Ultraviolet A-11768 lattice point or not (expanded gcd)

Now a days a very common problem is: "the coordinate of two points in Cartesian coordinate system is (200,300) and (4000,500 0 ). if these two points are connected we get a line segment. how manylattice points are there on this line segment. "You will have to do a similartask in this problem-the only difference is that the terminal coordinates canbe fractions.

 

Input

First line of the input file contains a positive integer n (n <= 50000) that denotes how many lines of inputs follow. this line isfollowed by n lines each of which contains four floating-point numbers X1, Y1, X2, Y2 (0 <| X1 |, | Y1 |, | X2 |, | Y2 | <= 200000 ). these floating-point numbers has exactly one digit after thedecimal point.

 

Output

For each line of input records Tthe first line produce one line of output. this line contains an integer whichdenotes how many lattice points are there on the line segment that connects thetwo points (x1, Y1) and (X2, Y2 ).

 

Sampleinput output for sample input

3 10.1 10.1 11.2 11.2 10.2 100.3 300.3 11.1 1.0 1.0 2.0 2.0

1 0 2

Problemsetter: Shahriar Manzoor

Special thanks: Derek kisman

Calculate the number of Integer Points after a line segment

Idea: first convert a line segment to a linear equation, then we can use the expanded GCD to solve the problem, and then find the solution within the range of the two points.

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>typedef long long ll;using namespace std;void gcd(ll a, ll b, ll &d, ll &x, ll &y) {  if (!b) { d = a; x = 1; y = 0; }  else { gcd(b, a%b, d, y, x); y -= x*(a/b); }  }  ll sovle(double X1, double Y1, double X2, double Y2) {ll x1 = X1*10, x2 = X2*10, y1 = Y1*10, y2 = Y2*10;if (x1 == x2) {if (x1 % 10)return 0;y1 = ceil(min(Y1, Y2));y2 = floor(max(Y1, Y2));return max(y2-y1+1, 0ll);}if (y1 == y2) {if (y1 % 10)return 0;if (X2 < X1)swap(X2, X1);x1 = ceil(X1), x2 = floor(X2);return max(x2-x1+1, 0ll);}ll a = (y2-y1)*10, b = (x1-x2)*10, c = x1*y2-x2*y1;ll x, y, d, k1 = 0;if (X2 < X1)swap(X2, X1);x1 = ceil(X1), x2 = floor(X2);if (x1 > x2)return 0;gcd(a, b, d, x, y);if (c % d != 0)return 0;a /= d, b /= d;x *= (c/d), y *= (c/d);if (b < 0)b = -b;x = x-(x-x1)/b*b;x -= b;while (x < x1)x += b;k1 = 0;while (x + k1 * b <= x2)k1++;return k1;}int main() {double x1, y1, x2, y2;int t;scanf("%d", &t);while (t--) {scanf("%lf%lf%lf%lf", &x1, &y1, &x2, &y2);ll ans = sovle(x1, y1, x2, y2);printf("%lld\n", ans);}return 0;}

Ultraviolet A-11768 lattice point or not (expanded gcd)