Add Chinese Remainder Theorem (TheAlgorithms#378)

Co-authored-by: Gent Binaku <[email protected]>

Author: GentBinaku

src/math/chinese_remainder_theorem.rs

@@ -0,0 +1,35 @@
+use super::extended_euclidean_algorithm;
+
+fn mod_inv(x: i32, n: i32) -> Option<i32> {
+    let (g, x, _) = extended_euclidean_algorithm(x, n);
+    if g == 1 {
+        Some((x % n + n) % n)
+    } else {
+        None
+    }
+}
+
+pub fn chinese_remainder_theorem(residues: &[i32], modulli: &[i32]) -> Option<i32> {
+    let prod = modulli.iter().product::<i32>();
+
+    let mut sum = 0;
+
+    for (&residue, &modulus) in residues.iter().zip(modulli) {
+        let p = prod / modulus;
+        sum += residue * mod_inv(p, modulus)? * p
+    }
+    Some(sum % prod)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn basic() {
+        assert_eq!(chinese_remainder_theorem(&[3, 5, 7], &[2, 3, 1]), Some(5));
+        assert_eq!(chinese_remainder_theorem(&[1, 4, 6], &[3, 5, 7]), Some(34));
+        assert_eq!(chinese_remainder_theorem(&[1, 4, 6], &[1, 2, 0]), None);
+        assert_eq!(chinese_remainder_theorem(&[2, 5, 7], &[6, 9, 15]), None);
+    }
+}

src/math/mod.rs

@@ -1,6 +1,7 @@
 mod amicable_numbers;
 mod armstrong_number;
 mod baby_step_giant_step;
+mod chinese_remainder_theorem;
 mod extended_euclidean_algorithm;
 mod fast_fourier_transform;
 mod fast_power;
@@ -33,6 +34,7 @@ mod zellers_congruence_algorithm;
 pub use self::amicable_numbers::amicable_pairs_under_n;
 pub use self::armstrong_number::is_armstrong_number;
 pub use self::baby_step_giant_step::baby_step_giant_step;
+pub use self::chinese_remainder_theorem::chinese_remainder_theorem;
 pub use self::extended_euclidean_algorithm::extended_euclidean_algorithm;
 pub use self::fast_fourier_transform::{
     fast_fourier_transform, fast_fourier_transform_input_permutation,