Problem of The Day: Count Total Number of Colored Cells

Problem Statement

Brute Force - Recursive Approach [Accepted]

class Solution:
    def coloredCells(self, n: int) -> int:
        def dfs(num, power):
            if num == 1:
                return 1
            return dfs(num - 1, power - 1) + 4*power
        return dfs(n, n - 1)

Brute Force - Iterative Approach [Accepted]

class Solution:
    def coloredCells(self, n: int) -> int:
        i = 1
        x = 1
        for i in range(1, n + 1):
            res = x + 4 * (i - 1)
            x = res
        return res

Editorial

Approach 1: Iterative Addition

class Solution:
    def coloredCells(self, n: int) -> int:
        num_blue_cells = 1
        addend = 4

        # Iterate n - 1 times
        while n - 1:

            # Add and update current multiple of 4
            num_blue_cells += addend
            addend += 4
            n -= 1

        return num_blue_cells

Approach 2: Mathematical Formula

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