Count the number of times this algorithm performs + operations. x←1fori∈{1,2,3}doforj∈{1,2,3,4}dox←x+xfork∈{1,2,3,4,5,6}dox←x+1x←x+5
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Count the number of times this
x←1fori∈{1,2,3}doforj∈{1,2,3,4}dox←x+xfork∈{1,2,3,4,5,6}dox←x+1x←x+5
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- Algorithm Bellman_Ford1: procedure Bellman_Ford(G,s)2: for all {v} ∈ V do initialize3: d[v]←∞4: p[v] ← Ø5: end for6: d[s] ← 0 s has 0 cost7: for k = 1 to n − 1 do8: for all (u, v) ∈ E do relaxation9: if d[v] > d[u] + w[u, v] then10: d[v] = d[u] + w[u, v]11: p[v] ← u12: end if13: end for14: end for15: for all (u, v) ∈ E do16: if d[v] > d[u] + W[u, v] then17: return Ø a negative cycle detected18: end if19: end for20: return d, P21: end procedure Make Python Implementation of given algorithmAssignment (Math application): Write a program that prompts the user to enter a 3 x 3 matrix of double values and tests whether it is a positive Markov matrix. E An nxn matrix is a positive Markov matrix if the following is true: o lf each of the elements is positive o The sum of the elements in each column is 1 Sample Program running Enter a 3 x 3 matrix by row 0.15 0.875 0.375 0.55 0.005 0.225 0.30 0.12 0.4 The sum of the columns 1.0 1.0 1.0 It is a Markov matrix Enter a 3x 3 matrix by row -0.2 0.875 0.375 0.75 0.005 0.225 0.45 0.12 0.4 The sum of the columns 1.0 1.0 1.0 It is not a Markov matrix Please note the following requirements: Dinclude a comment before each method explaining what the methods will do E All methods called from the main methods There will be two methods which will be called from the main method: public static double [] [] createArray() 1. Creates a 3 by 3 two dimensional array of doubles 2. Prompts the user for values as shown in the sample run 3. Stores the…CPE 300 - Optimization Techniques Topic: GA Implementation Scenario: Suppose a genetic algorithm uses chromosomes of the form x = abcdefgh with a fixed length of eight genes. Each gene can be any digit between 0 and 9. Let the fitness of individual x be calculated as: f(x) = (a + b) − (c + d) + (e + f) − (g + h) and let the initial population consist of four individuals with the followingchromosomes: x1 = 6 5 4 1 3 5 3 2x2 = 8 7 1 2 6 6 0 1x3 = 2 3 9 2 1 2 8 5x4 = 4 1 8 5 2 0 9 4 Evaluate the fitness of each individual, showing all your workings, and arrange them in order with the fittest first and the least fit last. Perform the following crossover operations: One–point crossover, Two–point crossover, and uniform crossover.
- Algorithm 1 [WhoKnows(a1, a2, ..., an: integers)] 1: m := 0 2: for (i := 1 to n – 1) do for (j := i+1 to n) do 3: if (Jai – a;| > m) then m := |ai – a;| 4: 5: 6: end if 7: end for 8: end for 9: return m (a) What does the algorithm compute? (b) Find the exact number of comparisons performed for an input of size n? (c) What is the complexity of the algorithm in terms of big-O notation for the size of input n? (d) Open question. Can you think of a more efficient algorithm solving the same problem as Algorithm (1)? Discuss the details and the complexity.Assignment (Math application):Write a program that prompts the user to enter a 3 x 3 matrix of double values and testswhether it is a positive Markov matrix. An n x n matrix is a positive Markov matrix if the following is true:o If each of the elements is positiveo The sum of the elements in each column is 1 Sample Program running Enter a 3 x 3 matrix by row0.15 0.875 0.3750.55 0.005 0.2250.30 0.12 0.4The sum of the columns1.0 1.0 1.0It is a Markov matrix Enter a 3 x 3 matrix by row-0.2 0.875 0.3750.75 0.005 0.2250.45 0.12 0.4The sum of the columns1.0 1.0 1.0It is not a Markov matrix Please note the following requirements: Include a comment before each method explaining what the methods will do All methods called from the main methods There will be two methods which will be called from the main method:public static double [] [] createArray() 1. Creates a 3 by 3 two dimensional array of doubles2. Prompts the user for values as shown in the sample run3. Stores the numbers in the…Euclid’s Algorithm states the following: gcd(a, b) - a and b are integers b ≠ 0 r is the remainder of integer division At each step, the remainder, r, decreases by at least 1 r must eventually become 0 Use Euclid’s Algorithm to calculate gcd(96, 128).
- PSEUDOCODE - (ONLY PSEUDOCODE) Write an algorithm that takes a vector of integers A[1..n] and an integer x and, in O(n log n) time, determines if there are indices 1 ≤ i < j ≤ n such that A[i] + A[j] = x. proof the correctness and time consumption of your algorithm.1- How many times is Step 4 executed in the following algorithm? What is the time complexity of the algorithm? 1. count←02. fori←1ton3. forj←1to⌊logn⌋4. count←count+15. end for 6. end for 2-How many times is Step 6 executed in the following algorithm? What is the time complexity of the algorithm?Help me please
- Merge sort is an efficient sorting algorithm with a time complexity of O(n log n). This means that as the number of elements (chocolates or students) increases significantly, the efficiency of merge sort remains relatively stable compared to other sorting algorithms. Merge sort achieves this efficiency by recursively dividing the input array into smaller sub-arrays, sorting them individually, and then merging them back together. The efficiency of merge sort is primarily determined by its time complexity, which is , where n is the number of elements in the array. This time complexity indicates that the time taken by merge sort grows logarithmically with the size of the input array. Therefore, even as the number of chocolates or students increases significantly, merge sort maintains its relatively efficient performance. Regarding the distribution of a given set of x to y using iterative and recursive functions, the complexity analysis depends on the specific implementation of each…calculate number of operations in this algorithm void my_dgemv(int n, double* A, double* x, double* y) { double alpha=1.0, beta=1.0; int lda=n, incx=1, incy=1; cblas_dgemv(CblasRowMajor, CblasNoTrans, n, n, alpha, A, lda, x, incx, beta, y, incy); }a- Apply A* algorithm to find the path from M to R. 1 12 B 30) A C (30 8 5 30 3 з (25) 4 21 R (0) 2 D. 5 40 E (2)