The task is as follows:
Write code that factorizes integers as quickly as possible subject to your code being no more than 140 bytes long. The output should be the list of all prime factors.
Your code can take input and give output in any way that is convenient including for example as argumen...
I have a formula, which I have no idea how to solve, because I don't know that double vertical-line sign: $\|{\rm Ax} \|$?
$${\rm x} \ne 0 \in \Bbb R^n, \quad 0 < m \le \frac {\| {\rm Ax} \|} {\| {\rm x} \|} \le M, \quad cond(A) \le \frac M m .$$
What does it mean? How should I solve this?
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).
A norm must also satisfy certain properties pertaining to scalability and additivity which are given in the formal definition below.
A simple example is two dimensional Euclidean space R2 equipped with the Euclidean norm. Elements in this vector...
Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5f3759df, is an algorithm that estimates 1/√x, the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number x in IEEE 754 floating-point format. This operation is used in digital signal processing to normalize a vector, i.e., scale it to length 1. For example, computer graphics programs use inverse square roots to compute angles of incidence and reflection for lighting and shading. The algorithm is best known for its implementation in 1999 in the source code of Quake...
House of cards
Simple challenge: given an integer, draw a house of cards with the given number of stories. If the number is negative, draw the house upside-down. Examples:
Input: 2
Output:
/\
--
/\/\
Input: 5
Output:
/\
--
/\/\
----
/\/\/\
------
/\/\/\/\
--------
/\/\/...
Haskell, 100 Bytes
f n=[h,div n h]where h=g 17(s 17);s x=mod(x*x+1)n;g a b|d>1=d|1<2=g(s a)(s$s b)where d=gcd(abs b-a)n
This works for the first 5 test cases in unnoticable time.
This will probably time-out on the second-largest test case. It will also not work on the last test case because it...The Lenstra elliptic curve factorization or the elliptic curve factorization method (ECM) is a fast, sub-exponential running time algorithm for integer factorization which employs elliptic curves. For general purpose factoring, ECM is the third-fastest known factoring method. The second fastest is the multiple polynomial quadratic sieve and the fastest is the general number field sieve. The Lenstra elliptic curve factorization is named after Hendrik Lenstra.
Practically speaking, ECM is considered a special purpose factoring algorithm as it is most suitable for finding small factors. Currently...
6
Imagine travelling to a point A miles away vertically and B miles away horizontally. Or in other words, travelling from (0, 0) to point (a, b). How far would you need to end up travelling? This seems like a straightforward question, but the answer depends on who you ask. If you're a crow, and you...
-1
Say I have an expression:
9 * 8 + 1 - 4
This expression can be interpreted in six different ways, depending on operator precedence:
(((9 * 8) + 1) - 4) = 69 (* + -)
((9 * 8) + (1 - 4)) = 69 (* - +)
((9 * (8 + 1)) - 4) = 77 (+ * -)
(9 * ((8 + 1) - 4)) = 45 (+ - *)
((9 * 8) + (1 - 4)) = 69 (- *...
