What is the brute force solution for Minimum Garden Perimeter to Collect Enough Apples?

The brute force approach for Minimum Garden Perimeter to Collect Enough Apples is Brute Force, with O(n²) time complexity and O(1) space complexity. We can start by checking each possible side length of the square plot and counting the apples inside it until we find a plot that meets the required number of apples. This method is straightforward but inefficient for large values of neededApples. The optimal Optimal Solution approach improves this to O(log n).

What algorithm or data structure is used to solve Minimum Garden Perimeter to Collect Enough Apples?

Minimum Garden Perimeter to Collect Enough Apples uses the following concepts: Math, Binary Search. The recommended patterns to study are: Mathematical Formulas, Binary Search.

What are the interview tips for Minimum Garden Perimeter to Collect Enough Apples?

Always start with a brute force solution to understand the problem better before optimizing. Think about mathematical properties and formulas that can simplify the problem. Practice binary search problems to become comfortable with the technique.

What are common mistakes when solving Minimum Garden Perimeter to Collect Enough Apples?

Failing to recognize that the problem can be solved using mathematical formulas instead of brute force. Not considering edge cases when calculating the number of apples in the square.

#1954

Minimum Garden Perimeter to Collect Enough Apples

Medium

MathBinary SearchMathematical FormulasBinary Search

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(log n)
Space	O(1)	O(1)

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Intuition

Time O(log n)Space O(1)

Instead of checking each side length one by one, we can use a mathematical formula to directly calculate the number of apples in a square plot of side length L. This allows us to use binary search to efficiently find the minimum L that meets the requirement.

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Algorithm

3 steps

1Step 1: Define a function to calculate the number of apples in a square of side length L.
2Step 2: Use binary search to find the smallest L such that the number of apples is at least neededApples.
3Step 3: Calculate the perimeter as 4 * L once the correct L is found.

solution.py13 lines

1# Full working Python code
2
3def minGardenPerimeter(neededApples):
4    def apples_in_square(L):
5        return (L // 2) * (L // 2 + 1) * 2
6    left, right = 1, 2 * 10**9
7    while left < right:
8        mid = (left + right) // 2
9        if apples_in_square(mid) < neededApples:
10            left = mid + 1
11        else:
12            right = mid
13    return 4 * left

ℹ

Complexity note: The time complexity is logarithmic because we are using binary search to narrow down the possible values of L, which significantly reduces the number of iterations needed compared to the brute force approach.

1The number of apples in a square plot can be calculated using a mathematical formula based on the side length.
2Using binary search allows us to efficiently find the minimum side length that meets the apple requirement.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.