## Algoritmo de LinearDionphanatic.

Cualquier duda no dudes en contactar.

``````/**
* Author: Isaac
* Date: 2009-04-06
* Source:
* Description: Linear Dionphanatic
*/
int extended_euclid(int a, int b, int &x, int &y) {
int xx = y = 0;
int yy = x = 1;
while (b) {
int q = a / b;
int t = b; b = a%b; a = t;
t = xx; xx = x - q*xx; x = t;
t = yy; yy = y - q*yy; y = t;
}
return a;
}
// Linear Diophantine Equation Solution: Given, a*x+b*y=c. Find valid x and y if possible.
bool linear_diophantine (int a, int b, int c, int & x0, int & y0, int & g) {
g = extended_euclid (abs(a), abs(b), x0, y0);
if (c % g != 0)
return false;
x0 *= c / g;
y0 *= c / g;
if (a < 0)   x0 *= -1;
if (b < 0)   y0 *= -1;
return true;
}
// for each integer k, // x1 = x + k * b/g // y1 = y - k * a/g
// is a solution to the equation where g = gcd(a,b).
void shift_solution (int & x, int & y, int a, int b, int cnt) {
x += cnt * b;
y -= cnt * a;
}
// Now How many solution where x in range[x1,x2] and y in range[y1,y2] ?
int find_all_solutions(int a,int b,int c,int &minx,int &maxx,int &miny,int &maxy)
{
int x,y,g;
if(linear_diophantine(a,b,c,x,y,g) == 0) return 0;
a/=g, b/=g;
int sign_a = a>0 ? +1 : -1;
int sign_b = b>0 ? +1 : -1;
shift_solution (x, y, a, b, (minx - x) / b);
if (x < minx)
shift_solution (x, y, a, b, sign_b);
if (x > maxx)
return 0;
int lx1 = x;
shift_solution (x, y, a, b, (maxx - x) / b);
if (x > maxx)
shift_solution (x, y, a, b, -sign_b);
int rx1 = x;
shift_solution (x, y, a, b, - (miny - y) / a);
if (y < miny)
shift_solution (x, y, a, b, -sign_a);
if (y > maxy)
return 0;
int lx2 = x;
shift_solution (x, y, a, b, - (maxy - y) / a);
if (y > maxy)
shift_solution (x, y, a, b, sign_a);
int rx2 = x;

if (lx2 > rx2)
swap (lx2, rx2);
int lx = max (lx1, lx2);
int rx = min (rx1, rx2);

return (rx - lx) / abs(b) + 1;
}``````