mt1fall07 - 22 C : 031 Algorithms Midterm This is a closed...

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Unformatted text preview: 22 C : 031 Algorithms Midterm This is a closed book exam. You have an hour and fifteen minutes. 1. Give an asymptotically tight bound on the worst case running time of the following algorithm as a function of n , the number of elements in input array A and output array C . (Express runing time as Θ( f ( n )) for some appropriate f .) (2 points) For i from 1 to n do C[i] := 0 endfor For i from 1 to n do For j from i to n do C[i] := C[i] + A[j] endfor endfor Return C 2. Give an asymptotic upper bound on the worst case running time of the following algorithm as a function of n , the number of elements in input array A and output array C . (Express running time as O ( f ( n )) for some appropriate f .) Pick as good an f as you can. (3 points) For i from 1 to n do C[i] := 0 endfor For i from 1 to n do j:= i While j is less than or equal to n do C[i] := C[i] + A[j] j:= 2 * j endwhile endfor Return C 3. In each of the following cases, say whether f ( n ) is O ( g ( n )) and whether f ( n ) is...
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mt1fall07 - 22 C : 031 Algorithms Midterm This is a closed...

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