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A perfect hash function for n keys is said to be minimal if its range consists of n consecutive integers, usually from 0 to n − 1.
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perfect and hash
( In an ideal " perfect hash function ", no bucket should have more than one record ; but a small number of collisions is virtually inevitable, even if n is much larger than m – see the birthday paradox ).
This hash function is perfect, as it maps each input to a distinct hash value.
A perfect hash function for the four names shown
A hash function that is injective — that is, maps each valid input to a different hash value — is said to be perfect.
A minimal perfect hash function for the four names shown
Besides providing single-step lookup, a minimal perfect hash function also yields a compact hash table, without any vacant slots.
Minimal perfect hash functions are much harder to find than perfect ones with a wider range.
It will however have more collisions than perfect hashing, and may require more operations than a special-purpose hash function.
* Given a small, privileged set of inputs ( e. g., reserved words for a compiler ), the permutation table can be adjusted so that those inputs yield distinct hash values, producing what is called a perfect hash function.
A perfect hash function for a set S is a hash function that maps distinct elements in S to a set of integers, with no collisions.
A perfect hash function has many of the same applications as other hash functions, but with the advantage that no collision resolution has to be implemented.
A perfect hash function for a specific set S that can be evaluated in constant time, and with values in a small range, can be found by a randomized algorithm in a number of operations that is proportional to the size of S. The minimal size of the description of a perfect hash function depends on the range of its function values: The smaller the range, the more space is required.
Any perfect hash functions suitable for use with a hash table require at least a number of bits that is proportional to the size of S.
perfect and function
If the function R is well-defined, its value must lie in the range, with 1 indicating perfect correlation and − 1 indicating perfect anti-correlation.
When the transfer function comprises only a perfect gain constant A and perfect delay T
The transfer function of an ideal amplifier, with perfect gain and delay, is only an approximation.
On the left, a mathematical function defining a bump map simulates a crumbling surface on a sphere, but the object's outline and shadow remain those of a perfect sphere.
This conception of eudaimonia derives from Aristotle ’ s essentialist understanding of human nature, the view that reason ( logos sometimes translated as rationality ) is unique to human beings and that the ideal function or work ( ergon ) of a human being is the fullest or most perfect exercise of reason.
If there are no repeated data values, a perfect Spearman correlation of + 1 or − 1 occurs when each of the variables is a perfect monotone function of the other.
perfect and for
`` we the People of the United States, in order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common Defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America ''.
Admirably written, it is a perfect introduction to Swedish history for readers of other countries.
The carved statues of the frieze against the low wall are for the most part headless, but their exquisitely graceful nude and draped torsos and the kneeling Atlantes are well preserved in their perfect proportion.
In the next few months of comparative silence, Pike waited patiently until conditions were perfect for a new attack, and then, displaying a remarkable grasp of the subtleties of political infighting, gained from his first bout with Woodruff, he used these changed conditions to excellent advantage.
Probably no location for a pool is perfect on all counts.
The energy for any isothermal work done by the perfect gas must come as thermal energy from its surroundings.
It is hard, on the other hand, to blame the policeman, blank, good-natured, thoughtless, and insuperably innocent, for being such a perfect representative of the people he serves.
He stumbled to the middle of the road and simply stood there, waiting for them, a perfect target.
So when old Mr. Lovejoy, the company president, talked about putting in a single sales manager for both branches after the head of the regular steels had gone with Carnegie-Illinois, it looked like the perfect chance for Bobbie.
Being a dimensionless fraction, it may also be expressed as a percentage, and is measured on a scale from zero for no reflecting power of a perfectly black surface, to 1 for perfect reflection of a white surface.
On the new earth God will provide an eternal home for all the redeemed and a perfect environment for everlasting life, where Eden will be restored.
" Stephen Ashby clarifies: " Arminius allowed for only two possible ways in which the sinner might be justified: ( 1 ) by our absolute and perfect adherence to the law, or ( 2 ) purely by God's imputation of Christ's righteousness.
There was an ongoing tradition of allowing anagrams to be " perfect " if the letters were all used once, but allowing for these interchanges.
Their goal was to regain access to Eden by finding the correct formula for perfect living, following specific rules governing agriculture, diet, and reproduction.
Kant argued that the goal of humanity it to achieve perfect happiness and virtue ( the summum bonum ) and believed that an afterlife must exist in order for this to be possible, and that God must exist to provide this.
* Umberto Eco, The search for the perfect language ( 1993 ).
The choirs typically range from 40 to 80 singers and are recognized for their efforts to perfect blend, intonation, phrasing and pitch in a large choral setting.
Alexander is also known for rejecting the idea that there are many things in God ’ s mind, instead claiming that it is more perfect to know just one thing.
The Aleut baidarka resembled that of an Eskimo Kayak, however, it was designed to be much more aerodynamically fast which was perfect for sea hunting.
He had seen BASIC on minicomputers and felt it would be the perfect match for new machines like the MITS Altair 8800.
First, it forms hardy spores, perfect for dispersal aerosols.
perfect and n
Equivalently, a perfect number is a number that is half the sum of all of its positive divisors ( including itself ) i. e. σ < sub > 1 </ sub >( n ) = 2n.
Lagrange proved that for any natural number n that is not a perfect square there are x and y > 0 that satisfy Pell's equation.
* Another proof that n < sup > th </ sup > roots of integers are irrational, except for perfect nth powers by Scott E. Brodie
It was announced on 1 July 2008 that Australia n scientists had created even more perfect spheres, accurate to 0. 3 nanometers, as part of an international hunt to find a new global standard kilogram.
Square roots of positive whole numbers that are not perfect squares are always irrational numbers: numbers not expressible as a ratio of two integers ( that is to say they cannot be written exactly as m / n, where m and n are integers ).
He came circa 1903 to classify any sign by three interdependent trichotomies, intersecting to form ten ( rather than 27 ) classes of sign .< ref > He worked on but did not perfect a finer-grained system of ten trichotomies, to be combined into 66 ( T < sub > n + 1 </ sub >) classes of sign.
This is equivalent to saying that each positive integer occurs only finitely many times as a difference of perfect powers: more generally, in 1931 Pillai conjectured that for fixed positive integers A, B, C the equation has only finitely many solutions ( x, y, m, n ) with ( m, n ) ≠ ( 2, 2 ).
Paul Erdős conjectured that there is some positive constant c such that if d is the difference of a perfect power n, then d > n < sup > c </ sup > for sufficiently large n.
Note that the leading coefficient of the polynomial bx − a is the integer b. As another special case, the square root √ n of a non-negative integer n is an algebraic integer, and so is irrational unless n is a perfect square.
" George P Pelecanos of Uncut magazine has called it " One of the great rock ' n roll performances, and as close to a perfect song as anyone's ever recorded ," while Chris T-T in the same publication declared " Never mind The Beatles or The Rolling Stones, this is the best rock ' n roll track of all time.
In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n ; i. e., if there exists an integer x such that:
* a perfect number equals the sum of its proper divisors ; that is, s ( n ) = n ; the only perfect numbers between 1 and 1000 are 6, 28 and 496
0.364 seconds.