Consider the problem to compute the transpose AT of an n x n matrix A. Consider...

  

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Consider the problem to compute the transpose AT of an n x n matrix A. Consider the pseudocode to compute the transpose of an n x n matrix A transposeMatrix (A) 1: 2: 234 3: 4: 5: 6: for i = 1 to n for i = 1 to j - 1 // swap A[i][j] and buffer = A[i][j] A[j] [] A[i][j] A[j] [i] buffer All the questions in this exercise are related to the transpose Matrix(A) algorithm. The objective of this exercise is to explore whether the time complexity will change if we count different "actions" B) (16 points) Assignment Action In this case, we count the number of assignments performed by Lines 4-6. Answer the following questions to determine the total number of assignments performed by the algorithm transposeMatrix(A). a. Let us call a the number of assignments performed by Lines 4-6 for a given value of j. Fill in this table: 1 2 3 j n-1 ai b. Express the function fa(n) that represents the overall total number of assignments performed by Lines 4-6 during the execution of transposeMatrix(A). c. The function fa(n) grows like which function? Consider the problem to compute the transpose AT of an n x n matrix A. Consider the pseudocode to compute the transpose of an n x n matrix A transposeMatrix (A) 1: 2: 234 3: 4: 5: 6: for i = 1 to n for i = 1 to j - 1 // swap A[i][j] and buffer = A[i][j] A[j] [] A[i][j] A[j] [i] buffer All the questions in this exercise are related to the transpose Matrix(A) algorithm. The objective of this exercise is to explore whether the time complexity will change if we count different "actions" B) (16 points) Assignment Action In this case, we count the number of assignments performed by Lines 4-6. Answer the following questions to determine the total number of assignments performed by the algorithm transposeMatrix(A). a. Let us call a the number of assignments performed by Lines 4-6 for a given value of j. Fill in this table: 1 2 3 j n-1 ai b. Express the function fa(n) that represents the overall total number of assignments performed by Lines 4-6 during the execution of transposeMatrix(A). c. The function fa(n) grows like which function?