From 4b3eaf5d392d5b675a6afe33b1203f4e239cae97 Mon Sep 17 00:00:00 2001
From: Shyam-Chen <shyamchen1994@gmail.com>
Date: Tue, 29 Oct 2024 10:11:21 +0800
Subject: [PATCH] 246th Commit

---
 README.md                                     |  3 ++-
 src/page-2/118. Pascal's Triangle/generate.ts | 20 +++++------------
 .../numTilings.test.ts                        |  8 +++++++
 .../numTilings.ts                             | 22 +++++++++++++++++++
 4 files changed, 38 insertions(+), 15 deletions(-)
 create mode 100644 src/page-8/790. Domino and Tromino Tiling/numTilings.test.ts
 create mode 100644 src/page-8/790. Domino and Tromino Tiling/numTilings.ts

diff --git a/README.md b/README.md
index 034e33c..c501592 100644
--- a/README.md
+++ b/README.md
@@ -245,11 +245,12 @@ Ace Coding Interview with 75 Qs
 | 1137. N-th Tribonacci Number   | [Solution][1137] | Easy   |
 | 746. Min Cost Climbing Stairs  | [Solution][746]  | Easy   |
 | 198. House Robber              | [Solution][198]  | Medium |
-| 790. Domino and Tromino Tiling | Solution         | Medium |
+| 790. Domino and Tromino Tiling | [Solution][790]  | Medium |
 
 [1137]: ./src/page-11/1137.%20N-th%20Tribonacci%20Number/tribonacci.ts
 [746]: ./src/page-7/746.%20Min%20Cost%20Climbing%20Stairs/minCostClimbingStairs.ts
 [198]: ./src/page-2/198.%20House%20Robber/rob.ts
+[790]: ./src/page-8/790.%20Domino%20and%20Tromino%20Tiling/numTilings.ts
 
 | DP - Multidimensional                                     |          |        |
 | --------------------------------------------------------- | -------- | ------ |
diff --git a/src/page-2/118. Pascal's Triangle/generate.ts b/src/page-2/118. Pascal's Triangle/generate.ts
index f5b25a0..912e348 100644
--- a/src/page-2/118. Pascal's Triangle/generate.ts	
+++ b/src/page-2/118. Pascal's Triangle/generate.ts	
@@ -4,24 +4,16 @@ type Generate = (numRows: number) => number[][];
  * Accepted
  */
 export const generate: Generate = (numRows) => {
-  if (numRows <= 0) return [];
+  const triangle: number[][] = [];
 
-  const triangle = [[1]]; // first row
+  for (let i = 0; i < numRows; i++) {
+    const row: number[] = Array(i + 1).fill(1);
 
-  if (numRows === 1) return triangle;
-
-  for (let i = 1; i < numRows; i++) {
-    const newRow = [1]; // first item of each row is 1
-    const prevRow = triangle[i - 1];
-
-    for (let j = 1; j <= i; j++) {
-      const prev = prevRow[j - 1];
-      const cur = prevRow[j] || 0; // last item plus 0
-
-      newRow.push(prev + cur);
+    for (let j = 1; j < i; j++) {
+      row[j] = triangle[i - 1][j - 1] + triangle[i - 1][j];
     }
 
-    triangle.push(newRow);
+    triangle.push(row);
   }
 
   return triangle;
diff --git a/src/page-8/790. Domino and Tromino Tiling/numTilings.test.ts b/src/page-8/790. Domino and Tromino Tiling/numTilings.test.ts
new file mode 100644
index 0000000..3394934
--- /dev/null
+++ b/src/page-8/790. Domino and Tromino Tiling/numTilings.test.ts	
@@ -0,0 +1,8 @@
+import { numTilings } from './numTilings';
+
+describe('790. Domino and Tromino Tiling', () => {
+  test('numTilings', () => {
+    expect(numTilings(3)).toBe(5);
+    expect(numTilings(1)).toBe(1);
+  });
+});
diff --git a/src/page-8/790. Domino and Tromino Tiling/numTilings.ts b/src/page-8/790. Domino and Tromino Tiling/numTilings.ts
new file mode 100644
index 0000000..b9f3a90
--- /dev/null
+++ b/src/page-8/790. Domino and Tromino Tiling/numTilings.ts	
@@ -0,0 +1,22 @@
+type NumTilings = (n: number) => number;
+
+/**
+ * Accepted
+ */
+export const numTilings: NumTilings = (n) => {
+  const MOD = 1_000_000_007;
+
+  // Create a DP array to store the number of ways
+  const dp: number[] = Array(n + 1).fill(0);
+  dp[0] = 1; // 1 way to tile a 2 x 0 board (empty board)
+  dp[1] = 1; // 1 way to tile a 2 x 1 board
+  dp[2] = 2; // 2 ways to tile a 2 x 2 board
+
+  // Fill the dp array for all values from 3 to n
+  for (let i = 3; i <= n; i++) {
+    dp[i] = (2 * dp[i - 1] + dp[i - 3]) % MOD;
+  }
+
+  // The result is stored in dp[n]
+  return dp[n];
+};