DDSA Solutions

790. Domino and Tromino Tiling

MediumView on LeetCode
Dynamic ProgrammingMatrix
Time: O(n)
Space: O(n)

Problem Overview

Domino and Tromino Tiling (Medium) asks you to solve a structured algorithmic task. This is a common Dynamic Programming / Matrix pattern in coding interviews. DP with recurrence dp[i] = 2·dp[i-1] + dp[i-3]; base cases dp[1]=1, dp[2]=2, dp[3]=5.

A full step-by-step explanation is being added. See the study guide for pattern-based practice.

Approach

DP with recurrence dp[i] = 2·dp[i-1] + dp[i-3]; base cases dp[1]=1, dp[2]=2, dp[3]=5.

Related patterns: Dynamic Programming, Matrix

790.cs
C#
// Approach: DP with recurrence dp[i] = 2·dp[i-1] + dp[i-3]; base cases dp[1]=1, dp[2]=2, dp[3]=5.
// Time: O(n) Space: O(n)

public class Solution
{
    public int NumTilings(int n)
    {
        int MOD = 1_000_000_007;
        long[] dp = new long[1001];

        if (n >= 1)
            dp[1] = 1;
        if (n >= 2)
            dp[2] = 2;
        if (n >= 3)
            dp[3] = 5;

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

        return (int)dp[n];
    }
}
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