In software, hashing is the process of taking a value and mapping it to a random-looking value. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Editing this answer is long been in my mind. One such use for this kind of hash function is to hash a 64 bit virtual address to a hash table index. 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. Right now I just generate two random numbers x and y and add the edge (x, y) if it doesn't already exist. The word integer originated from the Latin word “Integer” which means whole. Another usage is to hash two 32 bit integers into one hash value. Is there a simple way to create a unique integer key from a two-integer composite key? Hash Table is a data structure which stores data in an associative manner. The java.lang.Integer.hashCode() method of Integer class in Java is used to return the hash code for a particular Integer .. Syntax: public int hashCode() Parameters : The method does not take any parameters. Using a 64-bit integer is probably easiest. find a unique output based on two inputs? Put A on the most significant half and B on the least significant half. In mathematics and computing, universal hashing (in a randomized algorithm or data structure) refers to selecting a hash function at random from a family of hash functions with a certain mathematical property (see definition below). You could modify this to deal with negative x and y by encoding a flags with powers of 5 and 7 terms. Also hash(5, 0) == hash(0, 5) etc which may come up occasionally. 2 * a : -2 * a - 1); var B = (uint)(b >= 0 ? To learn more, see our tips on writing great answers. Asking for help, clarification, or responding to other answers. Examples of Integers – 1, 6, 15. Chain hashing avoids collision. How to effectively defeat an alien "infection"? rev 2020.11.30.38081, Stack Overflow works best with JavaScript enabled, Where developers & technologists share private knowledge with coworkers, Programming & related technical career opportunities, Recruit tech talent & build your employer brand, Reach developers & technologists worldwide. Notes. The idea here is that if you want for example that first number will be up to 10 bits and second number will be up to 12 bits, you can do this: Now you can store in num_a the maximum number that is 2^10 - 1 = 1023 and in num_b naximum value of 2^12 - 1 = 4095. You're looking for a bijective NxN -> N mapping. It can encode and decode. What is the difference between the remap, noremap, nnoremap and vnoremap mapping commands in Vim? I would personally avoid XOR - it means that any two equal values will result in 0 - so hash(1, 1) == hash(2, 2) == hash(3, 3) etc. How to convert a string to an integer in JavaScript? I'm not sure how to go about the same way for Cantor pairing function but didn't try as much as its not as efficient. If you don't want to make a distinction between the pairs (a, b) and (b, a), then sort a and b before applying the pairing function. You can prove The idea is to make each cell of hash table point to a linked list of records that have same hash … Do PhD students sometimes abandon their original research idea? For a secure crypto hash like SHA-2, see Kaveh's comments. You might want to “hash” these integers to other 64-bit values. My first idea was to have a hash function that takes x and y as parameters, computes c = x + y then adds an entry in the hash table at position c % hash_table_size (a prime number, I chose 666013). 10.3.1.3. Doesn't this produce the same result for a=5, b=14 and a=6, b=15? It’s cool. (Also MurmurHash.) Have a look at this PDF for an introduction to so-called pairing functions. Hash function is used by hash table to compute an index into an array in which an element will be inserted or searched. Double hashing is a collision resolving technique in Open Addressed Hash tables. In C language this gives (assuming sizeof(short)=2 and sizeof(int)=4): Is this even possible? Actually I lied. Although Stephan202's answer is the only truly general one, for integers in a bounded range you can do better. I am taking two integers, making them into a string, when then is turned into an integer. For every type Key for which neither the library nor the user provides an enabled specialization std::hash, that specialization exists and is disabled.Disabled specializations do not satisfy Hash, do not satisfy FunctionObject, and following values are all false: Its one drawback is that it can output very big numbers. Since each combination has to be unique AND result in an integer, you'll need some kind of magical integer that can contain this amount of numbers. You can modify the code to use 64 bits) However, to find possible sequences leading to a given hash table, we need to consider all possibilities. It is cache-friendly -- if two (a, b) pairs are close to each other, then f maps numbers to them which are close to each other (compared to other methods). In hash table, the data is stored in an array format where each data value has its own unique index value. As others have made clear, if you plan to implement a pairing function, you may soon find you need arbitrarily large integers (bignums). C# (pronounced see sharp, like the musical note C♯, but written with the number sign) is a general-purpose, multi-paradigm programming language encompassing strong typing, lexically scoped, imperative, declarative, functional, generic, object-oriented (class-based), and component-oriented programming disciplines. Also I just realized I should pick up my chance calculation (literal translation from Dutch) textbooks again. The result of OR is 1 if any of the two bits is 1. I guess it wouldn't get much bigger than 10 000 nodes / 1 000 000 edges. My first idea was to have a hash function that takes x and y as parameters, computes c = x + y then adds an entry in the hash table at position c % hash_table_size (a prime number, I chose 666013). What is the marginal posterior distribution? Bernstein's hash is often used in string dictionary data structure implementations, but of course there are many to choose from. A good hash function to use with integer key values is the mid-square method.The mid-square method squares the key value, and then takes out the middle \(r\) bits of the result, giving a value in the range 0 to \(2^{r}-1\).This works well because most or all bits of the key value contribute to the result. ', '! Let number a be the first, b the second. let us have two number B and C , encoding them into single number A. My first idea was to have a hash function that takes x and y as parameters, computes c = x + y then adds an entry in the hash table at position c % hash_table_size (a prime number, I chose 666013). The very nature of hashing algorithms is that they cannot provide a unique hash for each different input. They both have the range -2,147,483,648 to 2,147,483,647 but you will only take the positives. TL;DR Cantor pairing is a perfect, reversible, hashing function from multiple positive integers to a single positive integer. I'm talking about bounded integers in a low, positive range. The standard mathematical way for positive integers is to use the uniqueness of prime factorization. I absolutely always recommend using a CRC algorithm for the hash. Each specialization of this template is either enabled ("untainted") or disabled ("poisoned"). predicate on real numbers. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Examples– -2.4, 3/4, 90.6. Stack Overflow for Teams is a private, secure spot for you and Each pair has a key and a stack object. Can you detail how you generated it using an adjacency table (did you mean adjacency lists?)? for function to extract bits and thanks also to mouviciel answer in this post. It seems to be permutations right? Example: A = 300, B = 12. I usually use: But, as Boris says, if you want to run this as a computer program, you have to take into account the finiteness of the machine. I'm new to chess-what should be done here to win the game? bnum can be stored inside the class. I’ll spend the rest of it showing you four good ways to define a hash function for use in unordered_map under C++0x, and with Google’s help, it may end up providing the missing manual for this particular problem. But that's ok, why are we storing unbounded integers in a computer anyways. It is also injective -- f maps different values for different (a,b) pairs. You could do it like this for Szudzik's: What I do: After applying a weight of 2 to the the inputs and going through the function, I then divide the ouput by two and take some of them to negative axis by multiplying by -1. Say you have a 32 bit integer, why not just move A into the first 16 bit half and B into the other? I misunderstood the question - this is for integers that are word-sized. There are three Properties of Integers: 1. The mapping for two maximum most 16 bit signed integers (32767, 32767) will be 2147418112 which is just short of maximum value for signed 32 bit integer. Thanks for contributing an answer to Stack Overflow! For example, if your range is 0..10,000, then you can do: Results can fit in a single integer for a range up to the square root of the integer type's cardinality. 2 * b : -2 * b - 1); var C = (int)((A >= B ? One such use for this kind of hash function is to hash a 64 bit virtual address to a hash table index. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Choosing two of these where order doesn't matter and with repetition yields 2305843008139952128 combinations. Fractions, decimals, and percents are out of this basket. Hash (key) = Elements % table size; 2 = 42 % 10; 8 = 78 % 10; 9 = 89 % 10; 4 = 64 % 10; The table representation can be seen as below: I can't stress enough how good of a job it does as a hash function for a hash table. Double hashing can be done using : (hash1 (key) + i * hash2 (key)) % TABLE_SIZE To get num a: EDIT: It is also considerably simpler to decode; requiring no square roots, for starters :). You will always have collisions. C Program to Add Two Integers In this example, the user is asked to enter two integers. Image Processing: Algorithm Improvement for 'Coca-Cola Can' Recognition. A uniform hash function produces clustering C near 1.0 with high probability. Perfect hash functions may be used to implement a lookup table with constant worst-case access time. Imagine two positive integers A and B. I want to combine these two into a single integer C. There can be no other integers D and E which combine to C. The | (bitwise OR) in C or C++ takes two numbers as operands and does OR on every bit of two numbers. Then, the result is pq, if ab. This combination operation should also be deterministic (always yield the same result with the same inputs) and should always yield an integer on either the positive or the negative side of integers. (I know it sounds hacky, but it should work). Now bnum is all of the bits (32 bits in total. The mapping for two maximum most 16 bit integers (65535, 65535) will be 8589803520 which as you see cannot be fit into 32 bits. For every type Key for which neither the library nor the user provides an enabled specialization std::hash, that specialization exists and is disabled.Disabled specializations do not satisfy Hash, do not satisfy FunctionObject, and following values are all false: I know that this is not a mathematical answer, but a simple python (which has an in built hash function) script should do the job. Access of data becomes very fast, if we know the index of the desired data. Programming trick: Cantor Pairing (perfect hashing of two integers) Reading time: 2 min. Then, the sum of these two integers is calculated and displayed on the screen. Different strings can return the same hash code. I had written it before limit mattered to me. Yes, I had that afterthought too, but I thought the message is in essence the same, so I didn't bother recalcing. If A and B can be expressed with 2 bytes, you can combine them on 4 bytes. That makes 2147483647^2 = 4,61169E+18 combinations. Result = hash(H2+H1+H3) How can a hard drive provide a host device with file/directory listings when the drive isn't spinning? (-32768, -32768) => 4294967295 which is 32 bit for unsigned range or 64 bit for signed range, but still better. If you want to map. Hash Table is a data structure which stores data in an associative manner. How can I write (greater than), (less than) characters in this forum? Remaining option is (C) which is the answer. hash = y * width + x (in your case it would probably be x * height + y) So if your hash size is a signed 32 bits then sqrt(2,147,483,647) would give the width value, in this case 46340. https://www.geeksforgeeks.org/extract-k-bits-given-position-number/ Here we use two hash functions. I have deliberately used it for set hashing - if you want to hash a sequence of items and you don't care about the ordering, it's nice. That is, if my inputs are two 16 bit integers ranging from 0 to 2^16 -1, then there are 2^16 * (2^16 -1) combinations of inputs possible, so by the obvious Pigeonhole Principle, we need an output of size at least 2^16 * (2^16 -1), which is equal to 2^32 - 2^16, or in other words, a map of 32 bit numbers should be feasible ideally. Query to update one column of a table based on a column of a different table. How can I calculate the current flowing through this diode? Other than this being as space efficient as possible and cheap to compute, a really cool side effect is that you can do vector math on the packed number. These are used for e.g. f(a, b) = s(a+b) + a, where s(n) = n*(n+1)/2, should always yield an integer on D = 3, E=2 result = 302030012. If a key found more than one we simply add to stack (at the bottom using Data - or at the top using Push). When you apply this method to the string this method will return a 32-bit signed integer hash code of the given string. Suppose I had a class Nodes like this: class Nodes { … Associative 2. Thus, a contract such as (first-or/c (not/c real?) We can again obtain individual numbers by doing 5645/100 and 5645%100. There are many good ways to achieve this result, but let me add some constraints: The hashing … Continue reading Fast strongly universal 64-bit hashing everywhere! It is also extremely fast using a lookup table. a = {4,0,2,1,3}, let's say we want to encode 3 and 4, so: But we also need to take care of the value we changed; so it ends up as. If all of the arguments are procedures or flat contracts, the result is a flat contract and similarly if all of the arguments are chaperone contracts the result is too. Because the output of the hash function is narrower than the input, the result is no longer one-to-one. But look up in hash table should be amortized O (1) O(1) O (1) time as long as the hash function was chosen carefully. Say 0 to 10,000, If the order doesn't matter eg: (3,12) & (12,3) give the same result, i use "A+B"+"A*B". If I want to use for Combination can I just eliminate the IF and Else parts of the algorithm? is guaranteed to only invoke the positive? In this method, the hash function is dependent upon the remainder of a division. Suppose you want to encode numbers in the range 0-9 into one, eg. Types of a Hash Function In C. The types of hash functions are … If two string objects are equal, the GetHashCode method returns identical values. This is where this solution is ideal, it simply utilizes every single point in that space, so nothing can get more space efficient. Implementation in C Thanks for source: either the positive or the negative Magic world of numbers!! You should add that N must be greater than both B and C. Mapping two integers to one, in a unique and deterministic way, http://en.wikipedia.org/wiki/Pigeonhole_principle, https://www.geeksforgeeks.org/extract-k-bits-given-position-number/, Podcast 290: This computer science degree is brought to you by Big Tech. positive?) The result of AND is 1 only if both bits are 1. That is a good point. The tags on the question indicate 'algorithm', 'mathematical' and 'deterministic', not any particular language. In hashing there is a hash function that maps keys to some values. In hash table, the data is stored in an array format where each data value has its own unique index value. You are combining two integers. This answer confuses me. GetHashCode() method is used to get the hash code of the specified string. This packs slightly more efficiently than Stephan202's more general method. A * A + A + B : A + B * B) / 2); return a < 0 && b < 0 || a >= 0 && b >= 0 ? So combining them with the addition operator doesn't work. This is the real task, using two arrays as arguments in a function which return the hash table (an inventory object). @BlueRaja-DannyPflughoeft you're right. “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…, Congratulations VonC for reaching a million reputation. However, there is not a unique hash code value for each unique string value. This is a function -- it is deterministic. Too check for existence, I use a hash table. This defines are min as (-46340, -46340). To subscribe to this RSS feed, copy and paste this URL into your RSS reader. If you solve that problem, how is this answer different from the ones above? If A and B are 16-bit integers, and C is 32-bit, then you can simply use shifting. But for an array of size n, eg. To do that I needed a custom hash function. side of integers. Right now I just generate two random numbers x and y and add the edge (x, y) if it doesn't already exist. What's the etiquette for addressing a friend's partner or family in a greeting card? By ygfperson in forum A Brief History of Cprogramming.com, http://www.eternallyconfuzzled.com/t...hashtable.aspx, http://www.eternallyconfuzzled.com/a..._art_rand.aspx, http://www.boost.org/doc/libs/1_35_0/libs/crc/crc.html, http://www.gelato.unsw.edu.au/lxr/so...ib/crc-ccitt.c, http://www.gelato.unsw.edu.au/lxr/so...rc-ccitt.h#L11, http://www.concentric.net/~Ttwang/tech/inthash.htm, Cprogramming.com and AIHorizon.com's Artificial Intelligence Boards, Exactly how to get started with C++ (or C) today, The 5 Most Common Problems New Programmers Face, How to create a shared library on Linux with GCC, Rvalue References and Move Semantics in C++11, C and C++ Programming at Cprogramming.com. To understand this example, you should have the knowledge of the following C programming topics: C Data Types; (32767, 32767) => 1073741823, much smaller.. Let's account for negative integers. 10.3.1.3. I did not did it because my own needs Should live sessions be recorded for students when teaching a math course online? Its amazing to see that you could uniquely encode a pair of coordinates to a single number reversibly! You can, however fit this mapping in 61 bits. 5 and 6. The limitation of Cantor pairing function (relatively) is that the range of encoded results doesn't always stay within the limits of a 2N bit integer if the inputs are two N bit integers. In computer science, 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.In mathematical terms, it is an injective function.. How did you make sure no edge is added twice? The hash code itself is not guaranteed to be stable. Implementation in C Eg 30 + 10 = 40 = 40 + 0 = 39 + 1 Did medieval people wear collars with a castellated hem? If you want more control such as allocate X bits for the first number and Y bits for the second number, you can use this code: I use 32 bits in total. And also Secondary clustering also eliminated. Hash Table A hash table for a given key type consists of: Hash function h: keys-set →[0,m-1] Array (called table) of size … I will find time sometime soon. The first-or/c result tests any value by applying the contracts in order from left to right. In signed world, it will be even more space saving if we could transfer half the output to negative axis. I've used it numerous times and the results are nothing short of excellent. This is equivalent to Cantor pairing function, and as such doesn't work with negative integers. h1 (k) = (h1 (k) + i h2 (k)) mod n. Here h1 and h2 are two hash functions. All problems in computer science can be solved by another level of indirection. So for (8, 11) hash the string "8-11" and for (81, 1) hash the string "81-1". Too check for existence, I use a hash table. How do you make the Teams Retrospective Actions visible and ensure they get attention throughout the Sprint? This does not fit nicely in the set of 32-bit integers. +1 I think this is the correct answer for unbounded integers. You are looking for a bijective. You should clarify if you mean integers in software or integers in math. For positive integers as arguments and where argument order doesn't matter: For x ≠ y, here's a unique unordered pairing function: Check this: http://en.wikipedia.org/wiki/Pigeonhole_principle. The Mid-Square Method¶. Who classified Rabindranath Tagore's lyrics into the six standard categories? Double hashing is a collision resolving technique in Open Addressed Hash tables. Method 1 - A simple function. In order to map two objects to another single set, the mapped set must have a minimum size of the number of combinations expected: Assuming a 32-bit integer, you have 2147483647 positive integers. ', and anything with ASCII value less than 48) you will get a negative result and when you add it to the hash it will be sign-extended and converted to a huge unsigned value, something like 0xffffffffffffffxx? (Haversine formula), Fastest way to determine if an integer's square root is an integer, Determine Whether Two Date Ranges Overlap. The downside is that the image tends to span quite a large range of integers so when it comes to expressing the mapping in a computer algorithm you may have issues with choosing an appropriate type for the result. So now whenever the two integers are equal we still have to “confirm” that the two strings are identical by running character-by-character comparison. Suppose you are given 64-bit integers (a long in Java). What would be the modified unhash function for signed integers? If A, B and C are of same type, it cannot be done. This past week I ran into an interesting problem. Two products of two different primes can't have the same result (unique prime factor decomposition) a=5, b=14 -> result is 13*47 = 611 a=6, b=15 -> result is 17*53 = 901, Greater than and less than characters should work fine within. (-32768, -32768) => 8589803520 which is Int64. The math is fine. Let p be the a+1-th prime number, q be the b+1-th prime number. I had a program which used many lists of integers and I needed to track them in a hash table. It is a special set of whole numbers comprised of zero, positive numbers and negative numbers and denoted by the letter Z. Another usage is to hash two 32 bit integers into one hash value. Unforunately the asker did not specify if the integer is bounded or not. How do I generate random integers within a specific range in Java? This takes advantage of the fact that the only number that starts with 0, is 0. Are you aware that for the same expression c - '0' for a number of possible c values (e.g. ' While this is correct for unbounded integers, it's not best for bounded integers. See the results, for any input in the range of a signed 16 bit number, the output lies within the limits of a signed 32 bit integer which is cool. Yes your logic is correct by the pigeonhole principle. Each specialization of this template is either enabled ("untainted") or disabled ("poisoned"). Cons: Size of results is an issue. If a=b, let it be p^2. I think @blue-raja's comment makes the most sense by far. Spectral decomposition vs Taylor Expansion. Integer division with remainder in JavaScript? A hash table is a data structure which is used to store key-value pairs. Does Szudzik's function work for combinations or permutations. its also wrong because that task is to map two integers to a new integer, not a string with a symbol. Now all this while the output has always been positive. Now considering the fact that we typically deal with the signed implementations of numbers of various sizes in languages/frameworks, let's consider signed 16 bit integers ranging from -(2^15) to 2^15 -1 (later we'll see how to extend even the ouput to span over signed range). Essentially, yes I am mapping two integers to a new one. This is the real task, using two arrays as arguments in a function which return the hash table (an inventory object). To read inputs as integers in C#, use the Convert.ToInt32() method. You are given an array of n integers and a number k. Determine whether there is a pair of elements in the array that sums to exactly k. For example, given the array [1, 3, 7] and k = 8, the answer is “yes,” but given k = 6 the answer is “no.” Possible Follow­Up Questions: The input range may not be limited and the environment might have an unbounded integer type 'bigint'. Does your organization need a developer evangelist? You can obtain each number individually by dividing and finding mod of the resultant number. The C99 standard suggests that C++ implementations should not define the above limit, constant, or format macros unless the macros __STDC_LIMIT_MACROS, … The mapping for (65535, 65535) will now be 4294967295 which as you see is a 32 bit (0 to 2^32 -1) integer. But these hashing function may lead to collision that is two or more keys are mapped to same value. Making statements based on opinion; back them up with references or personal experience. Why is "threepenny" pronounced as THREP.NI? Type 3: Given a hash table with keys, verify/find possible sequence of keys leading to hash table – For a given hash table, we can verify which sequence of keys can lead to that hash table. I will update it. H1 = hash(str1) H2 = hash(str2) H3 = hash(str3) Sort those hashes by order of smallest to largest (treat as integers), concatenate, and hash them together. The hash function is a function that uses the constant-time operation to store and retrieve the value from the hash table, which is applied on the keys as integers and this is used as the address for values in the hash table. Example: elements to be placed in a hash table are 42,78,89,64 and let’s take table size as 10. It isn't that tough to construct a mapping: Figuring out how to get the value for an arbitrary a,b is a little more difficult. Using these to sources I could figure out more advanced solution. Since a and b have to be positive they range from 0 to 2^15 - 1. Here is an extension of @DoctorJ 's code to unbounded integers based on the method given by @nawfal. but (8,11) and (81,1) are mapped to the same number 811. Set the high word to the smaller integer and the low word to the larger one. You are given an array of n integers and a number k. Determine whether there is a pair of elements in the array that sums to exactly k. For example, given the array [1, 3, 7] and k = 8, the answer is “yes,” but given k = 6 the answer is “no.” Possible Follow­Up Questions: this using the fact: It returns quite small values -- good if your are going to use it for array indexing, as the array does not have to be big. Is this by any chance possible for floats? In C, the following 6 operators are bitwise operators (work at bit-level) The & (bitwise AND) in C or C++ takes two numbers as operands and does AND on every bit of two numbers. This obviously generates a lot of collisions, and wouldn't generate different values for edges made of nodes that add up to the same value ((1, 3) would have the same hash as (2, 2)). We can encode two numbers into one in O(1) space and O(N) time. Simple, Even for two digit integer let's say 56 and 45, 56*100 + 45 = 5645. @Boris: Kansrekening is "probability theory". Return Value: The method returns a hash code integer value for this object, which is equal to the uncomplicated primitive integer value, represented by this Integer object. Furthermore, more calculations involved in Cantor pairing function means its slower too. Commutative 3. Calculate distance between two latitude-longitude points? Since the intermediate calculations can exceed limits of 2N signed integer, I have used 4N integer type (the last division by 2 brings back the result to 2N). Distributive We are living in a world of numbe… If you iterate a node's adjacency list for each edge you attempt to add, it's excruciatingly slow... so how did you do it? In general, a hash table consists of two major components, a bucket array and a hash function, where a bucket array is used to store the data (key-value entries) according to their computed indices and a hash function h maps keys of a given type to integers in a fixed interval [0, N-1]. How does the title "Revenge of the Sith" suit the plot? Then let the output be hash(str). Advantages by this method are there is no chance of primary clustering. Because C++ interprets a character immediately following a string literal as a user-defined string literal, C code such as printf ("%" PRId64 " \n ",n); is invalid C++ and requires a space before PRId64.. How to do it? 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 … If so, how do they cope with it? My answer would be valid if range is not limited or unknown. Let me be more specific. How do you choose N to make this representation unique? dovetailing. Here the next prob position will depend on two functions h1 and h2 also. Access of data becomes very fast, if we know the index of the desired data. I shared the code and hope that it will be helpful. A good hash function to use with integer key values is the mid-square method.The mid-square method squares the key value, and then takes out the middle \(r\) bits of the result, giving a value in the range 0 to \(2^{r}-1\).This works well because most or all bits of the key value contribute to the result.