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from math import isqrt def sieve_of_Sundaram (n): """The sieve of Sundaram is a simple deterministic algorithm for finding all the prime numbers up to a specified integer.""" if n < 3: if n < 2: return 0 else: return 1 k = (n-3) // 2 + 1 integers_list = [True for i in range (k)] ops = 0 for i in range ((isqrt (n)-3) // 2 + 1): # if integers ...
These two one-sided range top-k queries return the top-(/) most frequent elements in each of their respective ranges in (/) time. These frequent elements make up the set of candidates for τ {\displaystyle \tau } -majorities in A [ i . . j ] {\displaystyle A[i..j]} in which there are O ( 1 / τ ) {\displaystyle O(1/\tau )} candidates some of ...
In mathematics, many sequences of numbers or of polynomials are indexed by nonnegative integers, for example, the Bernoulli numbers and the Bell numbers. In both mechanics and statistics , the zeroth moment is defined, representing total mass in the case of physical density , or total probability, i.e. one, for a probability distribution .
The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.
Bucket sort may be used in lieu of counting sort, and entails a similar time analysis. However, compared to counting sort, bucket sort requires linked lists, dynamic arrays, or a large amount of pre-allocated memory to hold the sets of items within each bucket, whereas counting sort stores a single number (the count of items) per bucket. [4]
Pandas (styled as pandas) is a software library written for the Python programming language for data manipulation and analysis.In particular, it offers data structures and operations for manipulating numerical tables and time series.
The main difference between these two models is in how memory may be addressed. The random access machine allows any value that is stored in a register to be used as the address of memory read and write operations, with unit cost per operation. This ability allows certain complex operations on data to be implemented quickly using table lookups.
The counting semaphore concept can be extended with the ability to claim or return more than one "unit" from the semaphore, a technique implemented in Unix. The modified V and P operations are as follows, using square brackets to indicate atomic operations , i.e., operations that appear indivisible to other processes: