Minimum Garden Perimeter to Collect Enough Apples
In a garden represented as an infinite 2D grid, there is an apple tree planted at every integer coordinate. The apple tree planted at an integer coordinate (i, j) has |i| + |j| apples growing on it.
You will buy an axis-aligned square plot of land that is centered at (0, 0).
Given an integer neededApples, return the minimum perimeter of a plot such that at least neededApples apples are inside or on the perimeter of that plot.
The value of |x| is defined as:
xifx >= 0-xifx < 0
Example 1
Input
neededApples = 1Output
8A square plot of side length 1 does not contain any apples, but a square plot of side length 2 has 12 apples inside, so its perimeter is 8.
Example 2
Input
neededApples = 13Output
16A plot with perimeter 8 contains only 12 apples, so the minimum perimeter that contains at least 13 apples is 16.
Constraints
- 1 <= neededApples <= 10^15