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QUICKSORT(A,p,r)
1    if p < r
2    q = PARTITION(A,p,r)
3    QUICKSORT(A, p , q-1)
4    QUICKSORT(A, q + 1, r)

How would you modify QUICKSORT to sort into nonincreasing order?

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If you observe PARTITION of the array algorithm carefully then you'll observe at line 4 i.e. in

$if A[j]\leq x$

simply the change it to $\leqslant$ which is

$if A[j]\geqslant x$

this will make all the elements greater than pivot move to the left of the array and rest to the right which is the desired result.

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