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(Solved) : 3 Following Algorithms Analyze Worst Case Running Time Give Answer Big Oh Notation Need Gi Q44018367 . . .

3. For each of the following algorithms, analyze the worst-caserunning time. You should give your answer in big-Oh notation. Youdo not need to give an input which achieves your worst-case bound,but you should try to give as tight a bound as possible. Justifyyour answer (show your work). This likely means discussing thenumber of atomic operations in each line, and how many times itruns, writing out a formal summation for the runtime complexityT(n) of each algorithm, and then simplifying your summation. (a) 1f(A): // A is a square, 2D array; indexed starting from 1 2 let dbe a copy of A 3 for i = 1 to len(A): 4 d[i][i] = 0 5 6 for i = 1to len(A): 7 for j = 1 to len(A): 8 for k = 1 to len(A): 9 if(d[i][k] + d[k][j]) < d[i][j]: 10 d[i][j] = d[i][k] + d[k][j] 1112 return d

(b) 1 g(A): // A is a list of integers 2 for i = 1 to len(A): 3for j = 1 to len(A)-i: 4 if A[j+1] > A[j]: 5 // swap A[j+1] andA[j] 6 tmp = A[j+1] 7 A[j+1] = A[j] 8 A[j] = tmp 9 return A

(c) Here, abs(n) returns the absolute value of its argument, andcan be treated as an atomic operation 1 h(A): // A is a list ofintegers, of length at least 2, first index is 1 2 min = abs(A[1] -A[2]) 3 for i = 1 to len(A): 4 for j = i+1 to len(A): 5 if abs(A[i]- A[j]) < min: 6 min = abs(A[i] – A[j]) 7 return min

3. For each of the following algorithms, analyze the worst-case running time. You should give your answer in big-Oh notation. You do not need to give an input which achieves your worst-case bound, but you should try to give as tight a bound as possible. Justify your answer (show your work). This likely means discussing the number of atomic operations in each line, and how many times it runs, writing out a formal summation for the runtime complerity Tn) of each algorithm, and then simplifying your summation. (a) 1 f(A): // A is a square, 2D array; indexed starting from 1 let d be a copy of A for i = 1 to len (A): d[i] [i] = 0 for i = 1 to len(A): for j = 1 to len(A): for k = 1 to len(A): if (d[i] [k] + d[k] [j]) < d[i][j]: d[i][j] = d[i] [k] + d[k] [j] 12 return d WN (b) 1 g(A): // A is a list of integers 2 for i = 1 to len(A): for j = 1 to len (A)-i: if A[j+1] > A[j]: // swap A [j+1] and A[j] tmp = A[j+1] A[j+1] = A[j] A[j] = tmp 9 return A 600 O (c) Here, abs(n) returns the absolute value of its argument, and can be treated as an atomic operation 1 h(A): // A is a list of integers, of length at least 2, first index is 1 2 min = abs(A[1] – A[2]) 3 for i = 1 to len(A): for j = i+1 to len(A): if abs (A[i] – A[j]) < min: min = abs(A[i] – A[j]) 7 return min Show transcribed image text 3. For each of the following algorithms, analyze the worst-case running time. You should give your answer in big-Oh notation. You do not need to give an input which achieves your worst-case bound, but you should try to give as tight a bound as possible. Justify your answer (show your work). This likely means discussing the number of atomic operations in each line, and how many times it runs, writing out a formal summation for the runtime complerity Tn) of each algorithm, and then simplifying your summation. (a) 1 f(A): // A is a square, 2D array; indexed starting from 1 let d be a copy of A for i = 1 to len (A): d[i] [i] = 0 for i = 1 to len(A): for j = 1 to len(A): for k = 1 to len(A): if (d[i] [k] + d[k] [j]) A[j]: // swap A [j+1] and A[j] tmp = A[j+1] A[j+1] = A[j] A[j] = tmp 9 return A 600 O
(c) Here, abs(n) returns the absolute value of its argument, and can be treated as an atomic operation 1 h(A): // A is a list of integers, of length at least 2, first index is 1 2 min = abs(A[1] – A[2]) 3 for i = 1 to len(A): for j = i+1 to len(A): if abs (A[i] – A[j])

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Answer to 3. For each of the following algorithms, analyze the worst-case running time. You should give your answer in big-Oh nota…