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100 Prisoners Problem
The 100 prisoners problem is a mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order to survive. The rules state that each prisoner may open only 50 drawers and cannot communicate with other prisoners. At first glance, the situation appears hopeless, but a clever strategy offers the prisoners a realistic chance of survival. Danish computer scientist Peter Bro Miltersen first proposed the problem in 2003. Problem The 100 prisoners problem has different renditions in the literature. The following version is by Philippe Flajolet and Robert Sedgewick: :''The director of a prison offers 100 death row prisoners, who are numbered from 1 to 100, a last chance. A room contains a cupboard with 100 drawers. The director randomly puts one prisoner's number in each closed drawer. The prisoners enter the room, one after another. Each prisoner may open and look into 50 drawers in any ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
100 Prisoners Problem Qtl1
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation Longest Cycle Length Pmf Qtl2
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set , namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empty Boxes
Empty may refer to: Music Albums * ''Empty'' (God Lives Underwater album) or the title song, 1995 * ''Empty'' (Nils Frahm album), 2020 * ''Empty'' (Tait album) or the title song, 2001 Songs * "Empty" (The Click Five song), 2007 * "Empty" (Garbage song), 2016 * "Empty", by Bebe Rexha from ''Better Mistakes'', 2021 * "Empty", by Belmont from ''Belmont'', 2018 * "Empty", by Blair St. Clair from ''Identity'', 2020 * "Empty", by Boyinaband featuring Jaiden Animations, 2018 * "Empty", by Cooliecut, Kin$oul, Craig Xen, and Ski Mask the Slump God from ''Members Only, Vol. 4'', 2019 * "Empty", by the Cranberries from ''No Need to Argue'', 1994 * "Empty", by Harry Chapin from '' Heads & Tales'', 1972 * "Empty", by Juice Wrld from ''Death Race for Love'', 2019 * "Empty", by King Gizzard & the Lizard Wizard from ''I'm in Your Mind Fuzz'', 2014 * "Empty", by Metric from ''Live It Out'', 2005 * "Empty", by Neurosis from '' Souls at Zero'', 1992 * "Empty", by Olivia O'Brien, 201 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ICALP
ICALP, the International Colloquium on Automata, Languages, and Programming is an academic conference organized annually by the European Association for Theoretical Computer Science and held in different locations around Europe. Like most theoretical computer science conferences its contributions are strongly peer-reviewed. The articles have appeared in proceedings published by Springer in their Lecture Notes in Computer Science, but beginning in 2016 they are instead published by the Leibniz International Proceedings in Informatics. The ICALP conference series was established by Maurice Nivat, who organized the first ICALP in Paris, France in 1972. The second ICALP was held in 1974, and since 1976 ICALP has been an annual event, nowadays usually taking place in July. Since 1999, the conference was thematically split into two tracks on "Algorithms, Complexity and Games" (Track A) and "Automata, Logic, Semantics, and Theory of Programming" (Track B), corresponding to the (at least ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conference Proceedings
In academia and librarianship, conference proceedings is a collection of academic papers published in the context of an academic conference or workshop. Conference proceedings typically contain the contributions made by researchers at the conference. They are the written record of the work that is presented to fellow researchers. In many fields, they are published as supplements to academic journals; in some, they are considered the main dissemination route; in others they may be considered grey literature. They are usually distributed in printed or electronic volumes, either before the conference opens or after it has closed. A less common, broader meaning of proceedings are the acts and happenings of an academic field, a learned society. For example, the title of the ''Acta Crystallographica'' journals is New Latin for "Proceedings in Crystallography"; the ''Proceedings of the National Academy of Sciences of the United States of America'' is the main journal of that academy. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set , namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonically Decreasing
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler–Mascheroni Constant
Euler's constant (sometimes also called the Euler–Mascheroni constant) is a mathematical constant usually denoted by the lowercase Greek letter gamma (). It is defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by \log: :\begin \gamma &= \lim_\left(-\log n + \sum_^n \frac1\right)\\ px&=\int_1^\infty\left(-\frac1x+\frac1\right)\,dx. \end Here, \lfloor x\rfloor represents the floor function. The numerical value of Euler's constant, to 50 decimal places, is: : History The constant first appeared in a 1734 paper by the Swiss mathematician Leonhard Euler, titled ''De Progressionibus harmonicis observationes'' (Eneström Index 43). Euler used the notations and for the constant. In 1790, Italian mathematician Lorenzo Mascheroni used the notations and for the constant. The notation appears nowhere in the writings of either Euler or Mascheroni, and was chosen at a later time perhaps because of the constant's connection ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral Test
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Number
In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: H_n= 1+\frac+\frac+\cdots+\frac =\sum_^n \frac. Starting from , the sequence of harmonic numbers begins: 1, \frac, \frac, \frac, \frac, \dots Harmonic numbers are related to the harmonic mean in that the -th harmonic number is also times the reciprocal of the harmonic mean of the first positive integers. Harmonic numbers have been studied since antiquity and are important in various branches of number theory. They are sometimes loosely termed harmonic series, are closely related to the Riemann zeta function, and appear in the expressions of various special functions. The harmonic numbers roughly approximate the natural logarithm function and thus the associated harmonic series grows without limit, albeit slowly. In 1737, Leonhard Euler used the divergence of the harmonic series to provide a new proof of the infinity of prime numbers. His work was extended into the comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complementary Event
In probability theory, the complement of any event ''A'' is the event ot ''A'' i.e. the event that ''A'' does not occur.Robert R. Johnson, Patricia J. Kuby: ''Elementary Statistics''. Cengage Learning 2007, , p. 229 () The event ''A'' and its complement ot ''A''are mutually exclusive and exhaustive. Generally, there is only one event ''B'' such that ''A'' and ''B'' are both mutually exclusive and exhaustive; that event is the complement of ''A''. The complement of an event ''A'' is usually denoted as ''A′'', ''Ac'', \neg''A'' or '. Given an event, the event and its complementary event define a Bernoulli trial: did the event occur or not? For example, if a typical coin is tossed and one assumes that it cannot land on its edge, then it can either land showing "heads" or "tails." Because these two outcomes are mutually exclusive (i.e. the coin cannot simultaneously show both heads and tails) and collectively exhaustive (i.e. there are no other possible outcomes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Event (probability Theory)
In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. An event consisting of only a single outcome is called an or an ; that is, it is a singleton set. An event S is said to if S contains the outcome x of the experiment (or trial) (that is, if x \in S). The probability (with respect to some probability measure) that an event S occurs is the probability that S contains the outcome x of an experiment (that is, it is the probability that x \in S). An event defines a complementary event, namely the complementary set (the event occurring), and together these define a Bernoulli trial: did the event occur or not? Typically, when the sample space is finite, any subset of the sample space is an event (that is, all e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
