Count Total Number of Colored Cells - Leetcode 2579 - Python | Soumil Speaks

LeetCode 2579 - Count Total Number of Colored Cells
This problem involves coloring an infinitely large grid based on a specific rule. Initially, a single cell is colored at the center. Every minute, all uncolored cells that touch a colored cell are also colored.

To find the total number of colored cells at the end of n minutes, we observe a pattern in how the grid expands:

At n = 1, only 1 cell is colored.
At n = 2, 4 more cells are added around the initial one, making the total 5.
At n = 3, 8 more cells are added, making the total 13.
At n = 4, 12 more cells are added, making the total 25.
From this, we can see that the total number of colored cells follows a quadratic pattern. The formula for the total number of cells at minute n is:

Total cells

Total cells=n ^ 2
+ (n−1) ^ 2

This formula directly calculates the answer in constant time.

This problem is a great example of pattern recognition and mathematical formula derivation, making it both an interesting and efficient problem to solve. 🚀

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