Count Total Number of Colored Cells — LeetCode 2579 Python Solution

The problem

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.

Example

Input

n = 1

Output

1

Explanation

After 1 minute, there is only 1 blue cell, so we return 1.

Python solution

class Solution:
    def coloredCells(self, n: int) -> int:
        return 2 * n * (n - 1) + 1

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 2579. Count Total Number of Colored Cells is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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