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How do we partition the array? First, to define “smaller” and “larger”, we simply choose a value, known as the “pivot”. Small means lesser than the pivot, large means greater. The partition algorithm, key to Quicksort, works like this: we start from the left of the array (where we eventually want only small elements) and move a cursor right, stopping when we find a large element. Symmetrically, we start another cursor from the right and move left, until we find a small element. If the two cursors have crossed, we are done: the array is partitioned. If not, we swap the two out-of-place elements, and we continue the process, both cursors picking up where they stopped. The partitioning time is clearly linear since we examine each element just once (the cursors never go back).
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