From e4e47d715f8a6d9c259f152126b43de48b19d32a Mon Sep 17 00:00:00 2001
From: EFanZh <efanzh@gmail.com>
Date: Thu, 14 Nov 2024 21:33:58 +0800
Subject: [PATCH] Add problem 2320: Count Number of Ways to Place Houses

---
 src/lib.rs                                    |  1 +
 .../matrix_multiplication.rs                  | 59 +++++++++++++++++++
 .../mod.rs                                    | 18 ++++++
 3 files changed, 78 insertions(+)
 create mode 100644 src/problem_2320_count_number_of_ways_to_place_houses/matrix_multiplication.rs
 create mode 100644 src/problem_2320_count_number_of_ways_to_place_houses/mod.rs

diff --git a/src/lib.rs b/src/lib.rs
index bea04a14..99868a21 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1722,6 +1722,7 @@ pub mod problem_2315_count_asterisks;
 pub mod problem_2316_count_unreachable_pairs_of_nodes_in_an_undirected_graph;
 pub mod problem_2317_maximum_xor_after_operations;
 pub mod problem_2319_check_if_matrix_is_x_matrix;
+pub mod problem_2320_count_number_of_ways_to_place_houses;
 
 #[cfg(test)]
 mod test_utilities;
diff --git a/src/problem_2320_count_number_of_ways_to_place_houses/matrix_multiplication.rs b/src/problem_2320_count_number_of_ways_to_place_houses/matrix_multiplication.rs
new file mode 100644
index 00000000..260c1edd
--- /dev/null
+++ b/src/problem_2320_count_number_of_ways_to_place_houses/matrix_multiplication.rs
@@ -0,0 +1,59 @@
+pub struct Solution;
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+type Matrix = (u64, u64);
+
+impl Solution {
+    const MODULUS: u64 = 1_000_000_007;
+
+    fn matrix_multiply(lhs: Matrix, rhs: Matrix) -> Matrix {
+        (
+            (lhs.0 * (rhs.0 + rhs.1) + lhs.1 * rhs.0) % Self::MODULUS,
+            (lhs.0 * rhs.0 + lhs.1 * rhs.1) % Self::MODULUS,
+        )
+    }
+
+    fn exp_mod(mut exponent: u32) -> Matrix {
+        let mut base = (1, 0);
+        let mut result = (0, 1);
+
+        loop {
+            if exponent & 1 != 0 {
+                result = Self::matrix_multiply(result, base);
+            }
+
+            exponent >>= 1;
+
+            if exponent == 0 {
+                break;
+            }
+
+            base = Self::matrix_multiply(base, base);
+        }
+
+        result
+    }
+
+    pub fn count_house_placements(n: i32) -> i32 {
+        let matrix = Self::exp_mod(n as _);
+
+        ((matrix.0 * 2 + matrix.1).pow(2) % Self::MODULUS) as _
+    }
+}
+
+// ------------------------------------------------------ snip ------------------------------------------------------ //
+
+impl super::Solution for Solution {
+    fn count_house_placements(n: i32) -> i32 {
+        Self::count_house_placements(n)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    #[test]
+    fn test_solution() {
+        super::super::tests::run::<super::Solution>();
+    }
+}
diff --git a/src/problem_2320_count_number_of_ways_to_place_houses/mod.rs b/src/problem_2320_count_number_of_ways_to_place_houses/mod.rs
new file mode 100644
index 00000000..0c3f35d0
--- /dev/null
+++ b/src/problem_2320_count_number_of_ways_to_place_houses/mod.rs
@@ -0,0 +1,18 @@
+pub mod matrix_multiplication;
+
+pub trait Solution {
+    fn count_house_placements(n: i32) -> i32;
+}
+
+#[cfg(test)]
+mod tests {
+    use super::Solution;
+
+    pub fn run<S: Solution>() {
+        let test_cases = [(0, 1), (1, 4), (2, 9), (3, 25), (4, 64), (5, 169), (1000, 500_478_595)];
+
+        for (n, expected) in test_cases {
+            assert_eq!(S::count_house_placements(n), expected);
+        }
+    }
+}