Algorithms

Count prime numbers not exceeding n(n>0)

Pseudocode:
Input: an integer n > 1

Let A be an array of Boolean values, indexed by integers 2 to n,
initially all set to true.

for i = 2, 3, 4, ..., not exceeding √n:
if A[i] is true:
for j = i2, i2+i, i2+2i, i2+3i, ..., not exceeding n :
A[j] := false

Output: all i such that A[i] is true.

The Sieve of Eratosthenes uses an extra O(n) memory and its runtime complexity is O(n log log n).

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