5. Give asymptotic bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for n ≤ 2. Make your bounds as tight as possible, and justify your answers. (a) T(n) = 8T(n/2) +n³ √n (b) T(n) = T(n - 1) + log n (c) T(n)=3T(n/27)+n0.25 (d) T(n) = 16T(n/4) + n² log² n

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Concept of Randomized Approximation Algorithms

Randomized algorithms are algorithms that use random numbers to determine what to do next at any point in their logic. This means that it uses randomization for operation in the logic. Due to this randomness, the time and space complexity of the standard algorithm is reduced.