Mid/SeniorMath
Count Total Number of Colored Cells
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.
Return the number of colored cells at the end of n minutes.
Example 1
Input
n = 1Output
1After 1 minute, there is only 1 blue cell, so we return 1.
Example 2
Input
n = 2Output
5After 2 minutes, there are 4 colored cells on the boundary and 1 in the center, so we return 5.
Constraints
- 1 <= n <= 10^5