Update Extended Euclidean Algorithm (Extensive).cpp

Extended Euclidean Algorithm (Extensive).cpp

@@ -1,84 +1,92 @@
 int xgcd(int a, int b, int &x, int &y) //Returns GCD of A, B
 {
-	if(a==0) 
+	if(a == 0)
 	{
-		x=0;
-		y=1;
+		x = 0;
+		y = 1;
 		return b;
 	}
 	int x1, y1;
 	int d = xgcd(b % a, a, x1, y1);
-	x = y1 - (b/a)*x1;
+	x = y1 - (b / a) * x1;
 	y = x1;
 	return d;
 }
-
+ 
 int modular_inverse(int a, int m)
 {
 	int x, y;
-	int g=xgcd(a, m, x, y);
-	if(g!=1)
+	int g = xgcd(a, m, x, y);
+	if(g != 1)
 		return -1;
 	else
 	{
-		x=(x%m + m)%m;
+		x = (x % m + m) % m;
 		return x;
 	}
 }
-
+ 
 void shift_solution(int &x, int &y, int a, int b, int cnt)
 {
-	x+=cnt*b;
-	y-=cnt*a;
+	x += cnt * b;
+	y -= cnt * b;
 }
-
-bool find_any_solution(int a, int b, int c, int &x0, int &y0)
+ 
+bool find_any_solution(int a, int b, int c, int &x0, int &y0, int &g)
 {
-	int g=xgcd(abs(a), abs(b), x0, y0);
-	if(c%g!=0)
+	g = xgcd(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;
+	if(a < 0)
+		x0 *= -1;
+	if(b < 0)
+		y0 *= -1;
 	return true;
 }
-
+
+pair<int, int> p; //Stores one particular answer in [minx, maxx] and [miny, maxy]
+
 int find_all_solutions(int a, int b, int c, int minx, int maxx, int miny, int maxy) //Returns number of solutions with x∈[minx, maxx], y∈[miny, maxy]
 {
 	int x, y, g;
 	if(!find_any_solution(a, b, c, x, y, g))
 		return 0;
 	a /= g;  
 	b /= g; 
-
-	int sign_a = a>0 ? +1 : -1;
-	int sign_b = b>0 ? +1 : -1;
-
+	c /= 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); 
-
+	int lx = max(lx1, lx2);
+	int rx = min(rx1, rx2); 
+
+	p = {lx, ((c - a * lx) / b)};
+
 	return (rx - lx) / abs(b) + 1;
 }
+
+//Problem 1: https://codeforces.com/problemset/problem/1089/F
+