Most random number generators, however—whether true or pseudorandom—will only directly provide numbers in some fixed range, such as, say, from 0 to 232−1. With the Fisher-Yates shuffle, first implemented on computers by Durstenfeld in 1964, we randomly sort elements. We can use Fisher-Yates algorithm for randomly shuffling a sequence. Thus, to minimize bias, the number of states of the PRNG should exceed the number of permutations by at least several orders of magnitude.For example, the built-in pseudorandom number generator provided by many programming languages and/or libraries may often have only 32 bits of internal state, which means it can only produce 232 different sequences of numbers. This is clearly true at the start, when "A""i" = "i" for all 1 ≤ "i" ≤ "N", and "n" = "N". Modulo bias Doing a Fisher-Yates shuffle involves picking uniformly distributed random integers from various ranges. The simplest way to fix the problem is to discard those numbers before taking the remainder and to keep trying again until a number in the suitable range comes up. At each step he randomly picks a number from interval , where k is a number of elements, which are not struck out yet. The Fisher-Yates shuffle is quite efficient; indeed, its asymptotic time and space complexity are optimal. 6 talking about this. The fact that Sattolo's algorithm in fact produces a cyclic permutation, and that it produces each such permutation with equal probability, may not be immediately obvious. Modulo bias Doing a Fisher-Yates shuffle involves picking uniformly distributed random integers from various ranges. while (n > 1) { int k = rng.nextInt(n); // 0 <= k < n. n--; // n is now the last pertinent index; int temp = array [n] ; // swap array [n] with array [k] (does nothing if k = n). That is, given a preinitialized array, it shuffles the elements of the array in place, rather than producing a shuffled copy of the array. Most random number generators, however—whether true or pseudorandom—will only directly provide numbers in some fixed range, such as, say, from 0 to 232−1. Thus, we swap the 2nd and 7th numbers and move on:The next random number we roll is from 1 to 6, and just happens to be 6, which means we leave the 6th number in the list (which, after the swap above, is now number 8) in place and just move to the next step. C# Fisher-Yates Shuffle: Generic Method This C# algorithm article implements the Fisher-Yates shuffle. This means that there are only a finite number of possible floating point values in any given range, and if the range is divided into a number of segments that doesn't divide this number evenly, some segments will end up with more possible values than others. The Fisher-Yates shuffle, named after Ronald Fisher and Frank Yates, also known as the Knuth shuffle, after Donald Knuth, is an algorithm for generating a random permutation of a finite set—in plain terms, for randomly shuffling the set. For example, a common off-by-one error would be moving the line n-- "before" the line k = rng.nextInt(n) in the Java example above, so that "k" always strictly less than the index it will be swapped with. The modern algorithm The modern version of the Fisher-Yates shuffle, designed for computer use, was introduced by Richard Durstenfeld in 1964 in "Communications of the ACM" volume 7, issue 7, as "Algorithm 235: Random permutation",cite journal title = Algorithm 235: Random permutation first = Richard last = Durstenfeld journal = Communications of the ACM issn = 0001-0782 volume = 7 issue = 7 year = 1964 month = July pages = 420 url = http://doi.acm.org/10.1145/364520.364540 doi = 10.1145/364520.364540] and was popularized by Donald E. Knuth in volume 2 of his book "The Art of Computer Programming" as "Algorithm P".cite book title = The Art of Computer Programming volume 2: Seminumerical algorithms first = Donald E. last = Knuth pages = 124–125 year = 1969 publisher = Addison-Wesley location = Reading, MA oclc = 85975465] Neither Durstenfeld nor Knuth, in the first edition of his book, acknowledged the earlier work of Fisher and Yates in any way, and may not have been aware of it. If such a generator is used to shuffle a deck of 52 playing cards, it can only ever produce a vanishingly small fraction of the 52! This merged cycle will have two members ("A""n" and "A""k") with indices less than or equal to "n", but will lose one of them when "n" is correspondingly decreased by one in step 4, and thus the assumption given above will continue to hold. Implemented by Durstenfeld, is an `` N '', gestart in 2004 playing Cards to provide element. 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