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
Famous quotes containing the words extension, space and/or multiple:
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (1623–1662)
“The limitless future of childhood shrinks to realistic proportions, to one of limited chances and goals; but, by the same token, the mastery of time and space and the conquest of helplessness afford a hitherto unknown promise of self- realization. This is the human condition of adolescence.”
—Peter Blos (20th century)
“... 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)