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You are given a circle and required to make some cuts in it. You can make a cut through the center to divide the circle into two equal parts. The task is to determine the minimum number of cuts needed so that the circle is divided into exactly n equal parts.

Clarifying Questions

1. Input Constraints:
   • What is the range of n?
   • Is n guaranteed to be a positive integer?
2. Output Format:
   • Should the output be the exact number of minimum cuts needed?

Given the standard nature of the problem, we will assume n is a positive integer and typically within a reasonable range for computation.

Strategy

To solve the problem, we need to understand that:

• If n = 1, the circle is already a single whole and no cuts are necessary.
• For n = 2, a single straight cut through the center is sufficient.
• For higher values of n, following general properties about circles and geometry, the problem essentially boils down to counting the radial cuts.

More specifically:

• If n is 1, no cuts are needed.
• If n is greater than 1, n radial cuts will divide the circle into n equal parts.

We can generalize from observing that to divide a circle into n equal parts, we need n - 1 cuts (each cut adds one part starting from a whole).

Code

Here’s how we can implement this logic in Python:

def minCuts(n: int) -> int:
    # Base case where no cuts are needed
    if n == 1:
        return 0
    else:
        return n - 1

# Example usage
print(minCuts(1))  # Output: 0
print(minCuts(2))  # Output: 1
print(minCuts(4))  # Output: 3

Explanation

• If n is 1, we return 0 since no cuts are needed.
• For any other value of n, it takes n - 1 cuts to create n equal parts:
  • Cutting a circle into 2 pieces requires 1 cut (2 - 1).
  • Cutting a circle into 3 pieces requires 2 cuts (3 - 1), and so forth.

Time Complexity

The time complexity of this function is O(1) since the calculation involves a simple arithmetic operation and does not depend on any input size.

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