Given a convex polygon with n+2 sides. The task is to calculate the number of ways in which triangles can be formed by connecting vertices with non-crossing line segments.
Input: n = 1
It is already a triangle so it can only be formed in 1 way.
Input: n = 2
It can be cut into 2 triangles by using either pair of opposite vertices.
The above problem is an application of a catalan numbers. So, the task is to only find the n’th Catalan Number. First few catalan numbers are 1 1 2 5 14 42 132 429 1430 4862, … (considered from 0th number)
Below is the program to find Nth catalan number:
- Number of triangles formed by joining vertices of n-sided polygon with two common sides and no common sides
- Number of triangles formed by joining vertices of n-sided polygon with one side common
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- Number of possible Triangles in a Cartesian coordinate system
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