2579. Count Total Number of Colored Cells

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.
• 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*.

Example 1:

Input: n = 1
Output: 1
Explanation: After 1 minute, there is only 1 blue cell, so we return 1.

Example 2:

Input: n = 2
Output: 5
Explanation: After 2 minutes, there are 4 colored cells on the boundary and 1 in the center, so we return 5.

Constraints:

• 1 <= n <= 105

Solution (Java)

class Solution {
    public long coloredCells(int n) {
        long sum=1L;
        if(n==1)return sum;
        for(int i=2;i<=n;i++){
            sum+=(long)(4L*(long)(i-1));
        }
        return sum;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).