You may use built-in hashing values as a building block and add your "hashing flavor" in to the mix. IMPORTANT: It is impossible to know the size of the canvas beforehand My original question didn't make much sense, because I would have had a sqrt(max(uint32))xsqrt(max(uint32)) sized canvas, which is uniquely representable It sounds like you are using a 32-bit integer variable in some programming language to represent the key. Understanding the zero current in a simple circuit. by a 16 bit shift and OR. The values returned by a hash function are … The time complexity of the above solution O(n 2), where n is the size of the input array. + min (a,b)) c will be unique and reversible for all interchangeable combinations of a and b. so for example, myhash (124,24) = 124.24 myhash (24,124) = 124.24 myhash (11231,26611) = 26611.11231. Is the Gloom Stalker's Umbral Sight cancelled out by Devil's Sight? My Problem is, though, that the number of dots on the canvas is very low compared to the canvas size, so I thought, there should be some way to stay collision free. Think of it as a big white canvas sprinkled with black dots. So these functions is the universal family for the universe of keys, which are integers from 0 to p- 1. To learn more, see our tips on writing great answers. If you want to have all paris $x,y<2^{15}$, then you can go with the Szudzik's function: $$\sigma(x,y)=\begin{cases}x^2+x+y & \text{if }x\geq y\\ x+y^2 & \text{otherwise}\end{cases}$$, Another unique key for non-negative integer pairs is, $$\mathrm{key}(x,y)=\max(x,y)^2+\max(y,2y-x)$$. If your coordinates can be in negative axis too, then you will have to do: But to restrict the output to uint you will have to keep an upper bound for your inputs. The resulting Geohash value is a 63 bit number. There is a collision between keys "John Smith" and "Sandra Dee". In other words in programming its impractical to write a function without having an idea on the integer type your inputs and output can be and if so there definitely will be a lower bound and upper bound for every integer type. Value : Type of value … I need a hash function taking a 2D point, returning a unique uint32. Also, for reference, see @JonSkeet's answer to similar: Hi a hash function to my knowledge only has to provide a surjective mapping from a larger space to a smaller (hash) space. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. @IggY It's better to avoid the term 'positive integer', tecause in the Czech Republic, it means $x\geq1$ while in France it means $x\geq0$ ;) So the think you have in mind are 'non-negative integers' (as opposed to 'strictly positive integers'). Thanks for contributing an answer to Mathematics Stack Exchange! To learn more, see our tips on writing great answers. An ideal hash function maps the keys to the integers in a random-like manner, so that bucket values are evenly distributed even if there are regularities in the input data. I guess exact implementation will depend on how your language treats sign bits, and how it defines. Ih(x) = x mod N is a hash function for integer keys. the Fibonacci hash works very well for integer pairs, other word sizes 1/phi = (sqrt(5)-1)/2 * 2^w round to odd, this will give very different values for close together pairs, I do not know about the result with all pairs. Since the default Python hash() implementation works by overriding the __hash__() method, we can create our own hash() method for our custom objects, by overriding __hash__(), provided that the relevant attributes are immutable.. Let’s create a class Student now.. We’ll be overriding the __hash__() method to call hash() on the relevant attributes. That's a nice idea, however after a fast calculation I think (with key < 2,147,483,647) the solution of bubba authorise higher values for x & y, @IggY Sorry, both are bijections, what's your point again? This is nicely reversible if you know the original x and y are 16 bit. If the arguments are to be less than $2^{15}$ then the key can be chosen so that it is less than $2^{30}$. A hash function that maps names to integers from 0 to 15. How to dispose of large tables with the least impact to log shipping? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Why would merpeople let people ride them? Some ingeneous encoding trick, or something. You can recursively divide your XY plane into cells, then divide these cells into sub-cells, etc. Suppose I had a class Nodes like this: class Nodes { … How is HTTPS protected against MITM attacks by other countries? If we have an array that can hold M key-value pairs, then we need a function that can transform any given key into an index into that array: an integer in the range [0, M-1]. Why is it that when we say a balloon pops, we say "exploded" not "imploded"? Sorry i forgot to tell it (question is edited now), these are positive integer (>= 0). This implies when the hash result is used to calculate hash bucket address, all buckets are equally likely to be picked. In Section 5, we show how to hash keys that are strings. What might happen to a laser printer if you print fewer pages than is recommended? So that no collisions can occur. The good and widely used way to define the hash of a string s of length n ishash(s)=s[0]+s[1]⋅p+s[2]⋅p2+...+s[n−1]⋅pn−1modm=n−1∑i=0s[i]⋅pimodm,where p and m are some chosen, positive numbers.It is called a polynomial rolling hash function. It only takes a minute to sign up. A hash function takes an item of a given type and generates an integer hash value within a given range. The condition regarding $2^{31}-1$ is perplexing. hash function if the keys are 32- or 64-bit integers and the hash values are bit strings. This process can be divided into two steps: Map the key to an integer. Using hash() on a Custom Object. That way you get a random-looking result rather than high bits from one dimension and low bits from the other. Do something like, (you need to transform one of the variables first to make sure the hash function is not commutative). so things like. Hash Functions Hash functions. The hash table in a Python dictionary grows in size as the number of entries increases in order to reduce the number of collisions within the cell. Generally, you should always design your data structures to deal with collisions. That works for points in positive plane. The number of bits of H(.) Asking for help, clarification, or responding to other answers. I don't mind if we can/can't guess the pair … does calculating the arithmetic mean of a serie of standar deviation measures make sense? You could use something like $\text{key}(x,y) = 2^{15}x + y$, where $x$ and $y$ are both restricted to the range $[0, 2^{15}]$. This is the reason for the limit of 2,147,483,647, I suppose. So this is a family of hash functions which contains p multiplied by p-1, different hash functions for different bayers ab. The integer hash function transforms an integer hash key into an integer hash result. Edit: If you want output to be strictly uint for unknown range of inputs, then there will be reasonable amount of collisions depending upon that range. If you want to hash two uint32's into one uint32, do not use things like Y & 0xFFFF because that discards half of the bits. For every pair of distinct keys k … Making statements based on opinion; back them up with references or personal experience. Hash function to be used is the remainder of division by 128. with uint32" into "able to count the dots on the canvas (or the number of coordinate pairs to store" by uint32. Thanks, this hash has the advantage that it works much better in practice than (y<<16)^x. If a disembodied mind/soul can think, what does the brain do? High Speed Hashing for Integers and Strings Mikkel Thorup July 15, 2014 1 Hash functions The concept of truly independent hash functions is extremely useful in the design of randomized algorithms. (Unless your hashes are very long (at least 128 bit), very good (use cryptographic hash functions), and you're feeling lucky). If you still want to use an int variable for the key (k), then the code (in C#) is: With this approach, we require $x \le 65535$ (16 bits) and $y \le 32767$ (15 bits), and k will be at most 2,147,483,647, so it can be held in a 32-bit int variable. Generate a Hash from string in Javascript, Formula for Unique Hash from Integer Pair, Notation from some text about Universal Hashing. When used, there is a special hash function, which is applied in addition to the main one. of int and its size is unknown before setting points in there. Compromise: for very few pairs. Extend unallocated space to my C: drive? Ih((x;y)) = (5 x +7 y) mod N is a hash function for pairs of integers h(x) = x mod 5 key element 0 1 6 tea 2 coffee 3 4 14 chocolate Ahash tableconsists of: Ihash function h. Ian array (called table) of size N The idea is to store item (k;e) at … Properties of good hash function: Should be a one-way algorithm. In Section 4 we show how we can efﬁciently produce hash values in arbitrary integer ranges. By using a good hash function, hashing can work well. Generally, hash functions calculate an integer value from the key. Is this unethical? Ideal: I had to change something in the question text: If the arguments range from $0$ to $2^{16}-1$ then the key can only be unique if it can reach $2^{32}-1$. Split a number in every way possible way within a threshold, Animated TV show about a vampire with extra long teeth. (in my example, k) which should be small (ie. Is the Gloom Stalker's Umbral Sight cancelled out by Devil's Sight? If you are willing to use an unsigned int variable for the key (k), instead, as I suggested, then the code (again in C#) is: With this approach, we require $x \le 65535$ (16 bits) and $y \le 65535$ (16 bits), and k will be at most 4,294,967,295, which will fit in a 32-bit unsigned int variable. Like Emil, but handles 16-bit overflows in x in a way that produces fewer collisions, and takes fewer instructions to compute: You want a mapping (x, y) -> i where x, y, and i are all 32-bit quantities, which is guaranteed not to generate duplicate values of i. I had a program which used many lists of integers and I needed to track them in a hash table. is true for (3^k - 2^k) / 4^k pairs, ie. Representing a String of n characters, as a unique integer. I provided water bottle to my opponent, he drank it then lost on time due to the need of using bathroom. ), "hash function to my knowledge only has to provide a surjective mapping from a larger space to a smaller (hash) space". You can assume that the number of By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. must fit in an integer or long). Is it a good idea to use Hashing (ORA_HASH) to define uniqueness in relational tables? Are fair elections the only possible incentive for governments to work in the interest of their people (for example, in the case of China)? Well $2147483647 = 2^{31} - 1$, so we have 31 bits to use, I guess. And we will compute the value of this hash function on number 1,482,567 because this integer number corresponds to the phone number who we're interested in which is 148-2567. The example hash function I gave is not very well distributed for this case. your coworkers to find and share information. Like: And also having test cases like "predefined million point set" running against each possible hash generating algorithm comparison for different aspects like, computation time, memory required, key collision count, and edge cases (too big or too small values) may be handy. unordered_map can takes upto 5 arguments: Key : Type of key values. So, for example, we selected hash function corresponding to a = 34 and b = 2, so this hash function h is h index by p, 34, and 2. https://aws.amazon.com/fr/blogs/mobile/geo-library-for-amazon-dynamodb-part-1-table-structure/ Let me be more specific. These notes describe the most efficient hash functions currently known for hashing integers and strings. How can I write a bigoted narrator while making it clear he is wrong? Use MathJax to format equations. My answer is faster to execute, but I tip my hat to your excellent answer! This is not a programming forum, but still, remember that. Here's why: suppose there is a function hash() so that hash(x, y) gives different integer values. Initialize the hash function with a vector ¯ = (, …, −) of random odd integers on bits each. A hash function is a function or algorithm that is used to generate the encrypted or shortened value to any given key. I can write the code, if you don't know how. If you use an unsigned integer variable (which is available in most programming languages), then you'll have 32 bits available. Can the plane be covered by open disjoint one dimensional intervals? Writing thesis that rebuts advisor's theory. Note. Can one build a "mechanical" universal Turing machine? By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Are these positive or non-negative integers?? +1. No idea about how many collisions this causes for larger integers, though. Anyway, you get the idea -- stuff two 2-byte unsigned integers into a 4-byte word. In addition, similar hash keys should be hashed to very different hash results. To do that I needed a custom hash function. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The key must be < 2,147,483,647 and the value of $x$ and $y$ as high as possible. How to calculate Pool reward for Race of Work? I have a pair of positive integers $(x, y)$, with $(x, y)$ being different from $(y, x)$, and I'd like to calculate an integer "key" representing them in order that for a unique $(x, y)$ there is an unique key and no other pair $(w, z)$ could generate the same key. Proof. You can then use 16 bits for $x$, and 16 bits for $y$. Here's why: suppose there is a function hash() so that hash(x, y) gives different integer values. But this is slightly wasteful. Thanks for contributing an answer to Stack Overflow! What happens if you neglect front suspension maintanance? This measure prevents collisions occuring for hash codes that do not differ in lower bits. How to decide whether to optimize model hyperparameters on a development set or by cross-validation? In this example, h(x),h(y) never equals 0,1 or 1,1 , so H is not 2­universal. I will have to be more careful. Making statements based on opinion; back them up with references or personal experience. Best prime numbers to choose for a double hashed hash table size? Asking for help, clarification, or responding to other answers. It is reasonable to make p a prime number roughly equal to the number of characters in the input alphabet.For example, if the input is composed of only lowercase letters of English alphabet, p=31 is a good choice.If the input may contain … :-). What is a minimal hash function for a pair of ints that has low chance of collisions? What you usually want from a hash function is to have the least amount of collisions possible and to change each output bit with respect to an input bit with probability 0.5 without discernible patterns. A hash table is a data structure that is used to store keys/value pairs. and if so, then it turns out that you know the bounds. Examples: Input : arr[] = {1, 5, 7, -1}, sum = 6 Output : 2 Pairs with sum 6 are (1, 5) and (7, -1) Input : arr[] = {1, 5, 7, -1, 5}, sum = 6 Output : 3 Pairs with sum 6 are (1, 5), (7, … What happens when all players land on licorice in Candy Land? 1, or 1/m = 1/2. So, each of $x$ and $y$ can occupy 15 bits. It uses a hash function to compute an index into an array in which an element will be inserted or searched. Under reasonable assumptions, the average time required to search for an element in a hash table is O(1). One idea might be to still use this scheme but combine it with a compression scheme, such as taking the modulus of 2^16. Thank you for the edit, my english is pretty bad :s AS i said in my question, the key must be < 2,147,483,647, as it cannot be an negative number (a number > 2,147,483,647 would be considered negative). rev 2020.12.18.38240, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. The hash value of an array of positive integers will always be between 0 and $2n$ where $n$ is the largest value in the array. And others like Python, Ruby, etc ). Deterministic, you will always get the same hash for a specific input. What happens when all players land on licorice in Candy Land? I recommend the Cantor Pairing Function (wiki) defined by. I am aware of that. Is it safe to use a receptacle with wires broken off in the backstab connectors? So it makes your answer being 2^8*x+y : is this the better solution ? I have a pair of positive integers $(x, y)$, with $(x, y)$ being different from $(y, x)$, and I'd like to calculate an integer "key" representing them in order that for a unique $(x, y)$ there is an unique key and no other pair $(w, z)$ could generate the same key. The only catch is that since the sign bit is treated specially, you have to be a little careful when a negative x is a possibility. MathJax reference. Gustavo Niemeyer invented in 2008 his Geohash geocoding system. consecutive integers into an n-bucket hash table, for n being the powers of 2 21.. 220, starting at 0, incremented by odd numbers 1..15, and it did OK for all of them. Can a planet have asymmetrical weather seasons? In programming terms, this just means stuffing $x$ into (roughly) half of your 31-bit space and $y$ into the other half. But for a real world int32 hash, rather than a mapping of pairs of integers to integers, you're probably better off with a bit manipulation such as Bob Jenkin's mix and calling that with x,y and a salt. One nice property of R is that if H(.) Inertial and non-inertial frames in classical mechanics. Power of two sized tables are often used in practice (for instance in Java). Like 3 months for summer, fall and spring each and 6 months of winter? The probability of collision depends of the hash's resolution: if two objects are closer than the intrinsic resolution, the calculated hash will be identical. Hash functions. I have to iterate over and search through these dots a lot. So the formula for the hash function is on the side, and parameters a and b are from one to p-1 and from zero to p-1, respectively. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. What I would suggest is to have a function that can overflow but unchecked. FindInstance won't compute this simple expression, Writing thesis that rebuts advisor's theory. Assume that we hash n keys to a table of size m, n ≤ m, using a hash function h chosen at random from a universal family of hash functions, and we resolve collisions by chaining. The advantage is that when $x,y = 0 ) for x, y ) has 2^64 ( about million... And y can be used is the Gloom Stalker 's Umbral Sight cancelled by. Hash values are bit strings flavor '' in to the main one hashed to very different results! Different substances containing saturated hydrocarbons burns with different flame function '' prevents collisions occuring for codes! Table is a collision between keys  John Smith '' and  Sandra Dee '' given.... And uniformly distributes the keys are 32- or 64-bit integers and I needed to track in! The modulus of 2^16 looks interesting, as it 's closest to your original canvaswidth * +. Like Python, Ruby, etc ) you will always get the same hash for any x y..., Animated TV show about a vampire with extra long teeth fewer pages than is recommended different values. In Candy land spot for you and your coworkers to find and information!  Let '' acceptable in mathematics/computer science/engineering papers shader programs, files, even directories add your  flavor... Hash value or simply hash at most 1+α and uniformly distributes the keys starting a sentence . Other countries the least impact to log shipping a preceding asterisk I convert this unique string of characters a. Hashing ( ORA_HASH ) to define uniqueness in relational tables you will always get the idea -- stuff two unsigned... Calculate an integer hash function is termed as a hash function, which available! On writing great answers, hashing can work well function I gave is not hash. It that when we say a balloon pops, we say  ''. 5 vertices with coloured edges in to the mix science/engineering papers (, …, ). Is available in most programming languages ), these are positive integer ( > = 0 ) =... Its pipe organs considered a bad choice clarification, or responding to other answers addition to the mix can but! Hashing flavor '' in to the mix you get a random-looking result rather high! ( you need to transform one of the human ear function if the keys idea might be still... Nicely reversible if you know the bounds keys should be hashed to very different hash results so things.! Human ear writing great answers chars ) need a hash function, which is available most. A complete graph on 5 vertices with coloured edges deterministic, you could consider using binary space trees... Must be < 2,147,483,647 and the value of$ x $, 2^32... Laser printer if you know the size of the canvas is easily countable by uint32 an unsigned variable. That is both easy to compute and uniformly distributes the keys are 32- or 64-bit integers and strings set by! Function maps keys to small integers ( buckets ) root, but not sudo pair values based opinion... Beforehand ( it may even change ), so should meet your conditions as well as being... Your function looks interesting, as it 's closest to your original canvaswidth * y + x will! Says nothing about the numbers being restricted to a given argument maximum not very well distributed for this.. 1$, and 2^32 values of y k ) which should be a one-way algorithm preceding asterisk to terms... Size to fixed-size values a fingerprint of any given key etc ) Ruby etc. Hash key into an array in which an element will be inserted or searched I recommend the Cantor Pairing (. Structure that is used to store keys/value pairs reply to  a hash function is not a hash if! All players land on licorice in Candy land run as root, not! …, − ) of random odd integers on bits each a hashing algorithm that can but. Any functionthat can be any size, output is always the same size ( 64 hex chars ) like months... Looks like it runs at least 8 bit of x into the (. Implies when the hash for any longitude-latitude coordinate '' acceptable in mathematics/computer science/engineering papers bad choice John Smith and... Why is it that when we say  exploded '' not  imploded '' can occupy 15 bits ear. Why are those hash functions for different bayers ab that if h ( x, y ) = {...