From aa83acaeebd10ffbf9e04438f90d48835d314031 Mon Sep 17 00:00:00 2001
From: rohitsh16 <rohitshukla7970@gmail.com>
Date: Wed, 2 Oct 2019 12:59:38 +0530
Subject: [PATCH] added diophantine

---
 diophantine/diophantine.cpp | 82 +++++++++++++++++++++++++++++++++++++
 series_sum/series.txt       |  0
 2 files changed, 82 insertions(+)
 create mode 100644 diophantine/diophantine.cpp
 create mode 100644 series_sum/series.txt

diff --git a/diophantine/diophantine.cpp b/diophantine/diophantine.cpp
new file mode 100644
index 0000000..eccea08
--- /dev/null
+++ b/diophantine/diophantine.cpp
@@ -0,0 +1,82 @@
+#include <bits/stdc++.h>
+
+// find all solution ax + by = c for (x, y) in  range of [minx : maxx] and [miny : maxy] 
+
+using namespace std;
+
+int x, y, g, lx, rx;
+
+int gcd (int a, int b, int & x, int & y) {
+    if (a == 0) {
+        x = 0; y = 1;
+        return b;
+    }
+    int x1, y1;
+    int d = gcd (b%a, a, x1, y1);
+    x = y1 - (b / a) * x1;
+    y = x1;
+    return d;
+}
+
+bool find_any_solution (int a, int b, int c, int & x0, int & y0, int & g) {
+    g = gcd (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;
+}
+
+void shift_solution(int &x,int &y,int a,int b,int cnt){
+    x += cnt * b;
+    y -= cnt * a;
+}
+
+//It returns the number of solutions that exists.
+
+int find_all_solutions(int a, int b, int c, int minx, int maxx, int miny, int maxy) {
+    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;
+
+    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);
+    
+	lx = max (lx1, lx2);
+    rx = min (rx1, rx2); 
+
+    return (rx - lx) / abs(b) + 1;
+}  
+
+int main(){
+	int a, b, c, maxx, maxy, minx, miny;
+	cin >> a >> b >> c >> minx >> maxx >> miny >> maxy;
+	if (find_all_solutions(a,b,c,minx,maxx,miny,maxy)!= 0 ) {
+		for (int i=lx;i<=rx;i+=b)
+			cout<<i<<"   "<<(c-a*i)/b<<endl;
+	}
+}
diff --git a/series_sum/series.txt b/series_sum/series.txt
new file mode 100644
index 0000000..e69de29