请问c++的编程思路一般是什么？

For any nonnegative integer a and any positive integer b,

gcd(a, b) = gcd(b, a mod b).

Proof We shall show that gcd(a, b) and gcd(b, a mod b) divide each other, so that by equation (31.5) they must be equal (since they are both nonnegative).

We first show that gcd(a, b) | gcd(b, a mod b). If we let d = gcd(a, b), then d | a and d | b. By equation (3.8), (a mod b) = a - qb, where q = ⌊a/b⌋. Since (a mod b) is thus a linear combination of a and b, equation (31.4) implies that d | (a mod b). Therefore, since d | b and d | (a mod b), Corollary 31.3 implies that d | gcd(b, a mod b) or, equivalently, that

(31.14) gcd(a,b) | gcd(b, a mod b)

Showing that gcd(b, a mod b) | gcd(a, b) is almost the same. If we now let d = gcd(b, a mod b), then d | b and d | (a mod b). Since a = qb + (a mod b), where q = ⌊a/b⌋, we have that a is a linear combination of b and (a mod b). By equation (31.4), we conclude that d | a. Sin