The equation
Problem Description
There is an equation ax by c = 0. Given a,b,c,x1,x2,y1,y2 you must determine, how many integer roots of this equation are satisfy to the following conditions : x1<=x<=x2, y1<=y<=y2. Integer root of this equation is a pair of integer numbers (x,y).
Input
Input contains integer numbers a,b,c,x1,x2,y1,y2 delimited by spaces and line breaks. All numbers are not greater than 108 by absolute value.
Output
Write answer to the output.
Sample Input
代码语言：javascript复制1 1 -3
0 4
0 4Sample Output
代码语言：javascript复制4Solution
代码语言：javascript复制#include <bits/stdc .h>
int main() {
std::ios::sync_with_stdio(false);
std::function<long long(long long, long long, long long&, long long&)> ext_gcd;
ext_gcd = [&ext_gcd](long long a, long long b, long long& x, long long& y) -> long long {
long long d = a;
if(b != 0) {
d = ext_gcd(b, a % b, y, x);
y -= (a / b) * x;
} else {
x = 1;
y = 0;
}
return d;
};
long long a, b, c;
long long x1, x2;
long long y1, y2;
std::cin >> a >> b >> c;
std::cin >> x1 >> x2;
std::cin >> y1 >> y2;
c = -c;
if (c < 0) {
c = -c;
a = -a;
b = -b;
}
if (a < 0) {
a = -a;
auto tmp = x1;
x1 = -x2;
x2 = -tmp;
}
if (b < 0) {
b = -b;
auto tmp = y1;
y1 = -y2;
y2 = -tmp;
}
long long res = 0;
if (a == 0 && b == 0) {
res = c == 0 ? (x2 - x1 1) * (y2 - y1 1) : 0;
} else if (a == 0 && b != 0) {
long long tmp_y = c / b;
res = (c % b == 0 && tmp_y >= y1 && tmp_y <= y2) ? (x2 - x1 1) : 0;
} else if (a != 0 && b == 0) {
long long tmp_x = c / a;
res = (c % a == 0 && tmp_x >= x1 && tmp_x <= x2) ? (y2 - y1 1) : 0;
} else {
long long x, y;
long long gcd = ext_gcd(a, b, x, y);
if(c % gcd != 0) {
res = 0;
} else {
long long kx, ky;
x *= c / gcd;
y *= c / gcd;
kx = b / gcd;
ky = -a / gcd;
long long left = std::max(std::ceil(1.0 * (x1 - x) / kx) , std::ceil(1.0 * (y2 - y) / ky));
long long right = std::min(std::floor(1.0 * (x2 - x) / kx), std::floor(1.0 * (y1 - y) / ky));
res = left > right ? 0 : std::max(0LL, right - left 1);
}
}
std::cout << res << std::endl;
return 0;
}
//1 1 -3
//0 4
//0 4
