(a) In the top-down heap-build method, we use MAX-HEAP-INSERT repeatedly, startingwith an empty heap and inserting from position 1 to n, resolving the heap structureby b̈ubbling upëach new insertion. This means the 2^i nodes on level i will eachcause up to i swaps, resulting in the following expression:total # swaps = ∑(# nodes)(#swaps)≤ 1 ·0 2 ·1 2^2 ·2 … 2^i ·i … (n)/(2) ·lognYour task: Argue that this expression isΘ(n logn).Hint: Lower bound is easy. For the upper bound, exaggerate
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