Add fast power (rust-lang#282)

* Add fast power

* Update README

Co-authored-by: imp2002 <[email protected]>

Author: fffzlfk

README.md

@@ -39,6 +39,7 @@ RESTART BUILD
 - [x] [Extended euclidean algorithm](./src/math/extended_euclidean_algorithm.rs)
 - [x] [Greatest common divisor](./src/math/greatest_common_divisor.rs)
 - [x] [Pascal's triangle](./src/math/pascal_triangle.rs)
+- [x] [Fast power algorithm](./src/math/fast_power.rs)
 
 ## [Dynamic Programming](./src/dynamic_programming)
 

src/math/fast_power.rs

@@ -0,0 +1,29 @@
+/// fast_power returns the result of base^power mod modulus
+pub fn fast_power(mut base: usize, mut power: usize, modulus: usize) -> usize {
+    assert!(base >= 1);
+
+    let mut res = 1;
+    while power > 0 {
+        if power & 1 == 1 {
+            res = (res * base) % modulus;
+        }
+        base = (base * base) % modulus;
+        power >>= 1;
+    }
+    res
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test() {
+        const MOD: usize = 1000000007;
+        assert_eq!(fast_power(2, 1, MOD), 2);
+        assert_eq!(fast_power(2, 2, MOD), 4);
+        assert_eq!(fast_power(2, 4, MOD), 16);
+        assert_eq!(fast_power(3, 4, MOD), 81);
+        assert_eq!(fast_power(2, 100, MOD), 976371285);
+    }
+}

src/math/mod.rs

@@ -1,4 +1,5 @@
 mod extended_euclidean_algorithm;
+mod fast_power;
 mod greatest_common_divisor;
 mod pascal_triangle;
 mod perfect_numbers;
@@ -7,6 +8,7 @@ mod prime_numbers;
 mod trial_division;
 
 pub use self::extended_euclidean_algorithm::extended_euclidean_algorithm;
+pub use self::fast_power::fast_power;
 pub use self::greatest_common_divisor::{
     greatest_common_divisor_iterative, greatest_common_divisor_recursive,
 };