_2579. Count Total Number of Colored Cells.md

2579. Count Total Number of Colored Cells

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First completed : March 05, 2025

Last updated : March 05, 2025

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Related Topics : Math

Acceptance Rate : 66.28 %

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Notes

    n   output
    1   1
    2   1 + 4 = 5
    3   1 + 4 + 8 = 13
    4   1 + 4 + 8 + 12 = 25
    5   1 + 4 + 8 + 12 + 16 = 41

The difference increases by 4 each time

V1

Iterative $O(n)$

V2

Math $O(1)$

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Solutions

• m2579 v1.py
• m2579 v2 o1 math solution.py

Python

m2579 v1.py

class Solution:
    def coloredCells(self, n: int) -> int:
        return 1 + sum(layer for layer in range(4, n * 4, 4))

m2579 v2 o1 math solution.py

class Solution:
    def coloredCells(self, n: int) -> int:
        return 1 + 4 * n // 2 * (n - 1)