UVa 10673 Play with Floor and Ceil（扩展欧几里得）

题意：

给定x, k，求p, q使得：

思路：

http://blog.csdn.net/fioman/article/details/2455698

利用扩展的欧几里得定理，ax + by = gcd(a, b)；x, y一定有整数解。

ax1+by1=gcd(a,b)=gcd(b,a%b)=bx2+(a%b)y2=bx2+(a-(a/b)*b)y2

#include <cstdio> #include <cstring> #include <cstring> #include <cmath>



void gcdextend(int a, int b, int &d, int &x, int &y) { if (!b) d = a, x = 1, y = 0; else gcdextend(b, a%b, d, y, x), y -= x * (a/b); } int main() { int cases; scanf("%d", &cases); while (cases--) { int a, b, c, k; scanf("%d %d", &c, &k); a = (int)floor(1.0*c/k); b = (int)ceil(1.0*c/k); int d, x, y; gcdextend(a, b, d, x, y); x *= (c / d); y *= (c / d); printf("%d %d\n", x, y); } return 0; }