Given a square with N points on each side of the square and none of these points co-incide with the corners of the square. The task is to calculate the total number of triangles that can be formed using these 4 * N points (n points on each side of the square) as vertices of the triangle.
Input: N = 1
Input: N = 2
Approach: The number of ways of choosing 3 points among 4 * N points is (4 * N)C3. However, some of them do not form a triangle. This happens when all the three chosen points are on the same side of the square. The count of these triplets is NC3 for each of the side i.e. 4 * NC3 in total. Therefore, the required count of triangles will be ((4 * N)C3) – (4 * NC3).
Below is the implementation of the above approach:
- Number of triangles that can be formed with given N points
- Number of triangles formed from a set of points on three lines
- Number of Triangles that can be formed given a set of lines in Euclidean Plane
- Total number of triangles formed when there are H horizontal and V vertical lines
- Number of triangles formed by joining vertices of n-sided polygon with one side common
- Number of triangles formed by joining vertices of n-sided polygon with two common sides and no common sides
- Number of triangles after N moves
- Count the number of possible triangles
- Count number of right triangles possible with a given perimeter
- Number of Triangles in an Undirected Graph
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- Number of Triangles in Directed and Undirected Graphs
- Number of triangles possible with given lengths of sticks which are powers of 2
- Number of possible Triangles in a Cartesian coordinate system
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