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LeetCode day313–790

Everyday has one random leetcode quiz. Today’s quiz is 790. Domino and Tromino Tiling

Description:

You have two types of tiles: a 2 x 1 domino shape and a tromino shape. You may rotate these shapes.

Given an integer n, return the number of ways to tile an 2 x n board. Since the answer may be very large, return it modulo 109 + 7.

In a tiling, every square must be covered by a tile. Two tilings are different if and only if there are two 4-directionally adjacent cells on the board such that exactly one of the tilings has both squares occupied by a tile.

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Example 1:

Input: n = 3
Output: 5
Explanation: The five different ways are show above.

Example 2:

Input: n = 1
Output: 1

n = 1, 1 case

|
|

n = 2, 1 case

||
||

n = 3, 5 cases

|||  --| |--  ┌ - |  | - ┐
|||, --|,|--, | - ┘, └ - |

n = 4, 11 cases

|||  --| |--  ┌ - |  | - ┐      |
|||, --|,|--, | - ┘, └ - |  add | at left and right, get 9 cases

┌ - - ┐ | - - |
| - - |,└ - - ┘, get 2 cases

…

At the end, we return ans as answer.

The time complexity is O(n)

/**
 * @param {number} n
 * @return {number}
 */
var numTilings = function (n) {
    const MOD = 1e9 + 7
    const dp = Array(n + 1).fill(0)
    dp[0] = 1
    dp[1] = 1
    dp[2] = 2
    dp[3] = 5

    for (let i = 4; i <= n; i++) {
        dp[i] = (2 * dp[i - 1] % MOD + dp[i - 3]) % MOD
    }

    return dp[n]
};