Skip to main content
Back to problems
#2579
Medium Algorithms

Count total number of colored cells

Math
66.1% acceptance
Feb 25, 2026
845
95
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.

Solution

Rust
Time O(1)
Space O(1)
LeetCode
solution.rs
impl Solution {
  pub fn colored_cells(n: i32) -> i64 {
    // Formula: 1 + 2*n*(n-1) = 2n^2 - 2n + 1
    let n = n as i64;
    2 * n * n - 2 * n + 1
  }
}