A Las Vegas algorithm is an algorithm that uses randomness. If the algorithm gives a result, this result will be the correct one. The algorithm gambles with the resources used. It may take a very long times to give back a result, or it may not give back a result at all.
A simple example would be a version of the QuickSort algorithm. Quicksort is used to quickly sort things (mostly numbers). For this, each element is compared to a central element (called pivot). Depending on how this element is selected the sorting can take more time or less.
Most often, a Las Vegas algorithm is used to pick the pivot randomly.
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