Extension To Space With Multiple Targets
If, instead of 1 matching entry, there are k matching entries, the same algorithm works but the number of iterations must be π(N/k)1/2/4 instead of πN1/2/4. There are several ways to handle the case if k is unknown. For example, one could run Grover's algorithm several times, with
iterations. For any k, one of iterations will find a matching entry with a sufficiently high probability. The total number of iterations is at most
which is still O(N1/2). It can be shown that this could be improved. If the number of marked items is k, where k is unknown, there is an algorithm that finds the solution in queries. This fact is used in order to solve the collision problem.
Read more about this topic: Grover's Algorithm
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—Socrates (469–399 B.C.)
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If nothing once, you nothing lose,
For when you die you are the same;
The space between, is but an hour,
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“... the generation of the 20’s was truly secular in that it still knew its theology and its varieties of religious experience. We are post-secular, inventing new faiths, without any sense of organizing truths. The truths we accept are so multiple that honesty becomes little more than a strategy by which you manage your tendencies toward duplicity.”
—Ann Douglas (b. 1942)