From b94d1bc1e7effb36543253c670280a611cd36dd2 Mon Sep 17 00:00:00 2001
From: jackfiled <xcrenchangjun@outlook.com>
Date: Mon, 5 May 2025 20:12:55 +0800
Subject: [PATCH] 20250505 finished.

---
 src/problem/mod.rs                            |  2 +
 src/problem/p790_domino_and_tromino_tiling.rs | 50 +++++++++++++++++++
 2 files changed, 52 insertions(+)
 create mode 100644 src/problem/p790_domino_and_tromino_tiling.rs

diff --git a/src/problem/mod.rs b/src/problem/mod.rs
index 020bacb..a74456e 100644
--- a/src/problem/mod.rs
+++ b/src/problem/mod.rs
@@ -634,3 +634,5 @@ mod p838_push_dominoes;
 mod p1007_minimum_domino_rotations_for_equal_row;
 
 mod p1128_number_of_equivalent_domino_pairs;
+
+mod p790_domino_and_tromino_tiling;
diff --git a/src/problem/p790_domino_and_tromino_tiling.rs b/src/problem/p790_domino_and_tromino_tiling.rs
new file mode 100644
index 0000000..f234cc0
--- /dev/null
+++ b/src/problem/p790_domino_and_tromino_tiling.rs
@@ -0,0 +1,50 @@
+/**
+ * [790] Domino and Tromino Tiling
+ */
+pub struct Solution {}
+
+// submission codes start here
+
+const MOD: i32 = 1_000_000_007;
+
+impl Solution {
+    pub fn num_tilings(n: i32) -> i32 {
+        let n = n as usize;
+        let mut dp = vec![0; n + 1];
+        dp[0] = 1;
+        let mut prefix = 0;
+
+        // dp的最后必须是平整的
+        // dp[n] = dp[n - 1] + dp[n - 2] + for i in 0..=n-3 Sum(dp[i] * 2)
+        for i in 1..=n {
+            dp[i] = dp[i - 1] % MOD;
+
+            if i >= 2 {
+                dp[i] = (dp[i] + dp[i - 2]) % MOD;
+            }
+
+            if i >= 3 {
+                prefix = (prefix + dp[i - 3] * 2 % MOD) % MOD;
+                dp[i] = (dp[i] + prefix) % MOD;
+            }
+        }
+
+        dp[n]
+    }
+}
+
+// submission codes end
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_790() {
+        assert_eq!(1, Solution::num_tilings(1));
+        assert_eq!(2, Solution::num_tilings(2));
+        assert_eq!(5, Solution::num_tilings(3));
+        assert_eq!(11, Solution::num_tilings(4));
+        assert_eq!(312342182, Solution::num_tilings(30));
+    }
+}