What if Indexes in Hoare's Quick Sort Algorithm Both Land on Values Less than Pivot? If I were to sort the list of numbers 1,7,5,7,1 using Hoare's algorithm as described at the very beginning of wikipedia item on Hoare partition scheme with 5 being the pivot, and the indexes start at 1 and 1, then what would happen? If they are switched, nothing is really sorted. And the same goes for the two indexes both landing on numbers greater than the pivot, for example, 7 and 7. How would Hoare's algorithm handle such a case?
You've misunderstood the algorithm and it doesn't have the behaviour you suggest.

Let the pivot value be&nbsp;$p$. The algorithm searches from the left for a value $\ell\geq p$ and from the right for a value $r\leq p$. It then only swaps them if they're in the wrong order relative to each other, i.e., if $\ell&gt;r$, so it will never exchange two identical array elements.

In your example, the algorithm would either swap the 1 on the left with the 7 on the right, or the 7 on the left with the 1 on the right, depending on exactly how it is implemented.