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Argue the correctness of Heapsort using the following loop invariant for the second loop in the...

Argue the correctness of Heapsort using the following loop invariant for the second loop in the algorithm (after the array has been heapified): "At the start of each iteration of the for loop, the subarray A[0 ... i-1] is a max-heap containing the i smallest elements of the original array, and the subarray A[i ... n-1] contains the n-i largest elements of the original array in sorted order

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According to question subarray A[i... n-1] is empty. According A[0] is largest value in the array A[0...i-1] and these values are smaller than values in A[i... n-1]. when we put that value in i-1 position than the subarray A[i... n-1] contains largest value. A[0...i-2] turns into max heap by decreasing the heap size. decrement of i sets invariant for next iteration. After the loop A[2...n-1] is sorted and A[0] is smallest value.

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