Show that the worst-case running time of MAX-HEAPIFY on a heap of size n is (lg n).

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Show that the worst-case running time of MAX-HEAPIFY on a heap of size n is Ω (lg n). (Hint: For a heap with n nodes, give node values that cause MAX-HEAPIFY to be called recursively at every node on a path from the root down to a leaf.)
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