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In combinatorics, stars and bars (also called "sticks and stones", [1] "balls and bars", [2] and "dots and dividers" [3]) is a graphical aid for deriving certain combinatorial theorems. It can be used to solve a variety of counting problems , such as how many ways there are to put n indistinguishable balls into k distinguishable bins. [ 4 ]
In regular expressions, the period (., also called "dot") is the wildcard pattern which matches any single character. Followed by the Kleene star operator, which is denoted as an asterisk ( * ), we obtain .* , which will match zero or more arbitrary characters.
In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters. In mathematics, it is more commonly known as the free monoid construction.
The Kleene star expression s * is converted to An ε-transition connects initial and final state of the NFA with the sub-NFA N ( s ) in between. Another ε-transition from the inner final to the inner initial state of N ( s ) allows for repetition of expression s according to the star operator.
A* (pronounced "A-star") is a graph traversal and pathfinding algorithm that is used in many fields of computer science due to its completeness, optimality, and optimal efficiency. [1] Given a weighted graph , a source node and a goal node, the algorithm finds the shortest path (with respect to the given weights) from source to goal.
A common pattern is to use it with return, like this: val foo = bar ()?: return; In Gosu, the ?: operator returns the right operand if the left is null as well. In C#, the null-conditional operator, ?. is referred to as the "Elvis operator", [10] but it does not perform the same function. Instead, the null-coalescing operator?? does.
The patterns generally have the form of either sequences or tree structures. Uses of pattern matching include outputting the locations (if any) of a pattern within a token sequence, to output some component of the matched pattern, and to substitute the matching pattern with some other token sequence (i.e., search and replace).
The first question was answered in the negative when in 1963, Eggan gave examples of regular languages of star height n for every n. Here, the star height h(L) of a regular language L is defined as the minimum star height among all regular expressions representing L. The first few languages found by Eggan are described in the following, by ...