lis_rec(arr) that outputs the length of the longest increasing sequence and the actual longest increasing sequence. This function should use divide and conquer strategy to the solve the problem, by using an auxiliary function that is recursive. For example, one possibility is to define a recursive function, lis_rec(arr, i, prev), that takes the array arr, an index i, and the previous element index prev of LIS (which is part of the array arr before index i), and returns the length of the LIS that can be obtained by considering the subarray arr[i:]. Write a dynamic programming version ofthe function, lis_dp(arr), that outputs the length of the longest increasing sequence and the actual longest increasing sequence by using a table to store the results of subproblems in a bottom-up manner. Test the performance of the two functions on arrays of length n = 100, 500, 1000, 5000, 10000. Compare the running times and memory usage of the two functions.

Write a function using Java   Function Name: winInRowParameters: board: 2D integer array, row: integer, piece: integerReturn: booleanAssume board is valid 2D int array, row is valid index in the board, piece is X==1/O==2Look at indicated row at given index in board. If that row has at least 3 consecutive entries withgiven type of piece (X/O) (3 in a row XXX, OOO), then return true, otherwise false.

In python find_substring("It was the best of times, it was the worst of times", "i") [20, 26, 47] >>> find_substring('Episode III: Revenge of the Sith', "e ") [6, 19, 26] >>> find_substring("bobbobob", "bob") [0, 3, 5]