Introduction

In this blog post, we will explore how to solve the LeetCode problem "2579" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

There exists an infinitely large two-dimensional grid of uncolored unit cells. You are given a positive integer n, indicating that you must do the following routine for n minutes: At the first minute, color any arbitrary unit cell blue. Every minute thereafter, color blue every uncolored cell that touches a blue cell. Below is a pictorial representation of the state of the grid after minutes 1, 2, and 3. Return the number of colored cells at the end of n minutes. Example 1: Input: n = 1 Output: 1 Explanation: After 1 minute, there is only 1 blue cell, so we return 1. Example 2: Input: n = 2 Output: 5 Explanation: After 2 minutes, there are 4 colored cells on the boundary and 1 in the center, so we return 5. Constraints: 1 <= n <= 105

Explanation

Here's the breakdown of the solution:

• Pattern Recognition: The colored cells form a diamond shape that expands outwards each minute. The number of cells can be calculated directly based on the side length of the diamond.
• Formula Derivation: The number of colored cells after n minutes can be determined by the formula: 2*n*n - 2*n + 1 which simplifies to (2 * n * n) - (2 * n) + 1.

• Direct Calculation: The code calculates the number of colored cells directly using the above formula.

• Complexity: O(1) runtime, O(1) storage.

Code

    def colored_cells(n: int) -> int:
    """
    Calculates the number of colored cells after n minutes.

    Args:
        n: The number of minutes.

    Returns:
        The number of colored cells after n minutes.
    """
    return (2 * n * n) - (2 * n) + 1