Sieve of Eratosthenes
Finding All Prime Numbers
Problem Statement
For a given number n, print all primes <= n. Also, n is a small number. Prime numbers are only divisible by themselves and 1.
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Input:
n =10
Output:
2 3 5 7
Explanation:
There are only 4 prime numbers less than or equal to 10.
Example:
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Simple Approach
1. Iterate from 2 to N.
2. Check for prime numbers.
3. Print the number if it is a prime number.
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Time complexity:
O(N*N)
Here, N = number
Space complexity:
O(1)
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1. Write all the numbers from 2,3,4…n.
2. Take 1st prime number and mark all of its multiples as visited.
Efficient Approach: Sieve of Eratosthenes
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3. Now, take the next unvisited number and follow step 2 with that number.
4. Numbers that remain unmarked at the end of the algorithm are prime numbers.
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Time Complexity:
O(N *(log(log(N))))
Space complexity:
O(1)
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How to implement the solution in different languages?
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