Given two positive integers N and M which denotes the sides of the convex regular polygon where N < M, the task is to check whether polygons have the same center or not if N-sided polygon was inscribed in an M-sided polygon.
Center of Polygon: Point inside a polygon which is equidistant from each vertex of the polygon.
Input: N = 9, M = 3
Polygon of side 3 when inscribed in a polygon of side 9, then both polygons have same center.
Input: N = 10, M = 3
Polygon of side 3 when inscribed in a polygon of side 10, then both polygons don’t have same center.
Approach: The key observation in this problem is that when M % N == 0, that means the sides of N-sided polygon equally covers the sides of M-sided polygon, which means both the polygons have same center.
- Check if M is divisible by N, If yes then both the polygons have same center.
- Otherwise both polygons have the different centers.
Below is the implementation of the above approach:
- Time Complexity: O(1).
- Auxiliary Space: O(1).