Runtime: 0 ms (Top 100.0%) | Memory: 2.20 MB (Top 10.53%)

Author: AnasImloul

scripts/algorithms/N/Nth Tribonacci Number/Nth Tribonacci Number.rs

@@ -0,0 +1,32 @@
+// Runtime: 0 ms (Top 100.0%) | Memory: 2.20 MB (Top 10.53%)
+
+impl Solution {
+    /*
+        | T(n+2) T(n+1) T(n)   |   | 1 1 0 |   | T(n+3) T(n+2) T(n+1) |
+        | T(n+1) T(n)   T(n-1) | * | 1 0 1 | = | T(n+2) T(n+1) T(n)   |
+        | T(n)   T(n-1) T(n-2) |   | 1 0 0 |   | T(n+1) T(n)   T(n-1) |
+    */
+    pub fn tribonacci(n: i32) -> i32 {
+        match n {
+            0 => 0,
+            1 | 2 => 1,
+            n => {
+                fn mul(m: &[[i32; 3]; 3], e: &[[i32; 3]; 3]) -> [[i32; 3]; 3] {
+                    let x = |row:usize, col:usize| m[row].iter().zip(e.iter().map(|r| r[col])).map(|(a,b)| a*b).sum();
+                    [[x(0,0), x(0,1), x(0,2)], [x(1,0), x(1,1), x(1,2)], [x(2,0), x(2,1), x(2,2)]]
+                }
+                let mut m = [[2, 1, 1], [1, 1, 0], [1, 0, 0]]; // initial matrix
+                let mut e = [[1, 1, 0], [1, 0, 1], [1, 0, 0]]; // linear operator
+                let mut n = n - 3;
+                while n > 0 {
+                    if n & 1 > 0 {
+                        m = mul(&m, &e);
+                    }
+                    e = mul(&e, &e);
+                    n >>= 1;
+                }
+                m[0][0]
+            }
+        }
+    }
+}