How do you solve Minimum Cuts to Divide a Circle on LeetCode?

Minimum Cuts to Divide a Circle (LeetCode #2481) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(1) time complexity and O(1) space complexity. Key insight: For even n, the number of cuts needed is n / 2.

What is the time complexity of Minimum Cuts to Divide a Circle?

The optimal solution for Minimum Cuts to Divide a Circle runs in O(1) time and uses O(1) space. The time complexity is O(1) because we are performing a constant number of operations regardless of the input size.

What is the brute force solution for Minimum Cuts to Divide a Circle?

The brute force approach for Minimum Cuts to Divide a Circle is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking every possible way to cut the circle and counting how many cuts are needed to achieve 'n' equal slices. This method is straightforward but inefficient as it doesn't leverage any mathematical insights. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Minimum Cuts to Divide a Circle?

Minimum Cuts to Divide a Circle uses the following concepts: Math, Geometry. The recommended patterns to study are: Mathematical reasoning, Even and odd properties.

What are the interview tips for Minimum Cuts to Divide a Circle?

Clearly explain your thought process when moving from brute force to optimal solutions. Always consider edge cases, such as the smallest values for n. Practice explaining the mathematical reasoning behind your solution.

What are common mistakes when solving Minimum Cuts to Divide a Circle?

Not considering the special case when n is 1. Confusing the number of slices with the number of cuts needed.

#2481

Minimum Cuts to Divide a Circle

Easy

MathGeometryMathematical reasoningEven and odd properties

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(1)Space O(1)

The optimal solution leverages the properties of even and odd numbers. If 'n' is even, we can achieve the slices with n/2 cuts. If 'n' is odd, we need 'n' cuts since each cut can only create two slices.

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Algorithm

3 steps

1Step 1: If n is 1, return 0.
2Step 2: If n is even, return n / 2.
3Step 3: If n is odd, return n.

solution.py6 lines

1# Full working Python code
2
3def minCuts(n):
4    if n == 1:
5        return 0
6    return n // 2 if n % 2 == 0 else n

ℹ

Complexity note: The time complexity is O(1) because we are performing a constant number of operations regardless of the input size.

1For even n, the number of cuts needed is n / 2.
2For odd n, the number of cuts needed is n.

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