Inner-function in Function
auto function = [](auto x){
return ...;
};Boolean Comporator
sort(q, q + n, [&](int A, int B) { return A < B; });-
Sum-Xor property
$a + b = a \oplus b + 2 (a \land b)$
$a + b = a | b + a \land b$
$a \oplus b = a | b - a \land b$ -
Conjecture: Any even number greater than 2 can be split into two prime numbers
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Pragmas for speedup
#pragma GCC optimize ("O3")
#pragma GCC optimize ("unroll-loops")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
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find all B that B is submask of A
(B = A; B > 0; --B, B&=A); -
find all D that A is submask of D
for (D = A; D < (1 << n); ++D, D |= A) -
Rotate board 45 degree by
$(x,y) \rightarrow (x+y,y-x)$ , so Manhattan distance between two points would be$max(|x1-x2|, |y1-y2|)$ . -
Find any x,y such that
$ax + by = gcd(a,b)$ for given two non-negative integers a and b with Extended Euclidean Algorithm -
There is no assumption that n1 and n2 are coprime. Find an integer x that satisfies:
$x \equiv a_1 (mod n_1)$ $x \equiv a_2 (mod n_2)$
where
$gcd(lcm(x, y_1), lcm(x, y_2), \dots, lcm(x, y_k)) = lcm(x, gcd(y1, y2, \dots, y_k))$ $lcm(gcd(x, y_1), gcd(x, y_2), \dots, gcd(x, y_k)) = gcd(x, lcm(y1, y2, \dots, y_k))$ - For any
$x \geq y$ the$gcd(x, y) = gcd(x - y, y)$ , which can be extended for multiple arguments$gcd(x, y, z, \dots) = gcd(x-y, y, z, \dots)$