Table of Contents
Which is the example of polynomial algorithm?
Many widely used algorithms have polynomial time complexity (like our algorithms readNumbers1 and readNumbers2 , quicksort, insertion sort, binary search etc. etc.). Examples of algorithms with non-polynomial time complexity are all kinds of brute-force algorithms that look through all possible configurations.
Is prime factorization NP complete?
No, its not known to be NP-complete, and it would be very surprising if it were. This is because its decision version is known to be in NP∩co-NP. (Decision version: Does n have a prime factor
What makes an algorithm polynomial time?
An algorithm is said to be of polynomial time if its running time is upper bounded by a polynomial expression in the size of the input for the algorithm, that is, T(n) = O(nk) for some positive constant k.
Why is the prime factorization algorithm called pseudo-polynomial?
As we increase the number of bits in N, we need exponentially more divisions to obtain the prime factors of a number. Of course the number N also increases enormously in magnitude as the number of bits goes up. That’s why this type of algorithm is sometimes referred to as being pseudo-polynomial.
Is it possible to factor integers polynomial time?
Classical algorithms for factoring integers require exponential time in the worst case. Factorization is not NP-complete though. If quantum computers with thousands of qbits become a reality, Shor’s algorithm can be used to factor integers in polynomial time.
How to find all the prime factors of N in Python?
To find all of the prime factors of N, that means all we need to do is try all possible factors from 2 to the square root of N inclusive. Below is a simple implementation of this algorithm in Python:
How hard is it to factor integers to primes?
Factoring integers to primes is a classic problem in computer science. Some widely used cryptographic algorithms, such as RSA, rely on it being a hard problem to solve as the numbers get bigger. Classical algorithms for factoring integers require exponential time in the worst case.