Given a regular polygon of N sides, the task is to find the maximum sided polygon that can be inscribed inside the given polygon by joining non-adjacent vertices. Print -1, if no such polygon exist.
Input: N = 8
At most a 4 sided polygon can be inscribed inside the given 8-sided polygon as shown below:
Input: N = 3
Approach: The idea is to observe the fact that a regular polygon can be inscribed inside another regular polygon of N sides if N is even. Follow the below steps to solve the problem:
- If N is even, then the inscribed polygon with the maximum sides can be formed by joining the non-adjacent vertices. Therefore, print N/2 as the required answer.
- Otherwise, print -1 as no regular polygon can be inscribed inside an odd-sided polygon.
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Number of triangles formed by joining vertices of n-sided polygon with two common sides and no common sides
- Minimum side of square embedded in Regular polygon with N sides
- Program to find Area of Triangle inscribed in N-sided Regular Polygon
- Largest square that can be inscribed within a hexagon which is inscribed within an equilateral triangle
- Largest right circular cylinder that can be inscribed within a cone which is in turn inscribed within a cube
- Largest right circular cone that can be inscribed within a sphere which is inscribed within a cube
- Largest sphere that can be inscribed in a right circular cylinder inscribed in a frustum
- Largest sphere that can be inscribed within a cube which is in turn inscribed within a right circular cone
- Largest ellipse that can be inscribed within a rectangle which in turn is inscribed within a semicircle
- Number of ways a convex polygon of n+2 sides can split into triangles by connecting vertices
- Number of ways to arrange 2*N persons on the two sides of a table with X and Y persons on opposite sides
- Count right angled triangles in a matrix having two of its sides parallel to sides of the matrix
- Area of a triangle inscribed in a rectangle which is inscribed in an ellipse
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
- Area of a circle inscribed in a rectangle which is inscribed in a semicircle
- Area of a square inscribed in a circle which is inscribed in a hexagon
- Radius of the biggest possible circle inscribed in rhombus which in turn is inscribed in a rectangle
- Biggest Reuleaux Triangle inscribed within a Square inscribed in an equilateral triangle
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within an ellipse
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.