Interchange Base Points Algorithm An integer j between 1 and k-l, a group G, a base [131,132,..... 13k] for G, and a strong generating set are all inputs. Output: a powerful generating set for G with base B = [131,132..... 13j-1, 13L.+1, 13j, 13j+2, 13j+3..... 13k];
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Interchange Base Points Algorithm
An integer j between 1 and k-l, a group G, a base [131,132,..... 13k] for G, and a strong generating set are all inputs.
Output: a powerful generating set for G with base B = [131,132..... 13j-1, 13L.+1, 13j, 13j+2, 13j+3..... 13k];
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- Write Algorithm to Removing Some RedundanciesInput : a base B = [91, ~2 ..... ~k];a strong generating set S of a group G;Output 9 a subset T of S that is also a strong generating set of G relative to B; write accurate ans otherwise you will get downvoteCreate an ABM function that takes the following parameters: n := number of paths to be simulated m := number of discretization points per path S0 := initial starting point dS=μdt+σdW Program the function by using two nested "for loops" def ABM(n,m,S0,mu,sigma,dt): np.random.seed(999) arr = # create 2D zeros array with the correct dimensions arr[,] = #initialize column 0 # fill in array entries for i in : for j in : arr[i,j] = return arrCourse:Analysis of Algorithms For the following code snippet, provide line-by-line analysis and construct function T(n) that give theruntime of this code snippet as a function of “n”. Also determine the big-Oh of for this code snippet. for (int i = 1; i <= n; i++) {if ( x < i)sum += foo( i )+ foo(i+1);system.out.print(sum);else if ( x > i)sum += foo( i ) – foo(i–1);system.out.print(sum);elsefor (j = 1; j <= i; j++)system.out.print( i );system.out.println( );} foo (a) {for (int i = 0; i < n; i++)sum += a * i;return sum;}
- Complexity The function accumulate operates on a list of n integers where each element was chosen inde- pendently from the set {1, 2, ..., 8} with uniform probability. In analyzing the running time of this code, we are only interested in the number of explicit assignment statements (lines 1, 4 and 8) not the loop controls. Your answers should be in terms of n and give actual values not asymptotic classes. Arrays are using 1-based indexing. def accumulate(A): 1 sum = 2 for i in 1 to n: #1-based indexing 3 if A[i] < 7: 4 sum = sum +A|i] else: 5 for j in 1 to n: for k in 1 to j: sum = sum + A[i]/A[j] 7 8 10 return sum (b) Worst Case Prove a worst-case analysis being careful to provide all the required pieces. Give an exact count of the operations of interest (total count of lines 1, 4 and 8), not an asymptotic bound. (c) Average case Give a formula for the total number of assignment statements (Lines #1, #4, and #8) executed in the average case. Explain each term in your formula so the…Recall that the divisor of an integer n, also called a factor of n, is an integer which divides nwithout leaving a remainder. Consider the below Computational Problem: CountDivisorsProblem: Input: Natural number n >= 1 Output: Number of divisors that n has, a natural number. Le, for the input 6 we have the output 4, as it has the four divisors 1, 2, 3, 6. For the input 7 we have the output 2, as it has the two divisors 1, 7. Consider the Java program CountDivisors that solves the problem CountDivisors: 01 public static int CountDivisors (int N) { 02 int testDivisor; 03 int counter = 0: 04 for (testDivisor = 1; testDivisor <= N; testDivisor++){ 05 if (N % testDivisor == 0) { 06 07 ) 08 1 09 return counter; 10 } Consider the test suite V: V: Name Expected Output T1 1 1 T2 2 2 Say what holds for the test suite V: Is test suite for C_p. There is a problem with the inputs or outputs w.r.t. CountDivisorsProblem. Is test suite for C_0. Is test suite for C_i(2). Is minimal test suite for C_0.…Given an array of integers and a positive integer k, determine the number of (i, j) pairs where i < j and ar[i] + ar[j] is divisible by k. Example ar [1, 2, 3, 4, 5, 6] k=5 Three pairs meet the criteria: [1, 4], [2, 3], and [4, 6]. Function Description Complete the divisibleSumPairs function in the editor below. divisibleSumPairs has the following parameter(s): • int n: the length of array ar ⚫int ar[n]: an array of integers . int k: the integer divisor Returns -int: the number of pairs Input Format The first line contains 2 space-separated integers, 11 and k. The second line contains space-separated integers, each a value of arr[i]. Constraints • 2 ≤ n ≤ 100 • 1<k<100 • 1 ≤ ar[i] ≤ 100 Sample Input fin Contest ends in 5 days Submissions: 45 Max Score: 20 Difficulty: Easy Rate This Challenge: More STDIN 63 1 3 2 6 12 Function n6, k3 ar [1, 3, 2, 6, 1, 2] Sample Output 5 Explanation Here are the 5 valid pairs when k = 3: (0,2) ar[0] + ar[2]=1+2=3 (0,5) ar[0] + ar[5]=1+2=3 •…
- Given an array of integers and a positive integer k, determine the number of (i, j) pairs where i < j and ar[i] + ar[j] is divisible by k. Example ar [1, 2, 3, 4, 5, 6] k=5 Three pairs meet the criteria: [1, 4], [2, 3], and [4, 6]. Function Description Complete the divisibleSumPairs function in the editor below. divisibleSumPairs has the following parameter(s): • int n: the length of array ar ⚫int ar[n]: an array of integers . int k: the integer divisor Returns -int: the number of pairs Input Format The first line contains 2 space-separated integers, 11 and k. The second line contains space-separated integers, each a value of arr[i]. Constraints • 2 ≤ n ≤ 100 • 1<k<100 • 1 ≤ ar[i] ≤ 100 Sample Input More STDIN 63 1 3 2 6 12 Function n6, k3 ar [1, 3, 2, 6, 1, 2] Sample Output 5 Explanation Here are the 5 valid pairs when k = 3: (0,2) ar[0] + ar[2]=1+2=3 (0,5) ar[0] + ar[5]=1+2=3 • (1,3) ar[1]+ar [3]=3+6=9 (2, 4) ar[2] + ar[4] = 2+1=3 • (4,5)→ ar[4] + ar[5]=1+ 2=3 with…Algorithm of Preis in AlgebraThe following steps make up the algorithm.A weighted graph G = as the first input (V, E, w)A maximum weighted matching M of G as the output.While E =, choose any v V at random, let e E be the largest edge incident to v, and then perform the following calculations: 3. M e; 4. E e; 5. V V; 6.11. Two different Python implementations of this algorithm are shown by E, E, and all edges that are adjacent to e.Write the algorithm for the problem that works in constant space and time complexity. Input: N OUTPUT: 1 if Tom wins, 0 if Jerry wins.
- By the "n queens problem" we mean the problem of placing n queens on an nXn “chessboard" in such a way that no queen can capture any other on the next move. In class we solved the "8 queens" problem. Write a function that inputs an integer n and returns the number of solutions to the “n queens" problem. Your function should use the one dimensional representation for the board, the algorithm we discussed in class, and no gotos. Test your function with a main program that prompts the user for an integer n. The main program then calls the function n times, once for each number from 1 – n, and then prints the number of solutions to each of these problems, one on a line. For example, if you enter n=5 your program should output: 1. There are 2. There are 3. There are 4. There are solutions to the 1 queens problem. solutions to the 2 queens problem. solutions to the 3 queens problem. solutions to the 4 queens problem. solutions to the 5 queens problem. 5. There are Now, since each time…Input: An odd integer B, and a set A= {a_1, . .. , a_2n} of 2n distinct positive integers. Question: Decide whether A can be partitioned inton disjoint pairs (a_i, a_j), where 1 s iAlgorithm 1 : Miniature SearchInput : a group G;a base [111,112 ..... 1]k] for G and a strong generating set;an integer j between 1 and k- 1;Output : a set T of coset representatives of G (j+2) in ~(j+l) ;SEE MORE QUESTIONS