Consider a generalization of Median-of-Five algorithm which hasa parameter α for an integer α ≥ 1. Instead of partitioning inputinto n/5 blocks of size 5, the algorithm partitions the input inton/(2α + 1) blocks of size 2α + 1 (assume n is a power of 2α + 1).Note that the algorithm becomes the median-of-five algorithm when α= 2. a) Follow the same steps as slide 14 of lecture notes to derivea recursive formula for the time complexity T(n) of this algorithmas a function of n and α (there is no need to solve the recursion;just deduce the recursive definition of T(n)). b) Assume α = 3 (the algorithm will be “median of 7”). Rewritethe recursion for this particular α and try to solve the recursionby guessing that T(n) ∈ O(n). Follow the same steps as in theslides and indicate whether we can state T(n) ∈ O(n). c) [bonus] Assume α = 1 (the algorithm will be “median of 3”).Rewrite the recursion for this particular α and solve the recursionto provide a tight bound (in terms of Θ) for the time complexity ofthis algorithm. Attached
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