(a) In the top-down heap-build method, we use MAX-HEAP-INSERT repeatedly, starting with an empty heap and inserting from position 1 to n, resolving the heap structure by "bubbling up" each new insertion. This means the 2^i nodes on level i will each cause up to i swaps, resulting in the following expression:total # swaps = Σ(# nodes)(# swaps)1.0 2.1 2^2.2 ... 2^i.i ... 2^n.nYour task: Argue that this expression is O(n log n). Hint: Lower bound is easy. For the upper bound, exaggerate
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