Question: Prove the correctness of HEAPSORT by using the following loop invariant: At the start of each iteration of the for loop, the subarray A[1..i] is

Prove the correctness of HEAPSORT by using the following loop invariant:

At the start of each iteration of the for loop,

the subarray A[1..i] is a Max-Heap containing the i smallest elements of A[1..n], and

the subarray A[i+1 .. n] contains the n-i largest elements of A[1..n] in sorted order.

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