Is Minimum Garden Perimeter to Collect Enough Apples easy or hard?

The problem is classified as Medium on LeetCode. The main challenge is identifying the mathematical pattern of apple growth and translating it into a formula. Once the pattern is known, the implementation using iteration or binary search is straightforward.

Minimum Garden Perimeter to Collect Enough Apples Python/Java solution

Most implementations compute the apple total using the formula 2 * k * (k + 1) * (2 * k + 1). Python, Java, and C++ solutions typically apply binary search to find the smallest valid k, then return 8 * k as the perimeter. This keeps the runtime O(log n) and memory usage constant.

What is the best approach for Minimum Garden Perimeter to Collect Enough Apples?

The most efficient solution uses a mathematical formula with binary search. The total apples after k layers is 2 * k * (k + 1) * (2 * k + 1). Since this value increases monotonically, binary search finds the smallest k where the apple count is at least neededApples. The final perimeter is 8 * k, giving O(log n) time complexity and O(1) space.

Is Minimum Garden Perimeter to Collect Enough Apples asked at Google/Amazon/Meta?

This problem represents the type of mathematical pattern and binary search optimization commonly asked in companies like Google and Amazon. It tests the ability to derive formulas from patterns and apply binary search on a monotonic function rather than searching arrays.

What data structure is used in Minimum Garden Perimeter to Collect Enough Apples?

The solution does not rely on complex data structures. It mainly uses mathematical formulas and optionally binary search over integers. The focus is recognizing the growth pattern of apples in expanding square layers.

What is the time complexity of Minimum Garden Perimeter to Collect Enough Apples?

The optimal solution runs in O(log n) time using binary search on the number of garden layers. Each step evaluates the formula 2 * k * (k + 1) * (2 * k + 1). A simpler iterative approach exists with O(sqrt(n)) time by expanding layers until the apple count reaches the target.

Description Hints 2 Solution Video 9:51

1954. Minimum Garden Perimeter to Collect Enough Apples

Q: How to solve Minimum Garden Perimeter to Collect Enough Apples in O(log n)?

Compute the total apples using the formula total = 2 * k * (k + 1) * (2 * k + 1). Perform binary search on k to find the smallest layer count where total >= neededApples. Because the function grows monotonically, each check narrows the search space. The resulting garden perimeter is 8 * k.

Medium55.5% acceptance1 company

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:

x if x >= 0
-x if x < 0

Example 1:

Input: neededApples = 1
Output: 8
Explanation: A square plot of side length 1 does not contain any apples.
However, a square plot of side length 2 has 12 apples inside (as depicted in the image above).
The perimeter is 2 * 4 = 8.

Example 2:

Input: neededApples = 13
Output: 16

Example 3:

Input: neededApples = 1000000000
Output: 5040

Constraints:

1 <= neededApples <= 10¹⁵

Asked at 1 company

Amazon

Topics

Binary Search Math

Hints open one at a time

Hint 1

Find a formula for the number of apples inside a square with a side length L.

Hint 2

Iterate over the possible lengths of the square until enough apples are collected.

9:51

Still stuck?Read 3 approaches, or watch a walkthrough.

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1class Solution:
2    def minimumPerimeter(self, neededApples: int) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

1000000000

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