Deparmtent of Computer Science & Information Technology, University of Engineering & Technology Peshawar.
Advance Analysis of Algorithms. Spring 2014. Dr. Iftikhar Ahmad. Practice Questions : Time Complexity of Algorithms.
Note Compute the time complexity of the following algorithms, some of the algorithms are without any purpose, so do not try to figure out what they actually do. If you want to challenge yourself, find the purpose of Algorithm 10. Algorithm 1 Algorithm to find the sum of all elements of a matrix of size n x m 1: procedure MatElementsSum(A[0 . . . n − 1, 0, . . . m − 1]) 2: sum = 0 3: for i = 0 to n − 1 do 4: for j = 0 to m − 1 do 5: sum = sum + A[i, j] 6: end for 7: end for 8: return sum 9: end procedure
Algorithm 2 Algorithm to find the maximum in an array of size n 1: procedure FindMax(A[0 . . . n − 1, 0]) 2: max = A[0] 3: for i = 1 to n − 1 do 4: if max < A[i] then 5: max = A[i] 6: end if 7: end for 8: return max 9: end procedure
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Algorithm 3 Algorithm which does something with an array of size n 1: procedure SomeAlg(A[0 . . . n − 1, 0]) 2: var = 1 3: i=n−1 4: while i ≥ 0 do 5: var = var ∗ 2A[i] 6: i=i−1 7: end while 8: return var 9: end procedure
Algorithm 4 Algorithm which does something with an array of size n 1: procedure SomeAlg1(A[0 . . . n − 1, 0]) 2: var = 1 3: while i > n do 4: var = var ∗ 2A[i] 5: i=i+2 6: end while 7: return var 8: end procedure
Algorithm 5 Algorithm which does something with an array of size n 1: procedure SomeAlg2(A[0 . . . n − 1, 0]) 2: var1 = 1 3: var2 = 100 4: for i = 1 to n − 1 do 5: j=i 6: var2 = var2 + var1 7: while j < n do 8: var1 = var2 /2 9: var2 = var2 − var1 /2 10: j =j+2 11: end while 12: end for 13: end procedure
Algorithm 6 Algorithm which just sums up for no apparent reason 1: procedure SomeAlg3(n) 2: sum = 0 √ 3: for i = 1 to n do 4: sum = sum + i 5: end for √ 6: for i = 1 to n/2 do 7: sum = sum + i 8: end for 9: for i = 1 to 10 do 10: sum = sum + i 11: end for 12: end procedure
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Algorithm 7 Algorithm which just sums up for no apparent reason 1: procedure SomeAlg4(n) 2: sum = 0 √ n do 3: for i = 1 to 4: for j = 1 to 5 do 5: sum = sum + i · j 6: end for 7: end for 8: end procedure
Algorithm 8 Algorithm which just sums up for no apparent reason in a weird fashion 1: procedure SomeAlg5(n) 2: sum = 0 3: for i = 1 to 2n do 4: for j = 1 to i · i do 5: for k = 1 to j do 6: sum = sum + 1 7: end for 8: end for 9: end for 10: end procedure
Algorithm 9 To calculate factorial of a given number n 1: procedure Factorial(n) 2: if n = 1 then 3: return 1 4: else 5: return n x Factorial(n − 1) 6: end if 7: end procedure
Algorithm 10 A Mystic Algorithm 1: procedure MysteryAlg(x , n) 2: if n = 0 then 3: return 1 4: end if 5: if n = 1 then 6: return x 7: end if 8: if n is even then 9: return MysteryAlg(x ∗ x, n/2) 10: else 11: return MysteryAlg(x ∗ x, n/2) ∗ x 12: end if 13: end procedure
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