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In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. [1] [2] Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers.
A standard order is often called ascending (corresponding to the fact that the standard order of numbers is ascending, i.e. A to Z, 0 to 9), the reverse order descending (Z to A, 9 to 0). For dates and times, ascending means that earlier values precede later ones e.g. 1/1/2000 will sort ahead of 1/1/2001.
The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists.
In underwater diving, ascending and descending is done using strict protocols to avoid problems caused by the changes in ambient pressure and the hazards of obstacles near the surface such as collision with vessels. Diver certification and accreditation organisations place importance on these protocols early in their diver training programmes. [1]
In this role, it is used while descending far more often than while ascending. A familiar example of the descending scale is heard in a Ring of bells . A ring of twelve is sometimes augmented with a 5♯ and 6♭ to make a 10 note harmonic minor scale from bell 2 to bell 11 (for example, Worcester Cathedral).
The descending 5-6 sequences, also known as descending third sequences, consist of a series of chords whose root notes descend by a third each sequential repetition. [8] The basic pattern of a descending 5-6 sequence (with intervening chords removed) in C major. The pattern in the lower staff descends by a third each time in this sequence. Play ⓘ
Grade 3 students learn how to work on projects on their own and with others. This may start as early as second grade and first grade as well. Social skills , empathy and leadership are considered by some educators [ citation needed ] to be as important to develop as the academic skills of reading , writing and arithmetic .
The longest increasing subsequence problem is closely related to the longest common subsequence problem, which has a quadratic time dynamic programming solution: the longest increasing subsequence of a sequence is the longest common subsequence of and , where is the result of sorting.
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related to: ascending and descending order worksheet for grade 3 printable pages 1