What is the optimal time complexity of solving Tiling Problem?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Tiling Problem?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Tiling Problem?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Tiling Problem?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Competitive ProgrammingEasy

Tiling Problem

Learn how to solve the 'Tiling Problem' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function tiling_ways(n) that returns the number of ways to tile a 2xn board using 2x1 dominoes. The dominoes can be placed vertically or horizontally.

Constraints

•1 <= n <= 50

Examples

Example 1

Input

tiling_ways(3)

Output

Explanation

For a 2x3 board, there are 3 ways: 3 vertical tiles, or 1 vertical and 2 horizontal tiles (in two configurations).

Example 2

Input

tiling_ways(4)

Output

Explanation

For a 2x4 board, there are 5 ways to tile it.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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