Data commit

Task/Pells-equation/Rust/pells-equation.rust

@@ -0,0 +1,59 @@
+use num_bigint::{ToBigInt, BigInt};
+use num_traits::{Zero, One};
+//use std::mem::replace in the loop if you want this to be more efficient
+
+fn main() {
+    test(61u64);
+    test(109u64);
+    test(181u64);
+    test(277u64);
+}
+
+struct Pair {
+    v1: BigInt,
+    v2: BigInt,
+}
+
+impl Pair {
+    pub fn make_pair(a: &BigInt, b: &BigInt) -> Pair {
+        Pair {
+            v1: a.clone(),
+            v2: b.clone(),
+        }
+    }
+
+}
+
+fn solve_pell(n: u64) -> Pair{
+    let x: BigInt = ((n as f64).sqrt()).to_bigint().unwrap();
+    if x.clone() * x.clone() == n.to_bigint().unwrap() {
+        Pair::make_pair(&One::one(), &Zero::zero())
+    } else {
+        let mut y: BigInt = x.clone();
+        let mut z: BigInt = One::one();
+        let mut r: BigInt = ( &z + &z) * x.clone();
+        let mut e: Pair = Pair::make_pair(&One::one(), &Zero::zero());
+        let mut f: Pair = Pair::make_pair(&Zero::zero() ,&One::one());
+        let mut a: BigInt = Zero::zero();
+        let mut b: BigInt = Zero::zero();
+        while &a * &a - n * &b * &b != One::one() {
+            //println!("{}  {}  {}", y, z, r);
+            y = &r * &z - &y;
+            z = (n - &y * &y) / &z;
+            r = (&x + &y) / &z;
+
+            e = Pair::make_pair(&e.v2, &(&r * &e.v2 + &e.v1));
+            f = Pair::make_pair(&f.v2, &(&r * &f.v2 + &f.v1));
+            a = &e.v2 + &x * &f.v2;
+            b = f.v2.clone();
+        }
+        let pa = &a;
+        let pb = &b;
+        Pair::make_pair(&pa.clone(), &pb.clone())
+    }
+}
+
+fn test(n: u64) {
+    let r: Pair = solve_pell(n);
+    println!("x^2 - {} * y^2 = 1 for x = {} and y = {}", n, r.v1, r.v2);
+}