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In mathematics and computer science, Recamán's sequence [1] [2] is a well known sequence defined by a recurrence relation. Because its elements are related to the previous elements in a straightforward way, they are often defined using recursion.
The novel is set in Michigan, the home state of the author. This is also the setting of his first novel, The Watsons Go to; Birmingham. [6] Bud Caldwell, the main character, travels from Flint to Grand Rapids, giving readers a glimpse of the midwestern state in the late 1930s; he meets a homeless family and a labor organizer and experiences life as an orphaned youth and the racism of the time ...
A multiple of a number is the product of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2.
This works regardless of the number of elements in the list, even if that number is 1. Knuth observed that a naive implementation of his Algorithm X would spend an inordinate amount of time searching for 1's. When selecting a column, the entire matrix had to be searched for 1's. When selecting a row, an entire column had to be searched for 1's.
Data types can also be defined by mutual recursion. The most important basic example of this is a tree, which can be defined mutually recursively in terms of a forest (a list of trees). Symbolically: f: [t[1], ..., t[k]] t: v f A forest f consists of a list of trees, while a tree t consists of a pair of a value v and a forest f (its children ...
In mathematics and computer science, mutual recursion is a form of recursion where two mathematical or computational objects, such as functions or datatypes, are defined in terms of each other. [1] Mutual recursion is very common in functional programming and in some problem domains, such as recursive descent parsers , where the datatypes are ...
A structure similar to LCGs, but not equivalent, is the multiple-recursive generator: X n = (a 1 X n−1 + a 2 X n−2 + ··· + a k X n−k) mod m for k ≥ 2. With a prime modulus, this can generate periods up to m k −1, so is a useful extension of the LCG structure to larger periods.
For LCS(R 2, C 1), A is compared with A. The two elements match, so A is appended to ε, giving (A). For LCS(R 2, C 2), A and G do not match, so the longest of LCS(R 1, C 2), which is (G), and LCS(R 2, C 1), which is (A), is used. In this case, they each contain one element, so this LCS is given two subsequences: (A) and (G).