Minimum Cuts to Divide a Circle - Problem
Imagine you're a pizza chef who needs to divide a circular pizza into n equal slices using the minimum number of cuts. But here's the catch - you can only make specific types of cuts!
Valid cuts in a circle can be:
- Type 1: A straight line that touches two points on the edge of the circle and passes through its center (like a diameter)
- Type 2: A straight line that touches one point on the edge of the circle and passes through its center (like a radius)
Given an integer n, return the minimum number of cuts needed to divide the circle into n equal slices.
Think about it: How do diameters and radii work together to create equal divisions? What's the mathematical relationship between the number of slices and the cuts needed?
Input & Output
example_1.py — Single Slice
$
Input:
n = 1
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Output:
0
💡 Note:
The circle is already one piece, so no cuts are needed.
example_2.py — Two Equal Halves
$
Input:
n = 2
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Output:
1
💡 Note:
One diameter cut divides the circle into 2 equal semicircles.
example_3.py — Four Equal Quarters
$
Input:
n = 4
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Output:
2
💡 Note:
Two perpendicular diameter cuts create 4 equal quarter-circles. This is more efficient than using 4 radius cuts.
example_4.py — Odd Number of Slices
$
Input:
n = 3
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Output:
3
💡 Note:
For 3 equal slices, we need 3 radius cuts from the center to the edge, creating 120° angles between each cut.
Constraints
- 1 ≤ n ≤ 106
- n is a positive integer
- All slices must be equal in area and shape
Visualization
Tap to expand
Understanding the Visualization
1
Base Cases
n=1 needs 0 cuts, n=2 needs 1 diameter cut
2
Even Numbers
For even n>2, use n/2 diameter cuts (each creates 2 pieces)
3
Odd Numbers
For odd n>2, use n radius cuts (each creates 1 piece from center)
Key Takeaway
🎯 Key Insight: Even numbers can use efficient diameter cuts (n/2), while odd numbers require individual radius cuts (n total)
💡
Explanation
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// Output will appear here after running code