Give an asymptotically tight bound (O) for each of the following recurrence relations. Prove your answers, and use the master theorem whenever possible. a) T(n)= 1 for every n<1 and T(n) = T() b) T(n) = 1 for every n<1 and T(n) = 2T(}) c) T(n)= 1 for every n<1 and T(n) = 2T(5). d) T(n)= 1 for every n<2 and T(n) = 2T(\n) + ©(log n / log log n) otherwise. + O(n) otherwise. + O(n³) otherwise. + O(log n) otherwise.

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Give an asymptotically tight bound (O) for each of the following recurrence relations.
Prove your answers, and use the master theorem whenever possible.
a) T(n)= 1 for every n<1 and T(n) = T() + O(n) otherwise.
b) T(n) = 1 for every n<1 and T(n) = 2T()
O(n') otherwise.
c) T(n)= 1 for every n<1 and T(n)= 2T(%) + ©(log n) otherwise.
d) T(n)= 1 for every n<2 and T(n) = 2T(\n) + ©(log n / log log n) otherwise.
Transcribed Image Text:Give an asymptotically tight bound (O) for each of the following recurrence relations. Prove your answers, and use the master theorem whenever possible. a) T(n)= 1 for every n<1 and T(n) = T() + O(n) otherwise. b) T(n) = 1 for every n<1 and T(n) = 2T() O(n') otherwise. c) T(n)= 1 for every n<1 and T(n)= 2T(%) + ©(log n) otherwise. d) T(n)= 1 for every n<2 and T(n) = 2T(\n) + ©(log n / log log n) otherwise.
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